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

Abstract

We introduce the Compression-Directional Entropic Stress (CoDeS) method 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. All the code, case settings, and code for plotting figures of this paper are available at https://github.com/xubonan/code\_for\_CoDeS.