A Sweeping Positivity-Preserving High Order Finite Difference WENO Scheme for Euler Equations
Schematic of WENO stencil structure for positivity-preserving corrections.Abstract
We present a sweeping positivity-preserving high order finite difference WENO scheme for the Euler equations with a general nonlinear pressure function. The method employs a simple and robust post-processing strategy that ensures non-negativity of density and pressure without destroying high-order accuracy. The sweeping procedure applies a compact, directional correction to maintain physical admissibility while avoiding excessive numerical dissipation. Numerical experiments demonstrate the scheme’s accuracy, robustness, and efficiency across a wide range of compressible flow problems.
Type
Publication
arXiv preprint arXiv:2510.27025
This preprint introduces a new sweeping positivity-preserving finite difference WENO method for the Euler equations. The method employs a simple correction strategy to maintain non-negativity of density and pressure while retaining high-order accuracy.
The work builds on numerical techniques for shock-capturing and high-order finite difference approximations, extending existing positivity-preserving frameworks through a directional sweeping correction. Numerical tests in 1D and 2D validate robustness across challenging compressible flow regimes.
