High order wellbalanced finite volume methods for multidimensional systems of hyperbolic balance laws
Abstract
We introduce a general framework for the construction of wellbalanced finite volume methods for hyperbolic balance laws. The phrase wellbalancing is used in a wider sense, since the method can be applied to exactly follow any solution of any system of hyperbolic balance laws in multiple spatial dimensions. The solution has to be known a priori, either as an analytical expression or as discrete data. The proposed framework modifies the standard finite volume approach such that the wellbalancing property is obtained. The potentially high order of accuracy of the method is maintained under the modification. We show numerical tests for the compressible Euler equations with and without gravity source term and with different equations of state, and for the equations of compressible ideal magnetohydrodynamics. Different grid geometries and reconstruction methods are used. We demonstrate high order convergence numerically.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.05154
 Bibcode:
 2019arXiv190305154B
 Keywords:

 Mathematics  Numerical Analysis;
 Physics  Computational Physics;
 41A05;
 41A10;
 65D05;
 65D17