Unified gas kinetic scheme combined with Cartesian grid method for intermediate Mach numbers

Abstract

Summary We develop a method to seamlessly simulate flows over a wide range of Knudsen numbers past arbitrarily shaped immersed boundaries. To achieve seamless computation, ie, not use any zone division to distinguish between continuum and non‐continuum regions, we use the unified gas kinetic scheme (UGKS), which is based on the Bhatnagar‐Groos‐Krook (BGK) approximation of the Boltzmann equation. We combine UGKS with an appropriately designed Cartesian grid method (CGM) to allow us to compute flows past arbitrary boundaries. The CGM we use here satisfies boundary conditions at the wall by using a constrained least square interpolation procedure. However, it differs from the usual, continuum CGMs in 2 ways. Firstly, to allow us capture non‐continuum effects at the boundaries, the CGM used herein interpolates the microscopic velocity distribution function in addition to the macroscopic variables. Secondly, even for the macroscopic variables, we use a gas kinetic method–based density interpolation procedure at the boundaries that allows the CGM to interface well with the UGKS method. We demonstrate the robustness and efficacy of the method by testing it on stationary immersed boundaries at various Knudsen numbers ranging from continuum to transition regimes.

Evaluation of Cubic-Spline Based Gas Kinetic Method for Simulating Compressible Turbulence

“…The gas-kinetic BGK method (GKM) has various advantages over the conventional Navier-Stokes (NS) based solvers due to its robustness over a wide range of turbulent Mach number and its ability to accurately capture flow physics. Furthermore, the GKM scheme is also capable of capturing deviations from equilibrium and effect of extremely rarefied flow physics (Ragta et al (2017b), Ragta et al (2017a)).…”

Arbitrary Lagrangian-Eulerian-type discrete unified gas kinetic scheme for low-speed continuum and rarefied flow simulations with moving boundaries

“…In this method, the uniform Cartesian grids are used near the region of wall at present stage, the moving boundary will be regarded as a set of Lagrangian nodes, and the influence of wall (no-slipping condition) to the nearby nodes of the Cartesian grid is considered with some interpolation methods. Besides the applications in the continuum flow regime, the IBM coupled the UGKS now can also deal with the rarefied flow moving boundary problems [18]. The primary disadvantage of IBM is in some applications, such as high Reynolds number flows, the amount of mesh is intolerable.…”