A Positivity-preserving High Order Finite Volume Compact-WENO Scheme for Compressible Euler Equations
Abstract
In this paper, a positivity-preserving fifth-order finite volume compact-WENO scheme is proposed for solving compressible Euler equations. As we know conservative compact finite volume schemes have high resolution properties while WENO (Weighted Essentially Non-Oscillatory) schemes are essentially non-oscillatory near flow discontinuities. We extend the main idea of WENO schemes to some classical compact finite volume schemes [32], where lower order compact stencils are combined with WENO nonlinear weights to get a higher order finite volume compact-WENO scheme. The newly developed positivity-preserving limiter [46,44] is used to preserve positive density and internal energy for compressible Euler equations of fluid dynamics. The HLLC (Harten, Lax, and van Leer with Contact) approximate Riemann solver [39,2] is used to get the numerical flux at the cell interfaces. Numerical tests are presented to demonstrate the high-order accuracy, positivity-preserving, high-resolution and robustness of the proposed scheme.
Keywords
Cite
@article{arxiv.1402.5618,
title = {A Positivity-preserving High Order Finite Volume Compact-WENO Scheme for Compressible Euler Equations},
author = {Yan Guo and Tao Xiong and Yufeng Shi},
journal= {arXiv preprint arXiv:1402.5618},
year = {2015}
}