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Journal articles on the topic 'Finite Volume Solver'

Author: Grafiati

Published: 6 September 2023

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1

Lourenço, Marcos Antonio de Souza, and Elie Luis Martínez Padilla. "An octree structured finite volume based solver." Applied Mathematics and Computation 365 (January 2020): 124721. http://dx.doi.org/10.1016/j.amc.2019.124721.

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2

Jiang, Yuewen. "Algebraic-volume meshfree method for application in finite volume solver." Computer Methods in Applied Mechanics and Engineering 355 (October 2019): 44–66. http://dx.doi.org/10.1016/j.cma.2019.05.048.

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3

Tuković, Željko, Aleksandar Karač, Philip Cardiff, Hrvoje Jasak, and Alojz Ivanković. "OpenFOAM Finite Volume Solver for Fluid-Solid Interaction." Transactions of FAMENA 42, no. 3 (October 19, 2018): 1–31. http://dx.doi.org/10.21278/tof.42301.

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4

Gonzalez-Juez, Esteban D., and Aleksandar Jemcov. "Finite Volume Time-Domain Solver to Estimate Combustion Instabilities." Journal of Propulsion and Power 31, no. 2 (March 2015): 632–42. http://dx.doi.org/10.2514/1.b35488.

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5

Haleem, Dilshad A., Georges Kesserwani, and Daniel Caviedes-Voullième. "Haar wavelet-based adaptive finite volume shallow water solver." Journal of Hydroinformatics 17, no. 6 (July 9, 2015): 857–73. http://dx.doi.org/10.2166/hydro.2015.039.

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This paper presents the formulation of an adaptive finite volume (FV) model for the shallow water equations. A Godunov-type reformulation combining the Haar wavelet is achieved to enable solution-driven resolution adaptivity (both coarsening and refinement) by depending on the wavelet's threshold value. The ability to properly model irregular topographies and wetting/drying is transferred from the (baseline) FV uniform mesh model, with no extra notable efforts. Selected hydraulic tests are employed to analyse the performance of the Haar wavelet FV shallow water solver considering adaptivity and practical issues including choice for the threshold value driving the adaptivity, mesh convergence study, shock and wet/dry front capturing abilities. Our findings show that Haar wavelet-based adaptive FV solutions offer great potential to improve the reliability of multiscale shallow water models.

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6

Solin, Pavel, and Karel Segeth. "Description of the Multi-Dimensional Finite Volume Solver EULER." Applications of Mathematics 47, no. 2 (April 2002): 169–85. http://dx.doi.org/10.1023/a:1021789203207.

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7

Sandhu, Jatinder, Anant Girdhar, Rakesh Ramakrishnan, R. Teja, and Santanu Ghosh. "FEST-3D: Finite-volume Explicit STructured 3-Dimensional solver." Journal of Open Source Software 5, no. 46 (February 10, 2020): 1555. http://dx.doi.org/10.21105/joss.01555.

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8

Chakravarthy, V. Kalyana, K. Arora, and D. Chakraborty. "A simple hybrid finite volume solver for compressible turbulence." International Journal for Numerical Methods in Fluids 77, no. 12 (February 11, 2015): 707–31. http://dx.doi.org/10.1002/fld.4000.

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9

Jalali, Alireza, and Carl Ollivier-Gooch. "Anhp-adaptive unstructured finite volume solver for compressible flows." International Journal for Numerical Methods in Fluids 85, no. 10 (June 7, 2017): 563–82. http://dx.doi.org/10.1002/fld.4396.

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10

Audusse, Emmanuel, and Marie-Odile Bristeau. "Finite-Volume Solvers for a Multilayer Saint-Venant System." International Journal of Applied Mathematics and Computer Science 17, no. 3 (October 1, 2007): 311–20. http://dx.doi.org/10.2478/v10006-007-0025-0.

