# Performance evaluation of high-order compact and second-order gas-kinetic schemes in compressible flow simulations

## TL;DR

This study compares high-order compact and second-order gas-kinetic schemes in compressible flow simulations, demonstrating that high-order schemes offer superior accuracy and efficiency, especially in turbulent flows with shocks and vortices.

## Contribution

It provides the first verification of high-order compact gas-kinetic schemes' advantages in viscous flow simulations with discontinuities.

## Key findings

- CGKS-5th achieves similar resolution to GKS-2nd at lower computational cost
- CGKS-5th delivers higher accuracy in turbulent flows with shocks
- Multi-GPU parallelization enables large-scale applications

## Abstract

The trade-off among accuracy, robustness, and computational cost remains a key challenge in simulating complex flows. Second-order schemes are computationally efficient but lack the accuracy required for resolving intricate flow structures, particularly in turbulence. High-order schemes, especially compact high-order schemes, offer superior accuracy and resolution at a relatively modest computational cost. To clarify the practical performance of high-order schemes in scale-resolving simulations, this study evaluates two representative gas-kinetic schemes: the newly developed fifth-order compact gas-kinetic scheme (CGKS-5th) and the conventional second-order gas-kinetic scheme (GKS-2nd). Test cases ranging from subsonic to supersonic flows are used to quantitatively assess their accuracy and efficiency. The results demonstrate that CGKS-5th achieves comparable resolution to GKS-2nd at roughly an order of magnitude lower computational cost. Under equivalent computational resources, CGKS-5th delivers significantly higher accuracy and resolution, particularly in turbulent flows involving shocks and small-scale vortices. This study provides the first clear verification of the advantages of high-order compact gas-kinetic schemes in simulating viscous flows with discontinuities. Additionally, multi-GPU parallelization using CUDA and MPI is implemented to enable large-scale applications.