A Compression-Directional Entropic Stress Method for Shock-Regularized Compressible Flow

TL;DR

The paper introduces CoDeS, a novel regularization method for shock-dominated compressible flows that selectively applies stress in compressive regions, improving shock resolution while preserving smooth flow features.

Contribution

CoDeS is a new finite-volume regularization technique inspired by information geometry, using a tensor stress aligned with compression directions to improve shock modeling.

Findings

CoDeS remains inactive in expansion and contact regions.

It supplies localized stress at shocks and concentrates regularization along compressive structures.

Results on various problems show CoDeS performs comparably or better than high-order methods.

Abstract

We introduce the Compression-Directional Entropic Stress method (CoDeS), a finite-volume regularization for shock-dominated compressible flows. Inspired by information geometric regularization, CoDeS replaces scalar multidimensional entropic pressure with a tensor stress aligned with the principal directions of compression. The stress has the form $\boldsymbol{\Pi}_{\Sigma}=\sigma\boldsymbol{M}$, where $\sigma$ is obtained from a modified-Helmholtz equation and $\boldsymbol{M}$ is constructed from the compressive eigenspace of the symmetric velocity-gradient tensor. The source is gated by volumetric and principal-strain compression, so the regularization vanishes in smooth expansion, rigid-body rotation, and ideal contacts, while recovering the compressive one-dimensional IGR mechanism at planar shocks. The same tensor stress is used in the conservative momentum flux and the stress-work energy flux. CoDeS is tested on one-, two-, and three-dimensional problems including smooth expansion, double rarefaction, the Sod shock tube, multidimensional Riemann flow, a viscous shock tube, a two-fluid triple point, a Mach-3 slot jet, and a supersonic Taylor--Green vortex. The results show that CoDeS remains inactive in expansive and contact regions, supplies localized stress at shocks, and concentrates regularization along compressive wave structures while remaining weak in shear- and vorticity-dominated regions. At matched resolutions, the three-dimensional Taylor--Green results are comparable to or more energetic than seventh-order WENO/TENO references. These results indicate that CoDeS provides a compression-selective shock regularization compatible with high-order finite-volume resolution of contacts, interfaces, shear layers, and vortical structures.