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Finite-Volume Solvers for a Multilayer Saint-Venant SystemWe consider the numerical investigation of two hyperbolic shallow water models. We focus on the treatment of the hyperbolic part. We first recall some efficient finite volume solvers for the classical Saint-Venant system. Then we study their extensions to a new multilayer Saint-Venant system. Finally, we use a kinetic solver to perform some numerical tests which prove that the 2D multilayer Saint-Venant system is a relevant alternative to 3D hydrostatic Navier-Stokes equations.

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11

Cai, Mingchao, Andy Nonaka, John B. Bell, Boyce E. Griffith, and Aleksandar Donev. "Efficient Variable-Coefficient Finite-Volume Stokes Solvers." Communications in Computational Physics 16, no. 5 (November 2014): 1263–97. http://dx.doi.org/10.4208/cicp.070114.170614a.

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AbstractWe investigate several robust preconditioners for solving the saddle-point linear systems that arise from spatial discretization of unsteady and steady variable-coefficient Stokes equations on a uniform staggered grid. Building on the success of using the classical projection method as a preconditioner for the coupled velocity pressure system [B. E. Griffith, J. Comp. Phys., 228 (2009), pp. 7565-7595], as well; established techniques for steady and unsteady Stokes flow in the finite-element literature, we construct preconditioners that employ independent generalized Helmholtz and Poisson solvers for the velocity and pressure subproblems. We demonstrate that only a single cycle of a standard geometric multigrid algorithm serves as an effective inexact solver for each of these subproblems. Contrary to traditional wisdom, we find that the Stokes problem can be solved nearly as efficiently as the independent pressure and velocity subproblems, making the overall cost of solving the Stokes system comparable to the cost of classical projection or fractional step methods for incompressible flow, even for steady flow and in the presence of large density and viscosity contrasts. Two of the five preconditioners considered here are found to be robust to GMRES restarts and to increasing problem size, making them suitable for large-scale problems. Our work opens many possibilities for constructing novel unsplit temporal integrators for finite-volume spatial discretizations of the equations of low Mach and incompressible flow dynamics.

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12

Chung, T., Y. D. Wang, R. T. Armstrong, and P. Mostaghimi. "Approximating Permeability of Microcomputed-Tomography Images Using Elliptic Flow Equations." SPE Journal 24, no. 03 (February 22, 2019): 1154–63. http://dx.doi.org/10.2118/191379-pa.

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Summary Direct simulation of flow on microcomputed-tomography (micro-CT) images of rocks is widely used for the calculation of permeability. However, direct numerical methods are computationally demanding. A rapid and robust method is proposed to solve the elliptic flow equation. Segmented micro-CT images are used for the calculation of local conductivity in each voxel. The elliptic flow equation is then solved on the images using the finite-volume method. The numerical method is optimized in terms of memory usage using sparse matrix modules to eliminate memory overhead associated with both the inherent sparsity of the finite-volume two-point flux-approximation (TPFA) method, and the presence of zero conductivity for impermeable grain cells. The estimated permeabilities for a number of sandstone and carbonate micro-CT images are compared against estimation of other solvers, and results show a difference of approximately 11%. However, the computational time is 80% lower. Local conductivity can furthermore be assigned directly into matrix voxels without a loss in generality, hence allowing the pore-scale finite-volume solver (PFVS) to be able to solve for flow in a permeable matrix as well as open pore space. This has been developed to include the effect of microporosity in flow simulation.

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13

Møyner, Olav, and Knut-Andreas Lie. "The Multiscale Finite-Volume Method on Stratigraphic Grids." SPE Journal 19, no. 05 (March 25, 2014): 816–31. http://dx.doi.org/10.2118/163649-pa.

