Journal articles: 'High Resolution Shock Capturing'

1

Lu, Hongqiang, and Qiang Sun. "A Straightforward hp-Adaptivity Strategy for Shock-Capturing with High-Order Discontinuous Galerkin Methods." Advances in Applied Mathematics and Mechanics 6, no. 01 (February 2014): 135–44. http://dx.doi.org/10.4208/aamm.2013.m-s1.

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AbstractIn this paper, high-order Discontinuous Galerkin (DG) method is used to solve the two-dimensional Euler equations. A shock-capturing method based on the artificial viscosity technique is employed to handle physical discontinuities. Numerical tests show that the shocks can be captured within one element even on very coarse grids. The thickness of the shocks is dominated by the local mesh size and the local order of the basis functions. In order to obtain better shock resolution, a straightforwardhp-adaptivity strategy is introduced, which is based on the high-order contribution calculated using hierarchical basis. Numerical results indicate that thehp-adaptivity method is easy to implement and better shock resolution can be obtained with smaller local mesh size and higher local order.

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Yee, H. C. "Explicit and Implicit Multidimensional Compact High-Resolution Shock-Capturing Methods:Formulation." Journal of Computational Physics 131, no. 1 (February 1997): 216–32. http://dx.doi.org/10.1006/jcph.1996.5608.

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Guo, Jia, Huajun Zhu, Zhen-Guo Yan, Lingyan Tang, and Songhe Song. "High-Order Hybrid WCNS-CPR Scheme for Shock Capturing of Conservation Laws." International Journal of Aerospace Engineering 2020 (October 14, 2020): 1–13. http://dx.doi.org/10.1155/2020/8825445.

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By introducing hybrid technique into high-order CPR (correction procedure via reconstruction) scheme, a novel hybrid WCNS-CPR scheme is developed for efficient supersonic simulations. Firstly, a shock detector based on nonlinear weights is used to identify grid cells with high gradients or discontinuities throughout the whole flow field. Then, WCNS (weighted compact nonlinear scheme) is adopted to capture shocks in these areas, while the smooth area is calculated by CPR. A strategy to treat the interfaces of the two schemes is developed, which maintains high-order accuracy. Convergent order of accuracy and shock-capturing ability are tested in several numerical experiments; the results of which show that this hybrid scheme achieves expected high-order accuracy and high resolution, is robust in shock capturing, and has less computational cost compared to the WCNS.

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Ekaterinaris, John A. "Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes." International Journal of Aeroacoustics 2, no. 2 (April 2003): 175–92. http://dx.doi.org/10.1260/147547203322775524.

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High-order accurate, finite-difference methods, such as the compact centered schemes with spectral-type or characteristic-based filters and the weighted essentially non-oscillatory (WENO) schemes, which are used in high resolution CFD solutions and for DNS or LES of compressible turbulence, are applied to aeroacoustics. Implicit and explicit schemes are used for time marching. The accuracy of the numerical solutions is evaluated for test problems. It is found that these methods are appropriate for sound propagation in complex flows that require use of curvilinear coordinates. Therefore they are applicable for the prediction of sound generation from both smooth subsonic flows, and transonic or supersonic flows with discontinuities.

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Yee, H. C., G. H. Klopfer, and J. L. Montagné. "High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows." Journal of Computational Physics 88, no. 1 (May 1990): 31–61. http://dx.doi.org/10.1016/0021-9991(90)90241-r.

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Neelan, Arun Govind, and Manoj T. Nair. "Discontinuity Preserving Scheme." International Journal of Mathematical, Engineering and Management Sciences 5, no. 4 (August 1, 2020): 631–42. http://dx.doi.org/10.33889/ijmems.2020.5.4.051.

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Non-linear schemes are widely used in high-speed flows to capture the discontinuities present in the solution. Limiters and weighted essentially non-oscillatory schemes (WENO) are the most common non-linear numerical schemes. Most of the high-resolution schemes use the piecewise parabolic reconstruction (PPR) technique for their robustness. However, it may be impossible to achieve non-oscillatory and dissipation-free solutions with the PPR technique without non-linear switches. Most of the shock-capturing schemes use excessive dissipation to suppress the oscillations present in the discontinuities. To eliminate these issues, an algorithm is proposed that uses the shock-capturing scheme (SCS) in the first step, and then the result is refined using a novel scheme called the Discontinuity Preserving Scheme (DPS). The present scheme is a hybrid shock capture-fitting scheme. The present scheme has outperformed other schemes considered in this work, in terms of shock resolution in linear and non-linear test cases. The most significant advantage of the present scheme is that it can resolve shocks with three grid points.

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Patel, Sumit Kumar, and Joseph Mathew. "Shock Capturing in Large Eddy Simulations by Adaptive Filtering." Fluids 4, no. 3 (July 15, 2019): 132. http://dx.doi.org/10.3390/fluids4030132.

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A method for shock capturing by adaptive filtering for use with high-resolution, high-order schemes for Large Eddy Simulations (LES) is presented. The LES method used in all the examples here employs the Explicit Filtering approach and the spatial derivatives are obtained with sixth-order, compact, finite differences. The adaptation is to drop the order of the explicit filter to two at gridpoints where a shock is detected, and to then increase the order from 2 to 10 in steps at successive gridpoints away from the shock. The method is found to be effective in a series of tests of common inviscid 1D and 2D problems of shock propagation and propagation of waves through shocks. As a prelude to LES, the 3D Taylor–Green problem for the inviscid and a finite viscosity case were simulated. An assessment of the overall performance of the method for LES was carried out by simulating an underexpanded round jet at a Reynolds number of 6.09 million, based in centerline velocity and diameter at nozzle exit plane. Very close quantitative agreement was found for the development of centerline mean pressure when compared to experiment. Simulations on several increasingly finer grids showed a monotonic extension of the computed part of the inertial range, with little change to low frequency content. Amplitudes and locations of large changes in pressure through several cells were captured accurately. A similar performance was observed for LES of an impinging jet containing normal and curved shocks.

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Montagne, J. L., H. C. Yee, and M. Vinokur. "Comparative study of high-resolution shock-capturing schemes for a real gas." AIAA Journal 27, no. 10 (October 1989): 1332–46. http://dx.doi.org/10.2514/3.10269.

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Kumar, Ritesh, and M. K. Kadalbajoo. "A class of high resolution shock capturing schemes for hyperbolic conservation laws." Applied Mathematics and Computation 195, no. 1 (January 2008): 110–26. http://dx.doi.org/10.1016/j.amc.2007.04.090.

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Wang, Wei, Chi-Wang Shu, H. C. Yee, Dmitry V. Kotov, and Björn Sjögreen. "High Order Finite Difference Methods with Subcell Resolution for Stiff Multispecies Discontinuity Capturing." Communications in Computational Physics 17, no. 2 (January 22, 2015): 317–36. http://dx.doi.org/10.4208/cicp.250214.130814a.

