Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems
Abstract
For a wide class of polynomially nonlinear systems of partial differential equations we suggest an algorithmic approach to the s(trong)-consistency analysis of their finite difference approximations on Cartesian grids. First we apply the differential Thomas decomposition to the input system, resulting in a partition of the solution set. We consider the output simple subsystem that contains a solution of interest. Then, for this subsystem, we suggest an algorithm for verification of s-consistency for its finite difference approximation. For this purpose we develop a difference analogue of the differential Thomas decomposition, both of which jointly allow to verify the s-consistency of the approximation. As an application of our approach, we show how to produce s-consistent difference approximations to the incompressible Navier-Stokes equations including the pressure Poisson equation.
Keywords
Cite
@article{arxiv.1904.12912,
title = {Algorithmic approach to strong consistency analysis of finite difference approximations to PDE systems},
author = {Vladimir P. Gerdt and Daniel Robertz},
journal= {arXiv preprint arXiv:1904.12912},
year = {2019}
}