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Summary Finding a pressure solution for large and highly detailed reservoir models with fine-scale heterogeneities modeled on a meter scale is computationally demanding. One way of making such simulations less compute-intensive is to use multiscale methods that solve coarsened flow problems by use of a set of reusable basis functions to capture flow effects induced by local geological variations. One such method, the multiscale finite-volume (MsFV) method, is well-studied for 2D Cartesian grids but has not been implemented for stratigraphic and unstructured grids with faults in three dimensions. We present an open-source implementation of the MsFV method in three dimensions along with a coarse partitioning algorithm that can handle stratigraphic grids with faults and wells. The resulting solver is an alternative to traditional upscaling methods, but can also be used for accelerating fine-scale simulations. To achieve better precision, the implementation can use the MsFV method as a preconditioner for Arnoldi iterations using the generalized minimal residual (GMRES) method or as a preconditioner in combination with a standard inexpensive smoother. We conduct a series of numerical experiments in which approximate solutions computed by the new MsFV solver are compared with fine-scale solutions computed by a standard two-point scheme for grids with realistic permeabilities and geometries. On the one hand, the results show that the MsFV method can produce accurate approximations for geological models with pinchouts, faults, and nonneighboring connections, but on the other hand, they also show that the method can fail quite spectacularly for highly heterogeneous and anisotropic systems in a way that cannot efficiently be mitigated by iterative approaches. Thus, the MsFV method is, in our opinion, not yet sufficiently robust to be applied as a black-box solver for models with industry-standard complexity. However, extending the method to realistic grids is an important step on the way toward a fast and accurate multiscale solution of large-scale reservoir models. In particular, our open-source implementation provides an efficient framework suitable for further experimentation with partitioning algorithms and MsFV variants.

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14

Kang, Kab S. "On the Finite Volume Multigrid Method: Comparison of Intergrid Transfer Operators." Computational Methods in Applied Mathematics 15, no. 2 (April 1, 2015): 189–202. http://dx.doi.org/10.1515/cmam-2014-0030.

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AbstractIn this paper, we consider finite volume multigrid methods on triangular meshes with control volume based intergrid transfer operators. We review the error analysis of the finite volume methods and the convergence analysis on the multigrid method. For several different triangulations, we investigate the error reduction factors of the multigrid method as a solver, and also as a preconditioner in the Preconditioned CGM and GMRES solvers. We also study the scaling properties of the finite volume multigrid method on a High Performance Computer. We identify that the intergrid transfer operator based on the trial function space has the best properties.

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15

Deng, Xi, Bin Xie, and Feng Xiao. "Multimoment Finite Volume Solver for Euler Equations on Unstructured Grids." AIAA Journal 55, no. 8 (August 2017): 2617–29. http://dx.doi.org/10.2514/1.j055581.

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16

Meng, Xucheng, and Guanghui Hu. "A NURBS-enhanced finite volume solver for steady Euler equations." Journal of Computational Physics 359 (April 2018): 77–92. http://dx.doi.org/10.1016/j.jcp.2017.12.041.

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17

Saleem, Ayhan H., and Jowhar R. Mohammad. "Simulation of Mosul Dam Break Using Finite Volume Method." Polytechnic Journal 10, no. 2 (December 30, 2020): 10–20. http://dx.doi.org/10.25156/ptj.v10n2y2020.pp10-20.

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Mosul dam is an earth-fill embankment located north of Iraq on the Tigris River forming a reservoir with 11.11 km3 water storage capacity which is the largest dam in the country. The dam is built on a rock bed foundation, in which the dissolution process is dynamic in the zone where gypsum and anhydrite layers present. During the construction development seepage locations were found in the dam foundation and the grouting process is in progress until now to control this problem. Therefore, the possibility of the Mosul dam break is highlighted by previous studies. In this research, a FORTRAN code based on the finite volume method is modified to solve the two-dimensional shallow water equations and simulating the Mosul dam break. The computational domain discretized using unstructured triangular mesh. The solver applied Harten lax van leer with contact (HLLC) wave approximate Riemann solver to calculate the cell interface fluxes, and the semi-implicit scheme employed to solve the friction source term. The numerical scheme applied to two benchmark test cases, and the results showed that the presented model was robust and accurate especially in handling wet/dry beds, mixed flow regimes, discontinuities, negative water depths, and complex topography. The results of this study demonstrate that flood waves may reach the center of Mosul city in < 6 h and water depth may rise to 34 m after 7 h of Mosul dam breaking. Finally, the simulation results of the Mosul dam break were used to prepare an emergency action plan.