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AbstractIn this paper, we extend the high order finite-difference method with subcell resolution (SR) in [34] for two-species stiff one-reaction models to multispecies and multireaction inviscid chemical reactive flows, which are significantly more difficult because of the multiple scales generated by different reactions. For reaction problems, when the reaction time scale is very small, the reaction zone scale is also small and the governing equations become very stiff. Wrong propagation speed of discontinuity may occur due to the underresolved numerical solution in both space and time. The present SR method for reactive Euler system is a fractional step method. In the convection step, any high order shock-capturing method can be used. In the reaction step, an ODE solver is applied but with certain computed flow variables in the shock region modified by the Harten subcell resolution idea. Several numerical examples of multispecies and multireaction reactive flows are performed in both one and two dimensions. Studies demonstrate that the SR method can capture the correct propagation speed of discontinuities in very coarse meshes.

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Yu, Cong. "An Efficient High-Resolution Shock-Capturing Scheme for Multi-Dimensional Flows I. Hydrodynamics." Chinese Journal of Astronomy and Astrophysics 6, no. 6 (October 2006): 680–88. http://dx.doi.org/10.1088/1009-9271/6/6/06.

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12

Caselles, Vicent, Rosa Donat, and Gloria Haro. "Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes." Computers & Fluids 38, no. 1 (January 2009): 16–36. http://dx.doi.org/10.1016/j.compfluid.2007.07.023.

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13

Li, Liang, Guo-Yan Zhao, Hong-Bo Wang, Ming-Bo Sun, Da-Peng Xiong, Tao Tang, and Ming-Jiang Liu. "A general framework of high-resolution hybrid central/WENO numerical scheme for turbulent compressible simulation." Modern Physics Letters B 35, no. 07 (February 18, 2021): 2150118. http://dx.doi.org/10.1142/s0217984921501189.

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This work presents a general framework of finite-difference hybrid scheme which contains a linear central scheme and a nonl-inear WENO scheme. A new optimal-designed shock sensor is used to distinguish the smoothness of flowfield and a binary-type weighting function is used to switch sub-schemes rationally. Based on the above improvements, the effects of different combinations of each component within the hybrid scheme are characterized in linear advection equation and Euler equations. The maximum reference threshold values are provided. Extensive test cases indicate the hybrid scheme’s numerical robustness, low-dissipation, and superior computational efficiency. Specifically, benefited from the high-resolution shock sensor which can accurately perceive shocks without excessive misidentifications, the hybrid scheme can achieve non-oscillatory solutions, and resolve more vortices in smooth regions compared to the original shock-capturing scheme. Meanwhile, the superiority of the hybrid scheme is further confirmed in the Reynolds-averaged Navier–Stokes equations/Lager Eddy Simulations (RANS/LES) for the DLR scramjet combustor case with viscous terms and/or sub-grid scale models are used. The present hybrid framework can be easily implemented within the existing numerical simulation code framework.

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Don, Wai-Sun, Antonio de Gregorio, Jean-Piero Suarez, and Gustaaf B. Jacobs. "Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference scheme with Computation of a Sonic Injector in Supersonic Cross Flow." Advances in Applied Mathematics and Mechanics 4, no. 06 (December 2012): 719–36. http://dx.doi.org/10.4208/aamm.12-12s03.

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AbstractA hybridization of a high order WENO-Zfinite difference scheme and a high order central finite difference method for computation of the two-dimensional Euler equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)] is extended to three-dimensions and for parallel computation. The Hybrid scheme switches dynamically from a WENO-Zscheme to a central scheme at any grid location and time instance if the flow is sufficiently smooth and vice versa if the flow is exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by a high order multi-resolution analysis. The method is tested on a benchmark sonic flow injection in supersonic cross flow. Increase of the order of the method reduces the numerical dissipation of the underlying schemes, which is shown to improve the resolution of small dynamic vortical scales. Shocks are captured sharply in an essentially non-oscillatory manner via the high order shock-capturing WENO-Zscheme. Computations of the injector flow with a WENO-Zscheme only and with the Hybrid scheme are in very close agreement. Thirty percent of grid points require a computationally expensive WENO-Zscheme for high-resolution capturing of shocks, whereas the remainder of grid points may be solved with the computationally more affordable central scheme. The computational cost of the Hybrid scheme can be up to a factor of one and a half lower as compared to computations with a WENO-Zscheme only for the sonic injector benchmark.

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15

Gupta, N. K., C. D. Munz, and B. Goel. "An efficient shock capturing scheme for ion beam target simulation." Laser and Particle Beams 8, no. 4 (December 1990): 807–25. http://dx.doi.org/10.1017/s0263034600009186.

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A high resolution shock capturing numerical scheme in Lagrangian geometry is presented for ion beam target simulations. The scheme can accommodate any given analytical or tabular equation of state. Numerical results for a number of test problems show that the scheme is free from spurious numerical oscillations near strong gradients. Results are also presented for the simulation of a typical proton beam from the pinch reflex diode of Karlsruhe light ion beam facility KALIF incident on slab aluminum target.

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Radice, D., and L. Rezzolla. "THC: a new high-order finite-difference high-resolution shock-capturing code for special-relativistic hydrodynamics." Astronomy & Astrophysics 547 (October 22, 2012): A26. http://dx.doi.org/10.1051/0004-6361/201219735.

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17

Thornber, B., D. Drikakis, R. J. R. Williams, and D. Youngs. "On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes." Journal of Computational Physics 227, no. 10 (May 2008): 4853–72. http://dx.doi.org/10.1016/j.jcp.2008.01.035.

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18

Baoguo, Wang, and Chen Naixing. "A new, high-resolution shock-capturing hybrid scheme of flux vector splitting-Harten's TVD." Acta Mechanica Sinica 6, no. 3 (August 1990): 204–13. http://dx.doi.org/10.1007/bf02487641.

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Liang, Qiuhua, and Luke S. Smith. "A high-performance integrated hydrodynamic modelling system for urban flood simulations." Journal of Hydroinformatics 17, no. 4 (January 20, 2015): 518–33. http://dx.doi.org/10.2166/hydro.2015.029.

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A new High-Performance Integrated hydrodynamic Modelling System (Hi-PIMS) is tested for urban flood simulation. The software solves the two-dimensional shallow water equations using a first-order accurate Godunov-type shock-capturing scheme incorporated with the Harten, Lax and van Leer approximate Riemann solver with the contact wave restored (HLLC) for flux evaluation. The benefits of modern graphics processing units are explored to accelerate large-scale high-resolution simulations. In order to test its performance, the tool is applied to predict flood inundation due to rainfall and a point source surface flow in Glasgow, Scotland, and a hypothetical inundation event at different spatial resolutions in Thamesmead, England, caused by embankment failure. Numerical experiments demonstrate potential benefits for high-resolution modelling of urban flood inundation, and a much-improved level of performance without compromising result quality.

