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Relevant bibliographies by topics / Lax-Friedrichs method

Academic literature on the topic 'Lax-Friedrichs method'

Author: Grafiati

Published: 9 March 2023

Last updated: 10 March 2023

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Journal articles on the topic "Lax-Friedrichs method"

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Shampine, L. F. "Two-step Lax–Friedrichs method." Applied Mathematics Letters 18, no. 10 (October 2005): 1134–36. http://dx.doi.org/10.1016/j.aml.2004.11.007.

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Yu, Simin. "A survey of numerical schemes for transportation equation." E3S Web of Conferences 308 (2021): 01020. http://dx.doi.org/10.1051/e3sconf/202130801020.

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The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temperature in an incompressible flow. In this paper, we discuss the famous numerical scheme, Lax-Friedrichs method, for the linear transport equation. The important ingredient of the design of the Lax-Friedrichs Method, namely the choice of the numerical fluxes will be discussed in detail. We give a detailed proof of the L1 stability of the Lax-Friedrichs scheme for the linear transport equation. We also address issues related to the implementation of this numerical scheme.

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Breuß, Michael. "The correct use of the Lax–Friedrichs method." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (May 2004): 519–40. http://dx.doi.org/10.1051/m2an:2004027.

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Sharma, Deepika, and Kavita Goyal. "Wavelet optimized upwind conservative method for traffic flow problems." International Journal of Modern Physics C 31, no. 06 (June 2020): 2050086. http://dx.doi.org/10.1142/s0129183120500862.

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Numerical schemes, namely, upwind nonconservative, upwind conservative, Lax–Friedrichs, Lax–Wendroff, MacCormack and Godunov are applied and compared on traffic flow problems. The best scheme, namely, upwind conservative is used for wavelet-optimized method using Daubechies wavelet for numerically solving the same traffic flow problems. Numerical results corresponding to the traffic flow problem with the help of wavelet-optimized, adaptive grid, upwind conservative method have been given. Moreover, the run time carried out by the developed technique have been compared to that of run time carried out by finite difference technique. It is observed that, in terms of run time, the proposed method performs better.

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Chatterjee, N., and U. S. Fjordholm. "A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws." IMA Journal of Numerical Analysis 40, no. 1 (November 9, 2018): 405–21. http://dx.doi.org/10.1093/imanum/dry074.

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Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

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Araujo, Isamara L. N., Panters Rodríguez-Bermúdez, and Yoisell Rodríguez-Núñez. "Numerical Study for Two-Phase Flow with Gravity in Homogeneous and Piecewise-Homogeneous Porous Media." TEMA (São Carlos) 21, no. 1 (March 27, 2020): 21. http://dx.doi.org/10.5540/tema.2020.021.01.21.

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In this work we study two-phase flow with gravity either in 1-rock homogeneous media or 2-rocks composed media, this phenomenon can be modeled by a non-linear scalar conservation law with continuous flux function or discontinuous flux function, respectively. Our study is essentially from a numerical point of view, we apply the new Lagrangian-Eulerian finite difference method developed by Abreu and Pérez and the Lax-Friedrichs classic method to obtain numerical entropic solutions. Comparisons between numerical and analytical solutions show the efficiency of the methods even for discontinuous flux function.

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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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Ali, Ali Hasan, Ahmed Shawki Jaber, Mustafa T. Yaseen, Mohammed Rasheed, Omer Bazighifan, and Taher A. Nofal. "A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model." Complexity 2022 (June 27, 2022): 1–9. http://dx.doi.org/10.1155/2022/9367638.

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In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a variational formulation of the problem, the finite element technique provides piecewise formulations of functions defined by a collection of grid data points, while the finite difference technique begins with a differential formulation of the problem and continues to discretize the derivatives. Finally, some graphical and numerical comparisons are provided to illustrate and corroborate the differences between these two main methods.

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Setiyowati, R., and Sumardi. "A Simulation of Shallow Water Wave Equation Using Finite Volume Method: Lax-Friedrichs Scheme." Journal of Physics: Conference Series 1306 (August 2019): 012022. http://dx.doi.org/10.1088/1742-6596/1306/1/012022.

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Kao, Chiu Yen, Carmeliza Navasca, and Stanley Osher. "The Lax–Friedrichs sweeping method for optimal control problems in continuous and hybrid dynamics." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (November 2005): e1561-e1572. http://dx.doi.org/10.1016/j.na.2005.01.061.

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Dissertations / Theses on the topic "Lax-Friedrichs method"

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Chen, Weitao. "Fast Sweeping Methods for Steady State Hyperbolic Conservation Problems and Numerical Applications for Shape Optimization and Computational Cell Biology." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366279632.

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ROSSI, ELENA. "Balance Laws: Non Local Mixed Systems and IBVPs." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/103090.