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18

BOUSHABA, FARID, ELMILOUD CHAABELASRI, NAJIM SALHI, IMAD ELMAHI, FAYSSAL BENKHALDOUN, and ALISTAIR G. L. BORTHWICK. "A COMPARATIVE STUDY OF FINITE VOLUME AND FINITE ELEMENT ON SOME TRANSCRITICAL FREE SURFACE FLOW PROBLEMS." International Journal of Computational Methods 05, no. 03 (September 2008): 413–31. http://dx.doi.org/10.1142/s0219876208001522.

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This paper presents details of finite volume and finite element numerical models based on unstructured triangular meshes that are used to solve the two-dimensional nonlinear shallow water equations (SWEs). The finite volume scheme uses Roe's approximate Riemann solver to evaluate the convection terms. Second order accuracy is achieved by means of the MUSCL approach with MinMod and VanAlbada limiters. The finite element model utilizes the Lax–Wendroff two-step scheme, which is second-order in space and time. The models are validated and their relative performance compared for several benchmark problems, including a hydraulic jump, and flows in converging and converging–diverging channels.

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19

Tchuen, Ghislain, Pascalin Tiam Kapen, and Yves Burtschell. "An accurate shock-capturing scheme based on rotated-hybrid Riemann solver." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 5 (June 6, 2016): 1310–27. http://dx.doi.org/10.1108/hff-01-2015-0031.

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Purpose – The purpose of this paper is to present a new hybrid Euler flux fonction for use in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Design/methodology/approach – The proposed scheme, called AUFSRR can be devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach (Sun and Takayama, 2003; Ren, 2003). The upwind direction is determined by the velocity-difference vector and idea is to apply the AUFS solver in the direction normal to shocks to suppress carbuncle and the Roe solver across shear layers to avoid an excessive amount of dissipation. The resulting flux functions can be implemented in a very simple manner, in the form of the Roe solver with modified wave speeds, so that converting an existing AUFS flux code into the new fluxes is an extremely simple task. Findings – The proposed flux functions require about 18 per cent more CPU time than the Roe flux. Accuracy, efficiency and other essential features of AUFSRR scheme are evaluated by analyzing shock propagation behaviours for both the steady and unsteady compressible flows. This is demonstrated by several test cases (1D and 2D) with standard finite-volume Euler code, by comparing results with existing methods. Practical implications – The hybrid Euler flux function is used in a finite-volume Euler/Navier-Stokes code and adapted to compressible flow problems. Originality/value – The AUFSRR scheme is devised by combining the AUFS solver and the Roe solver, based on a rotated Riemann solver approach.

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20

Lorin, Emmanuel, Amine Ben Haj Ali, and Azzeddine Soulaimani. "A positivity preserving finite element–finite volume solver for the Spalart–Allmaras turbulence model." Computer Methods in Applied Mechanics and Engineering 196, no. 17-20 (March 2007): 2097–116. http://dx.doi.org/10.1016/j.cma.2006.10.009.

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21

QU, KUN, CHANG SHU, and JINSHENG CAI. "DEVELOPING LBM-BASED FLUX SOLVER AND ITS APPLICATIONS IN MULTI-DIMENSION SIMULATIONS." International Journal of Modern Physics: Conference Series 19 (January 2012): 90–99. http://dx.doi.org/10.1142/s2010194512008628.

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In this paper, a new flux solver was developed based on a lattice Boltzmann model. Different from solving discrete velocity Boltzmann equation and lattice Boltzmann equation, Euler/Navier-Stokes (NS) equations were solved in this approach, and the flux at the interface was evaluated with a compressible lattice Boltzmann model. This method combined lattice Boltzmann method with finite volume method to solve Euler/NS equations. The proposed approach was validated by some simulations of one-dimensional and multi-dimensional problems.