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20

Li, Weihao, and Jian Xia. "Efficient Shock Capturing Based on Parallel Adaptive Mesh Refinement Framework." Journal of Physics: Conference Series 2329, no. 1 (August 1, 2022): 012018. http://dx.doi.org/10.1088/1742-6596/2329/1/012018.

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Abstract Based on AMReX, a software framework for massively parallel, block-structured adaptive mesh refinement (AMR) applications and in combination with finite difference weighted essential non-oscillatory (WENO) method, a numerical procedure is developed to provide universal discontinuity capturing capability for inviscid, compressible flow. Test cases of one-dimensional and two-dimensional flows containing shock waves, contact discontinuities, flow instabilities, and their interactions are considered to validate the high resolution of AMR for characteristic flow structure under unsteady conditions. The current elaborate AMR-based code is proven to have superior efficiency relative to global refinement via experiments including different initial mesh intervals, refinement ratios at all levels, and. Evidence in executions with multiple processes and domain division sizes indicates its high parallel scalability. Thus, the application built on AMReX is promising for simulations of phenomena undergoing rapid local variation such as compressible turbulence and multiphase interactions.

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QAMAR, SHAMSUL, and GERALD WARNECKE. "A HIGH ORDER KINETIC FLUX-SPLITTING METHOD FOR THE SPECIAL RELATIVISTIC HYDRODYNAMICS." International Journal of Computational Methods 02, no. 01 (March 2005): 49–74. http://dx.doi.org/10.1142/s0219876205000338.

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In this article we present a flux splitting method based on gas-kinetic theory for the special relativistic hydrodynamics (SRHD) [Landau and Lifshitz, Fluid Mechanics, Pergamon New York, 1987] in one and two space dimensions. This kinetic method is based on the direct splitting of the macroscopic flux functions with the consideration of particle transport. At the same time, particle "collisions" are implemented in the free transport process to reduce numerical dissipation. Due to the nonlinear relations between conservative and primitive variables and the consequent complexity of the Jacobian matrix, the multi-dimensional shock-capturing numerical schemes for SRHD are computationally more expensive. All the previous methods presented for the solution of these equations were based on the macroscopic continuum description. These upwind high-resolution shock-capturing (HRSC) schemes, which were originally made for non-relativistic flows, were extended to SRHD. However our method, which is based on kinetic theory is more related to the physics of these equations and is very efficient, robust, and easy to implement. In order to get high order accuracy in space, we use a third order central weighted essentially non-oscillatory (CWENO) finite difference interpolation routine. To achieve high order accuracy in time we use a Runge-Kutta time stepping method. The one- and two-dimensional computations reported in this paper show the desired accuracy, high resolution, and robustness of the method.

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Zhao, Fengxiang, Xing Ji, Wei Shyy, and Kun Xu. "An Acoustic and Shock Wave Capturing Compact High-Order Gas-Kinetic Scheme with Spectral-Like Resolution." International Journal of Computational Fluid Dynamics 34, no. 10 (September 23, 2020): 731–56. http://dx.doi.org/10.1080/10618562.2020.1821879.

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Glimm, James G., Bradley J. Plohr, and David H. Sharp. "Conservative Formulation of Large Deformation Plasticity." Applied Mechanics Reviews 46, no. 12 (December 1, 1993): 519–26. http://dx.doi.org/10.1115/1.3120313.

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We explain several ideas which may, either singly or in combination, help achieve high resolution in simulations of large-deformation plasticity. Because of the large deformations, we work in the Eulerian picture. The governing equations are written in a fully conservative form, which are correct for discontinuous as well as continuous solutions. Models of shear bands are discussed. These models describe the internal dynamics of a developed shear band in terms of time-asymptotic states; in other words, the smooth internal structure is replaced by a jump discontinuity, and the shear band evolution is determined by jump relations. This analysis is useful for high resolution numerical methods, including both shock capturing and shock tracking schemes, as well as for the understanding and validation of computations, independently of the underlying method. Preliminary computations, which illustrate the feasibility of these ideas, are presented.

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Wang, Min, and Xiaohua Zhang. "A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations." Mathematics 10, no. 9 (April 29, 2022): 1482. http://dx.doi.org/10.3390/math10091482.

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The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for the Savage–Hutter equations. Numerical examples in 1D and 2D space are presented to compare the resolution of shock waves and free surface capture. The numerical results show that the method proposed provides excellent performance with high accuracy and robustness.

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Delanaye, M., and J. A. Essers. "Finite Volume Scheme With Quadratic Reconstruction on Unstructured Adaptive Meshes Applied to Turbomachinery Flows." Journal of Turbomachinery 119, no. 2 (April 1, 1997): 263–69. http://dx.doi.org/10.1115/1.2841109.

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This paper presents a new finite volume cell-centered scheme for solving the two-dimensional Euler equations. The technique for computing the advective derivatives is based on a high-order Gauss quadrature and an original quadratic reconstruction of the conservative variables for each control volume. A very sensitive detector identifying discontinuity regions switches the scheme to a TVD scheme, and ensures the monotonicity of the solution. The code uses unstructured meshes whose cells are polygons with any number of edges. A mesh adaptation based on cell division is performed in order to increase the resolution of shocks. The accuracy, insensitivity to grid distortions, and shock capturing properties of the scheme are demonstrated for different cascade flow computations.

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Martí, José Ma, and Ewald Müller. "The analytical solution of the Riemann problem in relativistic hydrodynamics." Journal of Fluid Mechanics 258 (January 10, 1994): 317–33. http://dx.doi.org/10.1017/s0022112094003344.

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We consider the decay of an initial discontinuity in a polytropic gas in a Minkowski space–time (the special relativistic Riemann problem). In order to get a general analytical solution for this problem, we analyse the properties of the relativistic flow across shock waves and rarefactions. As in classical hydrodynamics, the solution of the Riemann problem is found by solving an implicit algebraic equation which gives the pressure in the intermediate states. The solution presented here contains as a particular case the special relativistic shock-tube problem in which the gas is initially at rest. Finally, we discuss the impact of this result on the development of high-resolution shock-capturing numerical codes to solve the equations of relativistic hydrodynamics.

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Cai, Xiao Wei, Jun Jie Tan, and Xin Jian Ma. "A 2D Meshless Solver Based on AUSM+ and MUSCL Scheme." Applied Mechanics and Materials 105-107 (September 2011): 2140–43. http://dx.doi.org/10.4028/www.scientific.net/amm.105-107.2140.

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When solving Euler equations of fluid dynamics around complex configurations, a meshless method which doesn’t use the information of the meshes may have the advantages to simulate the flow field. In this paper, a simple and accurate meshless algorithm based on AUSM+ and MUSCL scheme has been described. To assess the capability for capturing shock position and the resolvability of the complex shock waves, a number of typical test cases are calculated with the meshless method. The results obtained are in good agreement with the exact solution or some high-resolution numerical method as well as flux-corrected transport (FCT) algorithm with adaptive mesh refinement (AMR) technique.

