USING THE ADAPTIVE MESH FINITE VOLUME METHOD TO SOLVE THREE TEST PROBLEMS

2016 ◽  
Vol 95 (4) ◽  
pp. 283-310
Author(s):  
Lamien Kassiénou ◽  
Some Longin ◽  
Ouedraogo Mamadou
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Adaptive Mesh ◽  
Test Problems ◽  
Volume Method

scholarly journals A finite volume method for two-moment cosmic-ray hydrodynamics on a moving mesh

2021 ◽  
Author(s):  
T Thomas ◽  
C Pfrommer ◽  
R Pakmor
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Source Term ◽  
Cosmic Ray ◽  
Moving Mesh ◽  
Test Problems ◽  
Integration Step ◽  
Custom Made ◽  
Anisotropic Transport ◽  
Volume Method

Abstract We present a new numerical algorithm to solve the recently derived equations of two-moment cosmic ray hydrodynamics (CRHD). The algorithm is implemented as a module in the moving mesh Arepo code. Therein, the anisotropic transport of cosmic rays (CRs) along magnetic field lines is discretised using a path-conservative finite volume method on the unstructured time-dependent Voronoi mesh of Arepo. The interaction of CRs and gyroresonant Alfvén waves is described by short-timescale source terms in the CRHD equations. We employ a custom-made semi-implicit adaptive time stepping source term integrator to accurately integrate this interaction on the small light-crossing time of the anisotropic transport step. Both the transport and the source term integration step are separated from the evolution of the magneto-hydrodynamical equations using an operator split approach. The new algorithm is tested with a variety of test problems, including shock tubes, a perpendicular magnetised discontinuity, the hydrodynamic response to a CR overpressure, CR acceleration of a warm cloud, and a CR blast wave, which demonstrate that the coupling between CR and magneto-hydrodynamics is robust and accurate. We demonstrate the numerical convergence of the presented scheme using new linear and non-linear analytic solutions.

scholarly journals Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Sudi Mungkasi
Keyword(s):  
Shallow Water ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Shallow Water Equations ◽  
Adaptive Mesh Refinement ◽  
Adaptive Mesh ◽  
Error Indicator ◽  
Triangular Grids ◽  
Volume Method ◽  
Numerical Entropy

This paper presents a numerical entropy production (NEP) scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

scholarly journals A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement

2015 ◽  
Vol 123 ◽  
pp. 202-217 ◽  
Author(s):  
Stephen M. Guzik ◽  
Xinfeng Gao ◽  
Landon D. Owen ◽  
Peter McCorquodale ◽  
Phillip Colella
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Fourth Order ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Volume Method
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