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22

Deepu, M., M. P. Dhrishit, and S. Shyji. "Numerical simulation of high speed reacting shear layers using AUSM+- up scheme-based unstructured finite volume method solver." International Journal of Modeling, Simulation, and Scientific Computing 08, no. 03 (September 2017): 1750020. http://dx.doi.org/10.1142/s1793962317500209.

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Development of an Advection Upstream Splitting Method (AUSM[Formula: see text]-up) scheme-based Unstructured Finite Volume (UFVM) solver for the simulation of two-dimensional axisymmetric/planar high speed compressible turbulent reacting shear layers is presented. The inviscid numerical flux is evaluated using AUSM[Formula: see text]-up upwind scheme. An eight-step hydrogen–oxygen finite rate chemistry model is used to model the development of chemical species in a supersonic reacting flow field. The chemical species terms are alone solved implicitly in this explicit flow solver by rescaling the equation in time. The turbulence modeling has been done using RNG-based [Formula: see text]–[Formula: see text] model. Three-stage Runge–Kutta method has been used for explicit time integration. The nonreacting two-dimensional Cartesian version of the same solver has been successfully validated against experimental and numerical results reported for the wall static pressure data in sonic slot injection to supersonic stream. Detailed validation studies for reacting flow solver has been done using experimental results reported for a coaxial supersonic combustor, in which species profile at various axial locations has been compared. Present numerical solver is useful in simulating combustors of high speed air-breathing propulsion devices.

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23

Tasri, Adek. "Accuracy of Cell-Centre Derivation of Unstructured-Mesh Finite Volume Solver." International Journal of Engineering Trends and Technology 70, no. 8 (August 31, 2022): 166–71. http://dx.doi.org/10.14445/22315381/ijett-v70i8p217.

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24

Jalali, Alireza, Mahkame Sharbatdar, and Carl Ollivier-Gooch. "An efficient implicit unstructured finite volume solver for generalised Newtonian fluids." International Journal of Computational Fluid Dynamics 30, no. 3 (March 15, 2016): 201–17. http://dx.doi.org/10.1080/10618562.2016.1188202.

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25

Aguirre, Miquel, Antonio J. Gil, Javier Bonet, and Chun Hean Lee. "An upwind vertex centred Finite Volume solver for Lagrangian solid dynamics." Journal of Computational Physics 300 (November 2015): 387–422. http://dx.doi.org/10.1016/j.jcp.2015.07.029.

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26

Vacondio, R., A. Dal Palù, and P. Mignosa. "GPU-enhanced Finite Volume Shallow Water solver for fast flood simulations." Environmental Modelling & Software 57 (July 2014): 60–75. http://dx.doi.org/10.1016/j.envsoft.2014.02.003.

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27

Braeunig, J. P., B. Desjardins, and J. M. Ghidaglia. "A totally Eulerian finite volume solver for multi-material fluid flows." European Journal of Mechanics - B/Fluids 28, no. 4 (July 2009): 475–85. http://dx.doi.org/10.1016/j.euromechflu.2009.03.003.

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28

Singh, J. P. "Accelerated and robust finite volume Navier-Stokes solver for all speeds." Sadhana 24, no. 1-2 (February 1999): 121–45. http://dx.doi.org/10.1007/bf02747555.

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29

Tu, Shuangzhang, and Shahrouz Aliabadi. "Development of a hybrid finite volume/element solver for incompressible flows." International Journal for Numerical Methods in Fluids 55, no. 2 (2007): 177–203. http://dx.doi.org/10.1002/fld.1454.

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30

Kurganov, Alexander. "Finite-volume schemes for shallow-water equations." Acta Numerica 27 (May 1, 2018): 289–351. http://dx.doi.org/10.1017/s0962492918000028.