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San, Omer, and Kursat Kara. "Numerical assessments of high-order accurate shock capturing schemes: Kelvin–Helmholtz type vortical structures in high-resolutions." Computers & Fluids 89 (January 2014): 254–76. http://dx.doi.org/10.1016/j.compfluid.2013.11.006.

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Koyuncu, Fahrettin, and Orhan Dönmez. "Numerical simulation of the disk dynamics around the black hole: Bondi–Hoyle accretion." Modern Physics Letters A 29, no. 21 (July 7, 2014): 1450115. http://dx.doi.org/10.1142/s0217732314501156.

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We have solved the General Relativistic Hydrodynamic (GRH) equations using the high resolution shock capturing scheme (HRSCS) to find out the dependency of the disk dynamics to the Mach number, adiabatic index, the black hole rotation parameter and the outer boundary of the computational domain around the non-rotating and rotating black holes. We inject the gas to computational domain at upstream and downstream regions at the same time with different initial conditions. It is found that variety of the mass accretion rates and shock cone structures strongly depend on Mach number and adiabatic index of the gas. The shock cones on the accretion disk are important physical mechanisms to trap existing oscillation modes, thereupon these trapped modes may generate strong X-rays observed by different X-ray satellites. Besides, our numerical approach also show that the shock cones produces the flip–flop oscillation around the black holes. The flip–flop instabilities which are monitored in our simulations may explain the erratic spin behavior of the compact objects (the black holes and neutron stars) seen from observed data.

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Feo, Alessandra, and Fulvio Celico. "Investigating the migration of immiscible contaminant fluid flow in homogeneous and heterogeneous aquifers with high-precision numerical simulations." PLOS ONE 17, no. 4 (April 25, 2022): e0266486. http://dx.doi.org/10.1371/journal.pone.0266486.

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Numerical modeling of the migration of three-phase immiscible fluid flow in variably saturated zones is challenging due to the different behavior of the system between unsaturated and saturated zones. This behavior results in the use of different numerical methods for the numerical simulation of the fluid flow depending on whether it is in the unsaturated or saturated zones. This paper shows that using a high-resolution shock-capturing conservative method to resolve the nonlinear governing coupled partial differential equations of a three-phase immiscible fluid flow allows the numerical simulation of the system through both zones providing a unitary vision (and resolution) of the migration of an immiscible contaminant problem within a porous medium. In particular, using different initial scenarios (including impermeable “lenses” in heterogeneous aquifers), three-dimensional numerical simulation results are presented on the temporal evolution of the contaminant migration following the saturation profiles of the three-phases fluids flow in variably saturated zones. It is considered either light nonaqueous phase liquid with a density less than the water, or dense nonaqueous phase liquid, which has densities greater than the water initially released in unsaturated dry soil. Our study shows that the fate of the migration of immiscible contaminants in variably saturated zones can be accurately described, using a unique mathematical conservative model, with different evolution depending on the value of the system’s physical parameters, including the contaminant density, and accurately tracking the evolution of the sharp (shock) contaminant front.

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Feo, Alessandra, and Fulvio Celico. "Investigating the migration of immiscible contaminant fluid flow in homogeneous and heterogeneous aquifers with high-precision numerical simulations." PLOS ONE 17, no. 4 (April 25, 2022): e0266486. http://dx.doi.org/10.1371/journal.pone.0266486.

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Numerical modeling of the migration of three-phase immiscible fluid flow in variably saturated zones is challenging due to the different behavior of the system between unsaturated and saturated zones. This behavior results in the use of different numerical methods for the numerical simulation of the fluid flow depending on whether it is in the unsaturated or saturated zones. This paper shows that using a high-resolution shock-capturing conservative method to resolve the nonlinear governing coupled partial differential equations of a three-phase immiscible fluid flow allows the numerical simulation of the system through both zones providing a unitary vision (and resolution) of the migration of an immiscible contaminant problem within a porous medium. In particular, using different initial scenarios (including impermeable “lenses” in heterogeneous aquifers), three-dimensional numerical simulation results are presented on the temporal evolution of the contaminant migration following the saturation profiles of the three-phases fluids flow in variably saturated zones. It is considered either light nonaqueous phase liquid with a density less than the water, or dense nonaqueous phase liquid, which has densities greater than the water initially released in unsaturated dry soil. Our study shows that the fate of the migration of immiscible contaminants in variably saturated zones can be accurately described, using a unique mathematical conservative model, with different evolution depending on the value of the system’s physical parameters, including the contaminant density, and accurately tracking the evolution of the sharp (shock) contaminant front.

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Haack, Jeffrey, Shi Jin, and Jian‐Guo Liu. "An All-Speed Asymptotic-Preserving Method for the Isentropic Euler and Navier-Stokes Equations." Communications in Computational Physics 12, no. 4 (October 2012): 955–80. http://dx.doi.org/10.4208/cicp.250910.131011a.

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AbstractThe computation of compressible flows becomes more challenging when the Mach number has different orders of magnitude. When the Mach number is of order one, modern shock capturing methods are able to capture shocks and other complex structures with high numerical resolutions. However, if the Mach number is small, the acoustic waves lead to stiffness in time and excessively large numerical viscosity, thus demanding much smaller time step and mesh size than normally needed for incompressible flow simulation. In this paper, we develop an all-speed asymptotic preserving (AP) numerical scheme for the compressible isentropic Euler and Navier-Stokes equations that is uniformly stable and accurate for all Mach numbers. Our idea is to split the system into two parts: one involves a slow, nonlinear and conservative hyperbolic system adequate for the use of modern shock capturing methods and the other a linear hyperbolic system which contains the stiff acoustic dynamics, to be solved implicitly. This implicit part is reformulated into a standard pressure Poisson projection system and thus possesses sufficient structure for efficient fast Fourier transform solution techniques. In the zero Mach number limit, the scheme automatically becomes a projection method-like incompressible solver. We present numerical results in one and two dimensions in both compressible and incompressible regimes.

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Le, Minh H., Virgile Dubos, Marina Oukacine, and Nicole Goutal. "A Well-balanced Finite Volume Scheme for Shallow Water Equations with Porosity: Application to Modelling Flow through Rigid Vegetation." E3S Web of Conferences 40 (2018): 05032. http://dx.doi.org/10.1051/e3sconf/20184005032.

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Strong interactions exist between flow dynamics and vegetation in open-channel. Depth-averaged shallow water equations can be used for such a study. However, explicit representation of vegetation can lead to very high resolution of the mesh since the vegetation is often modelled as vertical cylinders. Our work aims to study the ability of a single porosity-based shallow water model for these applications. More attention on flux and source terms discretizations are required in order to archive the well-balancing and shock capturing properties. We present a new Godunov-type finite volume scheme based on a simple-wave approximation and compare it with some other methods in the literature. A first application with experimental data was performed.

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Cui, Yunsong, Qiuhua Liang, Gang Wang, Jiaheng Zhao, Jinchun Hu, Yuehua Wang, and Xilin Xia. "Simulation of Hydraulic Structures in 2D High-Resolution Urban Flood Modeling." Water 11, no. 10 (October 15, 2019): 2139. http://dx.doi.org/10.3390/w11102139.

