Convergent finite differences for 1D viscous isentropic flow in Eulerian coordinates
Numerical Analysis
2013-03-13 v1 Analysis of PDEs
Abstract
We construct a new finite difference method for the flow of ideal viscous isentropic gas in one spatial dimension. For the continuity equation, the method is a standard upwind discretization. For the momentum equation, the method is an uncommon upwind discretization, where the moment and the velocity are solved on dual grids. Our main result is convergence of the method as discretization parameters go to zero. Convergence is proved by adapting the mathematical existence theory of Lions and Feireisl to the numerical setting.
Cite
@article{arxiv.1303.2902,
title = {Convergent finite differences for 1D viscous isentropic flow in Eulerian coordinates},
author = {Trygve K. Karper},
journal= {arXiv preprint arXiv:1303.2902},
year = {2013}
}
Comments
34 pages