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Shallow-water equations are widely used to model water flow in rivers, lakes, reservoirs, coastal areas, and other situations in which the water depth is much smaller than the horizontal length scale of motion. The classical shallow-water equations, the Saint-Venant system, were originally proposed about 150 years ago and still are used in a variety of applications. For many practical purposes, it is extremely important to have an accurate, efficient and robust numerical solver for the Saint-Venant system and related models. As their solutions are typically non-smooth and even discontinuous, finite-volume schemes are among the most popular tools. In this paper, we review such schemes and focus on one of the simplest (yet highly accurate and robust) methods: central-upwind schemes. These schemes belong to the family of Godunov-type Riemann-problem-solver-free central schemes, but incorporate some upwinding information about the local speeds of propagation, which helps to reduce an excessive amount of numerical diffusion typically present in classical (staggered) non-oscillatory central schemes. Besides the classical one- and two-dimensional Saint-Venant systems, we will consider the shallow-water equations with friction terms, models with moving bottom topography, the two-layer shallow-water system as well as general non-conservative hyperbolic systems.

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31

Zhao, Di. "Quick finite volume solver for incompressible Navier-Stokes equation by parallel Gram-Schmidt process based GMRES and HSS." Engineering Computations 32, no. 5 (July 6, 2015): 1460–76. http://dx.doi.org/10.1108/ec-02-2014-0032.

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Purpose – The purpose of this paper is to develop Triple Finite Volume Method (tFVM), the author discretizes incompressible Navier-Stokes equation by tFVM, which leads to a special linear system of saddle point problem, and most computational efforts for solving the linear system are invested on the linear solver GMRES. Design/methodology/approach – In this paper, by recently developed preconditioner Hermitian/Skew-Hermitian Separation (HSS) and the parallel implementation of GMRES, the author develops a quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation. Findings – Computational results show that, the quick solver HSS-pGMRES-tFVM significantly increases the solution speed for saddle point problem from incompressible Navier-Stokes equation than the conventional solvers. Originality/value – Altogether, the contribution of this paper is that the author developed the quick solver, HSS-pGMRES-tFVM, for fast solving incompressible Navier-Stokes equation.

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32

El-Beltagy, Mohamed A., and Mohamed I. Wafa. "Stochastic 2D Incompressible Navier-Stokes Solver Using the Vorticity-Stream Function Formulation." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/903618.

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A two-dimensional stochastic solver for the incompressible Navier-Stokes equations is developed. The vorticity-stream function formulation is considered. The polynomial chaos expansion was integrated with an unstructured node-centered finite-volume solver. A second-order upwind scheme is used in the convection term for numerical stability and higher-order discretization. The resulting sparse linear system is solved efficiently by a direct parallel solver. The mean and variance simulations of the cavity flow are done for random variation of the viscosity and the lid velocity. The solver was tested and compared with the Monte-Carlo simulations and with previous research works. The developed solver is proved to be efficient in simulating the stochastic two-dimensional incompressible flows.

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33

Wagner, Simon, Manuel Münsch, and Antonio Delgado. "An Integrated OpenFOAM Membrane Fluid-Structure Interaction Solver." OpenFOAM® Journal 2 (March 4, 2022): 48–61. http://dx.doi.org/10.51560/ofj.v2.45.

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The scope of this paper is to present the design and verification of an integrated OpenFOAM membrane fluid-structure interaction (FSI) solver for small deflections, which employs the finite volume method (FVM) for solving the flow field and the finite area method (FAM) for solution of the membrane deflection. A key feature is that both the fluid and the solid solver operate on a common mesh geometry and are included into a single executable. Although the scope of applicability is narrow due to limitations of the membrane solver at its current state, positive verification results prove the practicability of the design, which allows for lightweight implementation as well as simple data transfers and post-processing.

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34

Danaila, Sterian, Delia Teleaga, and Luiza Zavalan. "Finite Volume Particle Method for Incompressible Flows." Applied Mechanics and Materials 656 (October 2014): 72–80. http://dx.doi.org/10.4028/www.scientific.net/amm.656.72.