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Urban flooding as a result of inadequate drainage capacity, failure of flood defenses, etc. is usually featured with highly transient hydrodynamics. Reliable and efficient prediction and forecasting of these urban flash floods is still a great technical challenge. Meanwhile, in urban environments, the flooding hydrodynamics and process may be influenced by flow regulation and flood protection hydraulic infrastructure systems, such as sluice gates, which should be effectively taken into account in an urban flood model. However, direct simulation of hydraulic structures is not a current practice in 2D urban flood modeling. This work aims to develop a robust numerical approach to directly simulate the effects of gate structures in a 2D high-resolution urban flood model. A new modeling component is developed and fully coupled to a finite volume Godunov-type shock-capturing shallow water model, to directly simulate the highly transient flood waves through hydraulic structures. Different coupling approaches, i.e., flux term coupling and source term coupling, are implemented and compared. A numerical experiment conducted for an analytical dam-break test indicates that the flux term coupling approach may lead to more accurate results, with the calculated RMSE against water level 28%–38% less than that produced by the source term coupling approach. The flux term coupling approach is therefore adopted to improve the current urban flood model, and it is further tested by reproducing the laboratory experiments of flood routing in a flume with partially open sluice gates, conducted in the hydraulic laboratory at the Zhejiang Institute of Hydraulics and Estuary, China. The numerical results are compared favorably with experimental measurements, with a maximum RMSE of 0.0851 for all the individual tests. The satisfactory results demonstrate that the flood model implemented with the flux coupling approach is able to accurately simulate the flow through hydraulic structures, with enhanced predictive capability for urban flood modeling.

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Yang, Jaw-Yen, Chih-Yuan Yan, Manuel Diaz, Juan-Chen Huang, Zhihui Li, and Hanxin Zhang. "Numerical solutions of ideal quantum gas dynamical flows governed by semiclassical ellipsoidal-statistical distribution." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2161 (January 8, 2014): 20130413. http://dx.doi.org/10.1098/rspa.2013.0413.

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The ideal quantum gas dynamics as manifested by the semiclassical ellipsoidal-statistical (ES) equilibrium distribution derived in Wu et al. (Wu et al . 2012 Proc. R. Soc. A 468 , 1799–1823 ( doi:10.1098/rspa.2011.0673 )) is numerically studied for particles of three statistics. This anisotropic ES equilibrium distribution was derived using the maximum entropy principle and conserves the mass, momentum and energy, but differs from the standard Fermi–Dirac or Bose–Einstein distribution. The present numerical method combines the discrete velocity (or momentum) ordinate method in momentum space and the high-resolution shock-capturing method in physical space. A decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. Computations of two-dimensional Riemann problems are presented, and various contours of the quantities unique to this ES model are illustrated. The main flow features, such as shock waves, expansion waves and slip lines and their complex nonlinear interactions, are depicted and found to be consistent with existing calculations for a classical gas.

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Nikonov, Valeriy. "A Semi-Lagrangian Godunov-Type Method without Numerical Viscosity for Shocks." Fluids 7, no. 1 (December 30, 2021): 16. http://dx.doi.org/10.3390/fluids7010016.

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One of the most important and complex effects in compressible fluid flow simulation is a shock-capturing mechanism. Numerous high-resolution Euler-type methods have been proposed to resolve smooth flow scales accurately and to capture the discontinuities simultaneously. One of the disadvantages of these methods is a numerical viscosity for shocks. In the shock, the flow parameters change abruptly at a distance equal to the mean free path of a gas molecule, which is much smaller than the cell size of the computational grid. Due to the numerical viscosity, the aforementioned Euler-type methods stretch the parameter change in the shock over few grid cells. We introduce a semi-Lagrangian Godunov-type method without numerical viscosity for shocks. Another well-known approach is a method of characteristics that has no numerical viscosity and uses the Riemann invariants or solvers for water hammer phenomenon modeling, but in its formulation the convective terms are typically neglected. We use a similar approach to solve the one-dimensional adiabatic gas dynamics equations, but we split the equations into parts describing convection and acoustic processes separately, with corresponding different time steps. When we are looking for the solution to the one-dimensional problem of the scalar hyperbolic conservation law by the proposed method, we additionally use the iterative Godunov exact solver, because the Riemann invariants are non-conserved for moderate and strong shocks in an ideal gas. The proposed method belongs to a group of particle-in-cell (PIC) methods; to the best of the author’s knowledge, there are no similar PIC numerical schemes using the Riemann invariants or the iterative Godunov exact solver. This article describes the application of the aforementioned method for the inviscid Burgers’ equation, adiabatic gas dynamics equations, and the one-dimensional scalar hyperbolic conservation law. The numerical analysis results for several test cases (e.g., the standard shock-tube problem of Sod, the Riemann problem of Lax, the double expansion wave problem, the Shu–Osher shock-tube problem) are compared with the exact solution and Harten’s data. In the shock for the proposed method, the flow properties change instantaneously (with an accuracy dependent on the grid cell size). The iterative Godunov exact solver determines the accuracy of the proposed method for flow discontinuities. In calculations, we use the iteration termination condition less than 10−5 to find the pressure difference between the current and previous iterations.

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Demeulenaere, A., and R. Van den Braembussche. "Three-Dimensional Inverse Method for Turbomachinery Blading Design." Journal of Turbomachinery 120, no. 2 (April 1, 1998): 247–55. http://dx.doi.org/10.1115/1.2841399.

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An iterative procedure for three-dimensional blade design is presented, in which the three-dimensional blade shape is modified using a physical algorithm, based on the transpiration model. The transpiration flux is computed by means of a modified Euler solver, in which the target pressure distribution is imposed along the blade surfaces. Only a small number of modifications is needed to obtain the final geometry. The method is based on a high-resolution three-dimensional Euler solver. An upwind biased evaluation of the advective fluxes allows for a very low numerical entropy generation, and sharp shock capturing. Non-reflecting boundary conditions are applied along the inlet/outlet boundaries. The capabilities of the method are illustrated by redesigning a transonic compressor rotor blade, to achieve, for the same mass flow and outlet flow angle, a shock-free deceleration along the suction side. The second example concerns the design of a low aspect ratio turbine blade, with a positive compound lean to reduce the intensity of the passage vortices. The final blade is designed for an optimized pressure distribution, taking into account the forces resulting from the blade lean angle.

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Garami, Tamás, Oliver Krammer, Gábor Harsányi, and Péter Martinek. "Method for validating CT length measurement of cracks inside solder joints." Soldering & Surface Mount Technology 28, no. 1 (February 1, 2016): 13–17. http://dx.doi.org/10.1108/ssmt-10-2015-0029.