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Scalar hyperbolic balance laws in several space dimensions play a central role in this thesis. First, we deal with a new class of mixed parabolic-hyperbolic systems on all R^n: we obtain the basic well-posedness theorems, devise an ad hoc numerical algorithm, prove its convergence and investigate the qualitative properties of the solutions. The extension of these results to bounded domains requires a deep understanding of the initial boundary value problem (IBVP) for hyperbolic balance laws. The last part of the thesis provides rigorous estimates on the solution to this IBVP, under precise regularity assumptions. In Chapter 1 we introduce a predator-prey model. A non local and non linear balance law is coupled with a parabolic equation: the former describes the evolution of the predator density, the latter that of prey. The two equations are coupled both through the convective part of the balance law and the source terms. The drift term is a non local function of the prey density. This allows the movement of predators to be directed towards the regions where the concentration of prey is higher. We prove the well-posedness of the system, hence the existence and uniqueness of solution, the continuous dependence from the initial data and various stability estimates. In Chapter 2 we devise an algorithm to compute approximate solutions to the mixed system introduced above. The balance law is solved numerically by a Lax-Friedrichs type method via dimensional splitting, while the parabolic equation is approximated through explicit finite-differences. Both source terms are integrated by means of a second order Runge-Kutta scheme. The key result in Chapter 2 is the convergence of this algorithm. The proof relies on a careful tuning between the parabolic and the hyperbolic methods and exploits the non local nature of the convective part in the balance law. This algorithm has been implemented in a series of Python scripts. Using them, we obtain information about the possible order of convergence and we investigate the qualitative properties of the solutions. Moreover, we observe the formation of a striking pattern: while prey diffuse, predators accumulate on the vertices of a regular lattice. The analytic study of the system above is on all R^n. However, both possible biological applications and numerical integrations suggest that the boundary plays a relevant role. With the aim of studying the mixed hyperbolic-parabolic system in a bounded domain, we noticed that for balance laws known results lack some of the estimates necessary to deal with the coupling. In Chapter 3 we then focus on the IBVP for a general balance law in a bounded domain. We prove the well-posedness of this problem, first with homogeneous boundary condition, exploiting the vanishing viscosity technique and the doubling of variables method, then for the non homogeneous case, mainly thanks to elliptic techniques. We pay particular attention to the regularity assumptions and provide rigorous estimates on the solution.

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Book chapters on the topic "Lax-Friedrichs method"

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Arminjon, P., A. St-Cyr, and A. Madrane. "Non-oscillatory Lax-Friedrichs Type Central Finite Volume Methods for 3-D Flows on Unstructured Tetrahedral Grids." In Hyperbolic Problems: Theory, Numerics, Applications, 59–68. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8370-2_7.

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"5. Convergence of Lax–Friedrichs Scheme, Godunov Scheme and Glimm Scheme." In Vanishing Viscosity Method, 485–530. De Gruyter, 2016. http://dx.doi.org/10.1515/9783110494273-005.

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Song, Lunji. "A Fully Discrete SIPG Method for Solving Two Classes of Vortex Dominated Flows." In Vortex Dynamics Theories and Applications. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.94316.

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To simulate incompressible Navier–Stokes equation, a temporal splitting scheme in time and high-order symmetric interior penalty Galerkin (SIPG) method in space discretization are employed, while the local Lax-Friedrichs flux is applied in the discretization of the nonlinear term. Under a constraint of the Courant–Friedrichs–Lewy (CFL) condition, two benchmark problems in 2D are simulated by the fully discrete SIPG method. One is a lid-driven cavity flow and the other is a circular cylinder flow. For the former, we compute velocity field, pressure contour and vorticity contour. In the latter, while the von Kármán vortex street appears with Reynolds number 50≤Re≤400, we simulate different dynamical behavior of circular cylinder flows, and numerically estimate the Strouhal numbers comparable to the existing experimental results. The calculations on vortex dominated flows are carried out to investigate the potential application of the SIPG method.

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Conference papers on the topic "Lax-Friedrichs method"

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Yulianti, Kartika, Rini Marwati, and Suci Permatahati. "A Modified Lax-Friedrichs Method for the Shallow Water Equations." In Proceedings of the 7th Mathematics, Science, and Computer Science Education International Seminar, MSCEIS 2019, 12 October 2019, Bandung, West Java, Indonesia. EAI, 2020. http://dx.doi.org/10.4108/eai.12-10-2019.2296327.

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Ye, Shijie, Yanping Guo, Jianliang Li, and Ming Lu. "Simulation Analysis for Peak Pressure of Shock Wave Based on Lax-Friedrichs Method." In 2012 Fifth International Conference on Information and Computing Science (ICIC). IEEE, 2012. http://dx.doi.org/10.1109/icic.2012.48.

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Feng, Fan, Chunwei Gu, and Xuesong Li. "Discontinuous Galerkin Solution of Three-Dimensional Reynolds-Averaged Navier-Stokes Equations With S-A Turbulence Model." In ASME Turbo Expo 2010: Power for Land, Sea, and Air. ASMEDC, 2010. http://dx.doi.org/10.1115/gt2010-23133.

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In this paper Discontinuous Galerkin Method (DGM) is applied to solve the Reynolds-averaged Navier-Stokes equations and S-A turbulence model equation in curvilinear coordinate system. Different schemes, including Lax-Friedrichs (LF) flux, Harten, Lax and van Leer (HLL) flux and Roe flux are adopted as numerical flux of inviscid terms at the element interface. The gradients of conservative variables in viscous terms are constructed by mixed formulation, which solves the gradients as auxiliary unknowns to the same order of accuracy as conservative variables. The methodology is validated by simulations of double Mach reflection problem and three-dimensional turbulent flowfield within compressor cascade NACA64. The numerical results agree well with the experimental data.

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Riestiana, V. A., R. Setiyowati, and V. Y. Kurniawan. "Numerical solution of the one dimentional shallow water wave equations using finite difference method : Lax-Friedrichs scheme." In THE THIRD INTERNATIONAL CONFERENCE ON MATHEMATICS: Education, Theory and Application. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0039545.

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