An Implicit Gas-Kinetic Scheme for Turbulent Flow on Unstructured Hybrid Mesh

TL;DR

This paper introduces an implicit gas-kinetic scheme on unstructured hybrid meshes, incorporating turbulence modeling to improve computational efficiency and accuracy in simulating laminar and turbulent flows.

Contribution

It develops an implicit gas-kinetic scheme with hybrid mesh support and turbulence modeling, enhancing efficiency over explicit schemes for flow simulations.

Findings

Improved convergence and efficiency compared to explicit schemes.

Good agreement with experimental and other numerical data.

Effective for both laminar and turbulent flow simulations.

Abstract

In this study, an implicit scheme for the gas-kinetic scheme (GKS) on the unstructured hybrid mesh is proposed. The Spalart-Allmaras (SA) one equation turbulence model is incorporated into the implicit gas-kinetic scheme (IGKS) to predict the effects of turbulence. The implicit macroscopic governing equations are constructed and solved by the matrix-free lower-upper symmetric-Gauss-Seidel (LU-SGS) method. To reduce the number of cells and computational cost, the hybrid mesh is applied. A modified non-manifold hybrid mesh data(NHMD) is used for both unstructured hybrid mesh and uniform grid. Numerical investigations are performed on different 2D laminar and turbulent flows. The convergence property and the computational efficiency of the present IGKS method are investigated. Much better performance are obtained compared with the standard explicit gas-kinetic scheme. Also, our numerical results are found to be in good agreement with experiment data and other numerical solutions, demonstrating the good applicability and high efficiency of the present IGKS for the simulations of laminar and turbulent flows.