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Purpose – This paper aims to develop a method to measure the length of cracks inside solder joints, which enables the validation of computed tomography (CT) crack length measurements. Design/methodology/approach – Cracks were formed inside solder joints intentionally by aging solder joints of 0603 size resistors with thermal shock (TS) test (−40 to +140°C, 2,000 cycles), and CT images were captured about them with different rotational increment (1/4, 1/2 and 1°) of sample projection. The length of cracks was also measured with our method, which is based on capturing high-resolution radiography X-ray images about the cracks in two perpendicular projection planes. The radiography results were compared to the CT measurements. The percentage error for the different CT rotational increment settings was calculated, and the optimal CT settings have been determined. Findings – The results have proven that reducing the rotational increment increases the sharpness of the captured images and the accuracy of crack length measurements. Nevertheless, the accuracy compared to high-resolution radiography measurements is only slightly better at 1/4° rotational increment than in the case of 1/2° rotational increment. It should be also noted that the 1/4° increment requires twice as much time for capturing the images as the 1/2° increment. So, the 1/2° rotational increment of sample projection is the optimal setting in our investigated case for measuring crack lengths. Practical implications – The developed method is applicable to find the optimal settings for CT crack length measurements, which provides faster analysation of large quantity samples used, e.g. at life-time tests. Originality/value – There is a lack of information in the literature regarding the optimisation of CT measurement set-up, e.g. a slightly larger value of the sample rotational increment can provide acceptable resolution with much faster processing time. Thus, the authors developed a method and performed research about optimising CT measurement parameters.

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Ahn, Myeonghwan, Duck-Joo Lee, and Mihai Mihaescu. "A numerical study on near-field pressure fluctuations of symmetrical and anti-symmetrical flapping modes of twin-jet using a high-resolution shock-capturing scheme." Aerospace Science and Technology 119 (December 2021): 107147. http://dx.doi.org/10.1016/j.ast.2021.107147.

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40

THORNTON, A. R., and J. M. N. T. GRAY. "Breaking size segregation waves and particle recirculation in granular avalanches." Journal of Fluid Mechanics 596 (January 17, 2008): 261–84. http://dx.doi.org/10.1017/s0022112007009445.

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Particle-size segregation is a common feature of dense gravity-driven granular free-surface flows, where sliding and frictional grain–grain interactions dominate. Provided that the diameter ratio of the particles is not too large, the grains segregate by a process called kinetic sieving, which, on average, causes the large particles to rise to the surface and the small grains to sink to the base of the avalanche. When the flowing layer is brought to rest this stratification is often preserved in the deposit and is known by geologists as inverse grading. Idealized experiments with bi-disperse mixtures of differently sized grains have shown that inverse grading can be extremely sharp on rough beds at low inclination angles, and may be modelled as a concentration jump or shock. Several authors have developed hyperbolic conservation laws for segregation that naturally lead to a perfectly inversely graded state, with a pure phase of coarse particles separated from a pure phase of fines below, by a sharp concentration jump. A generic feature of these models is that monotonically decreasing sections of this concentration shock steepen and eventually break when the layer is sheared. In this paper, we investigate the structure of the subsequent breaking, which is important for large-particle recirculation at the bouldery margins of debris flows and for fingering instabilities of dry granular flows. We develop an exact quasi-steady travelling wave solution for the structure of the breaking/recirculation zone, which consists of two shocks and two expansion fans that are arranged in a ‘lens’-like structure. A high-resolution shock-capturing numerical scheme is used to investigate the temporal evolution of a linearly decreasing shock towards a steady-state lens, as well as the interaction of two recirculation zones that travel at different speeds and eventually coalesce to form a single zone. Movies are available with the online version of the paper.

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41

Dang, Tong, Binzheng Zhang, Maodong Yan, John Lyon, Zhonghua Yao, Sudong Xiao, Tielong Zhang, and Jiuhou Lei. "A New Tool for Understanding the Solar Wind–Venus Interaction: Three-dimensional Multifluid MHD Model." Astrophysical Journal 945, no. 2 (March 1, 2023): 91. http://dx.doi.org/10.3847/1538-4357/acba88.

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Abstract In this paper, we present a new tool to investigate the interaction of the solar wind with Venus with the approach of a global multifluid magnetohydrodynamics (MHD) model. The continuity, momentum, and energy equations for H+, O+, O 2 + , and CO 2 + are solved self-consistently together with Faraday’s law. The photochemistry of ionospheric ions are considered as the source term in the density, momentum, and energy equations for each ion. We found that the simulated ionospheric density, temperature, and the bow shock location are consistent with previous observations and simulations for both the solar maximum and minimum. The simulated magnetic fields also agree well with the Venus Express observations. Meanwhile, the high-resolving power and low numerical diffusion makes the model capable of capturing the fine structures of the Venusian-induced magnetosphere, such as the Kelvin–Helmholtz instability and the nightside wake. The escape rates have also been estimated and the results are similar to previous estimations. The high-resolution model could be an efficient tool for the exploration of the fine structures of the Venusian space environment system, and also for the application to other unmagnetized planets.

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42

Nandan, Shambhavi, Christophe Fochesato, Mathieu Peybernes, Renaud Motte, and Florian De Vuyst. "Sharp Interface Capturing in Compressible Multi-Material Flows with a Diffuse Interface Method." Applied Sciences 11, no. 24 (December 19, 2021): 12107. http://dx.doi.org/10.3390/app112412107.

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Compressible multi-materialflows are encountered in a wide range of natural phenomena and industrial applications, such as supernova explosions in space, high speed flows in jet and rocket propulsion, underwater explosions, and vapor explosions in post accidental situations in nuclear reactors. In the numerical simulations of these flows, interfaces play a crucial role. A poor numerical resolution of the interfaces could make it difficult to account for the physics, such as material separation, location of the shocks and contact discontinuities, and transfer of the mass, momentum and heat between different materials/phases. Owing to such importance, sharp interface capturing remains an active area of research in the field of computational physics. To address this problem in this paper we focus on the Interface Capturing (IC) strategy, and thus we make use of a newly developed Diffuse Interface Method (DIM) called Multidimensional Limiting Process-Upper Bound (MLP-UB). Our analysis shows that this method is easy to implement, can deal with any number of material interfaces, and produces sharp, shape-preserving interfaces, along with their accurate interaction with the shocks. Numerical experiments show good results even with the use of coarse meshes.

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43

Yang, Jaw-Yen, Chin-Yuan Yan, Juan-Chen Huang, and Zhihui Li. "Numerical solutions of the semiclassical Boltzmann ellipsoidal-statistical kinetic model equation." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 470, no. 2168 (August 8, 2014): 20140061. http://dx.doi.org/10.1098/rspa.2014.0061.

