Cartesian Grid Method for Gas Kinetic Scheme

TL;DR

This paper introduces a Cartesian grid method combined with a simplified gas kinetic scheme for efficient simulation of subsonic and supersonic viscous flows around complex geometries, ensuring accurate boundary treatment and flow solutions.

Contribution

It presents a novel Cartesian grid approach with a simplified kinetic flux function and boundary treatment strategies for complex flow simulations.

Findings

Validated with numerical examples showing accuracy

Effective boundary condition reconstruction for viscous flows

Applicable to both subsonic and supersonic regimes

Abstract

A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four different categories, the fluid point, the solid point, the drop point, and the interpolation point. The boundaries are represented by a set of direction-oriented boundary points. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points. Different boundary conditions, including isothermal boundary, adiabatic boundary, and Euler slip boundary, are presented by different interpolation strategies. We also propose a simplified gas kinetic scheme as the flux solver for both subsonic and supersonic flow computations. The methodology of constructing a simplified kinetic flux function can be extended to other flow systems. A few numerical examples are used to validate the Cartesian grid method and the simplified flux function. The reconstruction scheme for recovering the boundary conditions of compressible viscous and heat conducting flow with a Cartesian mesh can provide a smooth distribution of physical quantities at solid boundary, and present an accurate solution for the flow study with complex geometry.