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This paper presents an application of the Finite Volume Particle Method to incompressible flows. The two-dimensional incompressible Navier-Stokes solver is based on Chorin’s projection method with finite volume particle discretization. The Finite Volume Particle Method is a meshless method for fluid dynamics which unifies advantages of particle methods and finite volume methods in one scheme. The method of manufactured solutions is used to examine the global discretization error and finally a comparison between finite volume particle method simulations of an incompressible flow around a fixed circular cylinder and the numerical simulations with the CFD code ANSYS FLUENT 14.0 is presented.

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35

Guermond, Jean-Luc, Christian Klingenberg, Bojan Popov, and Ignacio Tomas. "The Suliciu approximate Riemann solver is not invariant domain preserving." Journal of Hyperbolic Differential Equations 16, no. 01 (March 2019): 59–72. http://dx.doi.org/10.1142/s0219891619500036.

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36

Grosjean, Elise, and Yvon Maday. "Error estimate of the non-intrusive reduced basis method with finite volume schemes." ESAIM: Mathematical Modelling and Numerical Analysis 55, no. 5 (September 2021): 1941–61. http://dx.doi.org/10.1051/m2an/2021044.

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The context of this paper is the simulation of parameter-dependent partial differential equations (PDEs). When the aim is to solve such PDEs for a large number of parameter values, Reduced Basis Methods (RBM) are often used to reduce computational costs of a classical high fidelity code based on Finite Element Method (FEM), Finite Volume (FVM) or Spectral methods. The efficient implementation of most of these RBM requires to modify this high fidelity code, which cannot be done, for example in an industrial context if the high fidelity code is only accessible as a "black-box" solver. The Non-Intrusive Reduced Basis (NIRB) method has been introduced in the context of finite elements as a good alternative to reduce the implementation costs of these parameter-dependent problems. The method is efficient in other contexts than the FEM one, like with finite volume schemes, which are more often used in an industrial environment. In this case, some adaptations need to be done as the degrees of freedom in FV methods have different meanings. At this time, error estimates have only been studied with FEM solvers. In this paper, we present a generalisation of the NIRB method to Finite Volume schemes and we show that estimates established for FEM solvers also hold in the FVM setting. We first prove our results for the hybrid-Mimetic Finite Difference method (hMFD), which is part the Hybrid Mixed Mimetic methods (HMM) family. Then, we explain how these results apply more generally to other FV schemes. Some of them are specified, such as the Two Point Flux Approximation (TPFA).

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37

Johnson, Perry L., Jared M. Pent, Hrvoje Jasak, and J. Enrique Portillo. "Application of a Riemann Solver Unstructured Finite Volume Method to Combustion Instabilities." Journal of Propulsion and Power 31, no. 3 (May 2015): 937–50. http://dx.doi.org/10.2514/1.b35539.

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38

Tasri, Adek, and Anita Susilawati. "Accuracy of compact-stencil interpolation algorithms for unstructured mesh finite volume solver." Heliyon 7, no. 4 (April 2021): e06875. http://dx.doi.org/10.1016/j.heliyon.2021.e06875.

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39

van der Velden, W. C. P., J. T. Akhnoukh, and A. H. van Zuijlen. "Low-Order Finite-Volume Based Riemann Solver for Application to Aeroacoustic Problems." Journal of Computational Acoustics 25, no. 03 (September 2017): 1750010. http://dx.doi.org/10.1142/s0218396x17500102.

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The current study focuses on the development of a three-dimensional flow and aeroacoustic solver developed in a finite-volume framework which uses similar, dense meshes for both flow and acoustics while using low-order schemes from the finite volume framework to minimize the points per wavelength, overcomes interpolation errors between flow and acoustic meshes, since one-to-one mesh mapping will be applied, minimize the computational time for the acoustic loop with respect to the fluid flow loop and provides a practical, easy to use integrated numerical tool. As dispersion errors are common within this computational framework, Riemann fluxes are used to solve the linearized Euler equations with unsteady quadrupole and dipole sources. A coupling scheme is presented and common issues with boundary conditions, mesh topology and sub-cycling are discussed. Various verification and validation test cases show the expected behavior and trends with respect to analytic and reference results. An application case is presented, where airfoil self-noise is determined around a beveled flat plate.