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Computations of rarefied gas dynamical flows governed by the semiclassical Boltzmann ellipsoidal-statistical (ES) kinetic model equation using an accurate numerical method are presented. The semiclassical ES model was derived through the maximum entropy principle and conserves not only the mass, momentum and energy, but also contains additional higher order moments that differ from the standard quantum distributions. A different decoding procedure to obtain the necessary parameters for determining the ES distribution is also devised. The numerical method in phase space combines the discrete-ordinate method in momentum space and the high-resolution shock capturing method in physical space. Numerical solutions of two-dimensional Riemann problems for two configurations covering various degrees of rarefaction are presented and various contours of the quantities unique to this new model are illustrated. When the relaxation time becomes very small, the main flow features a display similar to that of ideal quantum gas dynamics, and the present solutions are found to be consistent with existing calculations for classical gas. The effect of a parameter that permits an adjustable Prandtl number in the flow is also studied.

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Li, Xiang-Yu, and Lars Mattsson. "Coagulation of inertial particles in supersonic turbulence." Astronomy & Astrophysics 648 (April 2021): A52. http://dx.doi.org/10.1051/0004-6361/202040068.

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Coagulation driven by supersonic turbulence is primarily an astrophysical problem because coagulation processes on Earth are normally associated with incompressible fluid flows at low Mach numbers, while dust aggregation in the interstellar medium for instance is an example of the opposite regime. We study coagulation of inertial particles in compressible turbulence using high-resolution direct and shock-capturing numerical simulations with a wide range of Mach numbers from nearly incompressible to moderately supersonic. The particle dynamics is simulated by representative particles and the effects on the size distribution and coagulation rate due to increasing Mach number is explored. We show that the time evolution of particle size distribution mainly depends on the compressibility (Mach number). We find that the average coagulation kernel ⟨Cij⟩ scales linearly with the average Mach number ℳrms multiplied by the combined size of the colliding particles, that is, 〈Cij〉∼〈(ai+aj)3〉 ℳrmsτη−1, which is qualitatively consistent with expectations from analytical estimates. A quantitative correction 〈Cij〉∼〈(ai+aj)3〉(vp,rms/cs)τη−1 is proposed and can serve as a benchmark for future studies. We argue that the coagulation rate ⟨Rc⟩ is also enhanced by compressibility-induced compaction of particles.

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45

Li, Qijie, Kensuke Yokoi, Zhihua Xie, Syazana Omar, and Jingjing Xue. "A fifth-order high-resolution shock-capturing scheme based on modified weighted essentially non-oscillatory method and boundary variation diminishing framework for compressible flows and compressible two-phase flows." Physics of Fluids 33, no. 5 (May 2021): 056104. http://dx.doi.org/10.1063/5.0045635.

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Le Roy, S., R. Pedreros, C. André, F. Paris, S. Lecacheux, F. Marche, and C. Vinchon. "Coastal flooding of urban areas by overtopping: dynamic modelling application to the Johanna storm (2008) in Gâvres (France)." Natural Hazards and Earth System Sciences 15, no. 11 (November 11, 2015): 2497–510. http://dx.doi.org/10.5194/nhess-15-2497-2015.

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Abstract. Recent dramatic events have allowed significant progress to be achieved in coastal flood modelling over recent years. Classical approaches generally estimate wave overtopping by means of empirical formulas or 1-D simulations, and the flood is simulated on a DTM (digital terrain model), using soil roughness to characterize land use. The limits of these methods are typically linked to the accuracy of overtopping estimation (spatial and temporal distribution) and to the reliability of the results in urban areas, which are places where the assets are the most crucial. This paper intends to propose and apply a methodology to simulate simultaneously wave overtopping and the resulting flood in an urban area at a very high resolution. This type of 2-D simulation presents the advantage of allowing both the chronology of the storm and the particular effect of urban areas on the flows to be integrated. This methodology is based on a downscaling approach, from regional to local scales, using hydrodynamic simulations to characterize the sea level and the wave spectra. A time series is then generated including the evolutions of these two parameters, and imposed upon a time-dependent phase-resolving model to simulate the overtopping over the dike. The flood is dynamically simulated directly by this model: if the model uses adapted schemes (well balanced, shock capturing), the calculation can be led on a DEM (digital elevation model) that includes buildings and walls, thereby achieving a realistic representation of the urban areas. This methodology has been applied to an actual event, the Johanna storm (10 March 2008) in Gâvres (South Brittany, in western France). The use of the SURF-WB model, a very stable time-dependent phase-resolving model using non-linear shallow water equations and well-balanced shock-capturing schemes, allowed simulating both the dynamics of the overtopping and the flooding in the urban area, taking into account buildings and streets thanks to a very high resolution (1 m). The results obtained proved to be very coherent with the available reports in terms of overtopping sectors, flooded area, water depths and chronology. This method makes it possible to estimate very precisely not only the overtopping flows, but also the main characteristics of flooding in a complex topography like an urban area, and indeed the hazard at a very high resolution (water depths and vertically integrated current speeds). The comparison with a similar flooding simulation using a more classical approach (a digital terrain model with no buildings, and a representation of the urban area by an increased soil roughness) has allowed the advantages of an explicit representation of the buildings and the streets to be identified: if, in the studied case, the impact of the urbanization representation on water levels does indeed remain negligible, the flood dynamics and the current speeds can be considerably underestimated when no explicit representation of the buildings is provided, especially along the main streets. Moreover, on the seaside, recourse to a time-dependent phase-resolving model using non-stationary conditions allows a better representation of the flows caused by overtopping. Finally, this type of simulation is shown to be of value for hazard studies, thanks to the high level of accuracy of the results in urban areas where assets are concentrated. This methodology, although it is currently still quite difficult to implement and costly in terms of calculation time, can expect to be increasingly resorted to in years to come, thanks to the recent developments in wave models and to the increasing availability of LiDAR data.

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47

Le Roy, S., R. Pedreros, C. André, F. Paris, S. Lecacheux, F. Marche, and C. Vinchon. "Coastal flooding of urban areas by overtopping: dynamic modelling application to the Johanna storm (2008) in Gâvres (France)." Natural Hazards and Earth System Sciences Discussions 2, no. 8 (August 4, 2014): 4947–85. http://dx.doi.org/10.5194/nhessd-2-4947-2014.

