An immersed-boundary method for compressible viscous flow and its application in gas-kinetic BGK scheme

TL;DR

This paper introduces an immersed-boundary method integrated with the gas-kinetic BGK scheme, enabling accurate simulation of both incompressible and compressible viscous flows with stationary or moving boundaries, addressing key challenges like ghost-cell singularity and the fresh-cell problem.

Contribution

The paper presents a novel IB method with local boundary determination and simple extrapolation for moving boundaries, enhancing simulation accuracy and robustness in gas-kinetic schemes.

Findings

Validated second-order spatial accuracy with Taylor-Couette flow

Observed super-convergence of the BGK scheme

Successfully simulated flows around stationary and moving boundaries

Abstract

An immersed-boundary (IB) method is proposed and applied in the gas-kinetic BGK scheme to simulate incompressible/compressible viscous flow with stationary/moving boundary. In present method the ghost-cell technique is adopted to fulfill the boundary condition on the immersed boundary. A novel idea "local boundary determination" is put forward to identify the ghost cells, each of which may have several different ghost-cell constructions corresponding to different boundary segments, thus eliminating the singularity of the ghost cell. Furthermore, the so-called "fresh-cell" problem when implementing the IB method in moving-boundary simulation is resolved by a simple extrapolation in time. The method is firstly applied in the gas-kinetic BGK scheme to simulate the Taylor-Couette flow, where the second-order spatial accuracy of the method is validated and the "super-convergence" of the BGK scheme is observed. Then the test cases of supersonic flow around a stationary cylinder, incompressible flow around an oscillating cylinder and compressible flow around a moving airfoil are conducted to verify the capability of the present method in simulating compressible flows and handling the moving boundary.