An effective implementation of high-order compact gas-kinetic scheme on structured meshes for compressible flows

TL;DR

This paper introduces a high-order compact gas-kinetic scheme for simulating compressible flows on structured meshes, emphasizing accuracy, efficiency, and robustness through innovative reconstruction and parallelization techniques.

Contribution

It presents a novel fifth-order compact reconstruction method and a unified approach for non-orthogonal meshes, reducing computational cost and enhancing robustness in compressible flow simulations.

Findings

Achieves high accuracy and resolution in compressible flow simulations.

Demonstrates robustness across subsonic to supersonic turbulence.

Efficiently implemented with multi-GPU parallelization.

Abstract

A novel fifth-order compact gas-kinetic scheme is developed for high-resolution simulation of compressible flows on structured meshes. Its accuracy relies on a new multidimensional fifth-order compact reconstruction that uses line-averaged derivatives to introduce additional degrees of freedom, enabling a compact stencil with superior resolution. For non-orthogonal meshes, reconstruction is performed on a standard reference cell in a transformed computational space. This approach provides a unified polynomial form, significantly reducing memory usage and computational cost while simplifying implementation compared to direct multi-dimensional or dimension-by-dimension methods. A nonlinear adaptive method ensures high accuracy and robustness by smoothly transitioning from the high-order linear scheme in smooth regions to a second-order scheme at discontinuities. The method is implemented with multi-GPU parallelization using CUDA and MPI for large-scale applications. Comprehensive numerical tests, from subsonic to supersonic turbulence, validate the scheme's high accuracy, resolution and excellent robustness.