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Abstract. Recent dramatic events have allowed significant progress to be achieved in coastal flood modelling over recent years. Classical approaches generally estimate wave overtopping by means of empirical formulas or 1-dimensional simulations, and the flood is simulated on a DTM (Digital Terrain Model), using soil roughness to characterize land use. The limits of these methods are typically linked to the accuracy of overtopping estimation (spatial and temporal distribution) and to the reliability of the results in urban areas, which are places where the assets are the most crucial. This paper intends to propose and apply a methodology to simulate simultaneously wave overtopping and the resulting flood in an urban area at a very high resolution. This type of two-dimensional simulation presents the advantage of allowing both the chronology of the storm and the particular effect of urban areas on the flows to be integrated. This methodology is based on a downscaling approach, from regional to local scales, using hydrodynamic simulations to characterize the sea level and the wave spectra. A time series is then generated including the evolutions of these two parameters, and imposed upon a time-dependent phase-resolving model to simulate the overtopping over the dike. The flood is dynamically simulated directly by this model: if the model uses adapted schemes (well-balanced, shock-capturing), the calculation can be led on a DEM (Digital Elevation Model) that includes buildings and walls, thereby achieving a realistic representation of the urban areas. This methodology has been applied to an actual event, the Johanna storm (10 March 2008) in Gâvres (South Brittany, in western France). The use of the SURF-WB model, a very stable time-dependent phase-resolving model using NLSW equations and well-balanced shock-capturing schemes, allowed simulating both the dynamics of the overtopping and the flooding in the urban area, taking into account buildings and streets thanks to a very high resolution (1 m). The results obtained proved to be very coherent with the available reports in terms of overtopping sectors, flooded area, water heights and chronology. This method makes it possible to estimate very precisely not only the overtopping flows, but also the main characteristics of flooding in a complex topography like an urban area, and indeed the hazard at a very high resolution (water heights and vertically integrated current speeds). The comparison with a similar flooding simulation using a more classical approach (a Digital Terrain Model with no buildings, and a representation of the urban area by an increased soil roughness) has allowed the advantages of an explicit representation of the buildings and the streets to be identified: if, in the studied case, the impact of the urbanization representation on water heights does indeed remain negligible, the flood dynamics and the current speeds can be considerably underestimated when no explicit representation of the buildings is provided, especially along the main streets. Moreover, on the seaside, recourse to a time-dependent phase-resolving model using non-stationary conditions allows a better representation of the flows caused by overtopping. Finally, this type of simulation is shown to be of value for hazard studies, thanks to the high level of accuracy of the results in urban areas where assets are concentrated. This methodology, although it is currently still quite difficult to implement and costly in terms of calculation time, can expect to be increasingly resorted to in years to come, thanks to the recent developments in wave models and to the increasing availability of LiDAR data.

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48

Guzmán, F. S., and L. F. Mendoza Mendoza. "Tests of a new code that simulates the evolution of solar winds and CMEs." Journal of Physics: Conference Series 2307, no. 1 (September 1, 2022): 012020. http://dx.doi.org/10.1088/1742-6596/2307/1/012020.

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Abstract We present the tests of a new code that solves Euler equations in three dimensions used to simulate the dynamics of the Solar Wind. The code is based on a finite volume discretization and uses high resolution shock capturing methods, with second order variable reconstructors and approximate flux formulae of the HLL class. It uses Cartesian coordinates and fixed mesh refinement. The equations are written in flux balance law form, which allows the evolution of conservative variables. The evolution is carried out using the method of lines with second order time integration. For the simulation of a solar wind we assume the Sun lies at the coordinate origin, and inject the fluid variables through the surface of a lego-sphere with radius 20R ⊙, where all the characteristic speeds point outwards from the solar surface. We manage to obtain stationary winds that reproduce winds of literature in terms of density, velocity and temperature of the plasma. On top of the stationary wind it is possible to launch Coronal Mass Ejections (CMEs) that propagate through the stationary Solar Wind from the injection surface all the way to the Earth. Finally, in order to incorporate the role of orbiting satellites that monitor Solar Winds and CMEs, the code also measures wind variables at detector locations on their actual trajectories around the Sun.

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Leakey, Shannon, Vassilis Glenis, and Caspar Hewett. "Artificial Compressibility with Riemann Solvers: Convergence of Limiters on Unstructured Meshes." OpenFOAM® Journal 2 (March 4, 2022): 31–47. http://dx.doi.org/10.51560/ofj.v2.49.

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Free-surface flows and other variable density incompressible flows have numerous important applications in engineering.One way such flows can be modelled is to extend established numerical methods for compressible flows to incompressible flows using the method of artificial compressibility. Artificial compressibility introduces a pseudo-time derivative for pressure and, in each real-time step, the solution advances in pseudo-time until convergence to an incompressible limit - a fundamentally different approach than SIMPLE, PISO, and PIMPLE, the standard methods used in OpenFOAM. Although the artificial compressibility method is widespread in the literature, its application to free-surface flows is not. In this paper, we apply the method to variable density flows on 3D unstructured meshes for the first time, implementing a Godunov-type scheme with MUSCL reconstruction and Riemann solvers, where the free surface gets captured automatically by the contact wave in the Riemann solver. The critical problem in this implementation lies in the slope limiters used in the MUSCL reconstruction step. It is well-known that slope limiters can inhibit convergence to steady state on unstructured meshes; the problem is exacerbated here as convergence in pseudo-time is required not just once, but at every real-time step. We compare the limited gradient schemes included in OpenFOAM with an improved limiter from the literature, testing the solver against dam-break and hydrostatic pressure benchmarks. This work opens OpenFOAM up to the method of artificial compressibility, breaking the mould of PIMPLE and harnessing high-resolution shock-capturing schemes that are easier to parallelise.

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Meliani, Zakaria, Yosuke Mizuno, Hector Olivares, Oliver Porth, Luciano Rezzolla, and Ziri Younsi. "Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer." Astronomy & Astrophysics 598 (January 27, 2017): A38. http://dx.doi.org/10.1051/0004-6361/201629191.

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Context. In many astrophysical phenomena, and especially in those that involve the high-energy regimes that always accompany the astronomical phenomenology of black holes and neutron stars, physical conditions that are achieved are extreme in terms of speeds, temperatures, and gravitational fields. In such relativistic regimes, numerical calculations are the only tool to accurately model the dynamics of the flows and the transport of radiation in the accreting matter. Aims. We here continue our effort of modelling the behaviour of matter when it orbits or is accreted onto a generic black hole by developing a new numerical code that employs advanced techniques geared towards solving the equations of general-relativistic hydrodynamics. Methods. More specifically, the new code employs a number of high-resolution shock-capturing Riemann solvers and reconstruction algorithms, exploiting the enhanced accuracy and the reduced computational cost of adaptive mesh-refinement (AMR) techniques. In addition, the code makes use of sophisticated ray-tracing libraries that, coupled with general-relativistic radiation-transfer calculations, allow us to accurately compute the electromagnetic emissions from such accretion flows. Results. We validate the new code by presenting an extensive series of stationary accretion flows either in spherical or axial symmetry that are performed either in two or three spatial dimensions. In addition, we consider the highly nonlinear scenario of a recoiling black hole produced in the merger of a supermassive black-hole binary interacting with the surrounding circumbinary disc. In this way, we can present for the first time ray-traced images of the shocked fluid and the light curve resulting from consistent general-relativistic radiation-transport calculations from this process. Conclusions. The work presented here lays the ground for the development of a generic computational infrastructure employing AMR techniques to accurately and self-consistently calculate general-relativistic accretion flows onto compact objects. In addition to the accurate handling of the matter, we provide a self-consistent electromagnetic emission from these scenarios by solving the associated radiative-transfer problem. While magnetic fields are currently excluded from our analysis, the tools presented here can have a number of applications to study accretion flows onto black holes or neutron stars.

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Journal articles on the topic 'High Resolution Shock Capturing'

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