An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations
Abstract
In this work we construct a high-order, single-stage, single-step positivity-preserving method for the compressible Euler equations. Space is discretized with the finite difference weighted essentially non-oscillatory (WENO) method. Time is discretized through a Lax-Wendroff procedure that is constructed from the Picard integral formulation (PIF) of the partial differential equation. The method can be viewed as a modified flux approach, where a linear combination of a low- and high-order flux defines the numerical flux used for a single-step update. The coefficients of the linear combination are constructed by solving a simple optimization problem at each time step. The high-order flux itself is constructed through the use of Taylor series and the Cauchy-Kowalewski procedure that incorporates higher-order terms. Numerical results in one- and two-dimensions are presented.
Cite
@article{arxiv.1411.0328,
title = {An explicit high-order single-stage single-step positivity-preserving finite difference WENO method for the compressible Euler equations},
author = {David C. Seal and Qi Tang and Zhengfu Xu and Andrew J. Christlieb},
journal= {arXiv preprint arXiv:1411.0328},
year = {2015}
}