A gradient-compression-based compact high-order gas-kinetic scheme on three-dimensional hybrid unstructured mesh

TL;DR

This paper introduces a high-order, compact gas-kinetic scheme for 3D hybrid unstructured meshes that improves robustness and accuracy in simulating compressible flows, including hypersonic regimes, by using gradient compression techniques.

Contribution

It extends the gas-kinetic scheme to hybrid unstructured meshes with a novel gradient compression method, enhancing robustness and accuracy for high-speed flow simulations.

Findings

Effective in simulating flows from incompressible to hypersonic speeds.

Improves robustness of high-order schemes on irregular meshes.

Maintains high accuracy with gradient compression in discontinuous flows.

Abstract

In this paper, the compact gas-kinetic scheme for compressible flow is extended to hybrid unstructured mesh. Based on both cell-averaged flow variables and their gradients updated from time accurate gas evolution model at cell interfaces, a compact third-order least-square-constrained reconstruction can be obtained on unstructured mesh and a multi-resolution WENO reconstruction is adopted in case of discontinuous solutions. Moreover, a compression factor for the cell-averaged gradients is proposed to take into account the possible discontinuity in flow variables at cell interface, which significantly improves the robustness of the compact scheme for high-speed flow computation on irregular mesh and preserves the accuracy. Numerical tests from incompressible to hypersonic flow are presented to demonstrate the broad applicability of the gradient-compression-based high-order compact scheme.