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40

Darwish, M., A. Abdel Aziz, and F. Moukalled. "A Coupled Pressure-Based Finite-Volume Solver for Incompressible Two-Phase Flow." Numerical Heat Transfer, Part B: Fundamentals 67, no. 1 (October 23, 2014): 47–74. http://dx.doi.org/10.1080/10407790.2014.949500.

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Pimenta, F., and M. A. Alves. "Stabilization of an open-source finite-volume solver for viscoelastic fluid flows." Journal of Non-Newtonian Fluid Mechanics 239 (January 2017): 85–104. http://dx.doi.org/10.1016/j.jnnfm.2016.12.002.

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Cardiff, P., A. Karač, and A. Ivanković. "Development of a finite volume contact solver based on the penalty method." Computational Materials Science 64 (November 2012): 283–84. http://dx.doi.org/10.1016/j.commatsci.2012.03.011.

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Clair, G., J. M. Ghidaglia, and J. P. Perlat. "A multi-dimensional finite volume cell-centered direct ALE solver for hydrodynamics." Journal of Computational Physics 326 (December 2016): 312–33. http://dx.doi.org/10.1016/j.jcp.2016.08.050.

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Fainberg, J., and H. J. Leister. "Finite volume multigrid solver for thermo-elastic stress analysis in anisotropic materials." Computer Methods in Applied Mechanics and Engineering 137, no. 2 (October 1996): 167–74. http://dx.doi.org/10.1016/s0045-7825(96)01063-8.

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Dong, Haibo, Fan Zhang, Chunguang Xu, and Jun Liu. "An improved uncoupled finite volume solver for simulating unsteady shock-induced combustion." Computers & Fluids 167 (May 2018): 146–57. http://dx.doi.org/10.1016/j.compfluid.2018.03.001.

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Pimenta, F., and M. A. Alves. "A coupled finite-volume solver for numerical simulation of electrically-driven flows." Computers & Fluids 193 (October 2019): 104279. http://dx.doi.org/10.1016/j.compfluid.2019.104279.

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Mohsen Karimian, S. A., and Anthony G. Straatman. "Discretization and parallel performance of an unstructured finite volume Navier–Stokes solver." International Journal for Numerical Methods in Fluids 52, no. 6 (2006): 591–615. http://dx.doi.org/10.1002/fld.1189.

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Wang, Yuan, Xueshang Feng, Yufen Zhou, and Xinbiao Gan. "A multi-GPU finite volume solver for magnetohydrodynamics-based solar wind simulations." Computer Physics Communications 238 (May 2019): 181–93. http://dx.doi.org/10.1016/j.cpc.2018.12.003.

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Sharbatdar, Mahkame, and Carl Ollivier-Gooch. "Mesh adaptation usingC1interpolation of the solution in an unstructured finite volume solver." International Journal for Numerical Methods in Fluids 86, no. 10 (October 19, 2017): 637–54. http://dx.doi.org/10.1002/fld.4471.

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Studer, Léo, Sylvain Detrembleur, Benjamin J. Dewals, Michel Pirotton, and Anne Marie Habraken. "Modeling the Vertical Spincasting of Large Bimetallic Rolling Mill Rolls." Key Engineering Materials 443 (June 2010): 15–20. http://dx.doi.org/10.4028/www.scientific.net/kem.443.15.

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In order to take into account the dynamic effects of molten metal during solidification, a methodology is presented to interface a metal solidification solver (coupled thermal mechanical metallurgical finite elements solver) with a specifically developed flow dynamics solver. (flow dynamics and thermics finite volume solver) The numerical set of tools is designed to be used for the simulation of bimetallic hot rolling mill rolls vertical spincasting. Modeling the industrial process for these products imply certain specifications on the numerical methods used, mainly due to the size of the geometrical domain, low Rossby & Ekman numbers, and a high Reynolds number.

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