Simplification of the Flux Function for a Higher-order Gas-kinetic Evolution Model

TL;DR

This paper simplifies the flux function in a higher-order gas-kinetic scheme to improve computational efficiency while maintaining accuracy, by redefining coefficients and removing non-essential terms based on physical analysis.

Contribution

The paper introduces a simplified higher-order gas-kinetic scheme that reduces computational cost without sacrificing accuracy through coefficient redefinition and term removal.

Findings

Significant increase in computational efficiency.

Maintains accuracy and robustness in numerical tests.

Effective reduction of complexity in the flux function.

Abstract

The higher-order gas-kinetic scheme for solving the Navier-Stokes equations has been studied in recent years. In addition to the use of higher-order reconstruction techniques, many terms are used in the Taylor expansion of the gas distribution functions. Therefore, a large number of coefficients need to be determined in the calculation of the time evolution of the gas distribution function at cell interfaces. As a consequence, the higher-order flux function takes much more computational time than that of a second-order gas-kinetic scheme. This paper aims to simplify the evolution model by two steps. Firstly, the coefficients related to the higher-order spatial and temporal derivatives of a distribution function are redefined to reduce the computational cost. Secondly, based on the physical analysis, some terms can be removed without loss of accuracy. Through the simplifications, the computational efficiency of the higher-order scheme is increased significantly. In addition, a self-adaptive numerical viscosity is designed to minimize the necessary numerical dissipation. Several numerical examples are tested to demonstrate the accuracy and robustness of the current scheme.