An Explicit High-Order Single-Stage Single-Step Positivity-Preserving Finite Difference WENO Method for the Compressible Euler Equations
Document Type
Article
Publication Date
7-2016
Department
Department of Mathematical Sciences
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 method. Time is discretized through a Lax–Wendroff procedure that is constructed from the Picard integral formulation 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.
Publication Title
Journal of Scientific Computing
Recommended Citation
Seal, D.,
Tang, Q.,
Xu, Z.,
&
Christlieb, A.
(2016).
An Explicit High-Order Single-Stage Single-Step Positivity-Preserving Finite Difference WENO Method for the Compressible Euler Equations.
Journal of Scientific Computing,
68(1), 171-190.
http://doi.org/10.1007/s10915-015-0134-0
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/4950
