LAUSR

Summary We develop a method to seamlessly simulate flows over a wide range of Knudsen numbers past arbitrarily shaped immersed boundaries. In order to achieve seamless computation, i.e. not use any zone division to distinguish between continuum and non-continuum regions, we employ the Unified Gas Kinetic Scheme (UGKS), which is based on the 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 Cartesian Grid Method we use here satisfies boundary conditions at the wall by using a constrained least square interpolation procedure. However, it differs from the usual, continuum Cartesian Grid Methods in two ways. Firstly, in order 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 which 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. This article is protected by copyright. All rights reserved.