An immersed boundary method for the fluid--structure--thermal interaction in rarefied gas flow

Abstract

An immersed boundary method for the fluid--structure--thermal interaction in rarefied gas flow is presented. In this method, the slip model is incorporated with the penalty immersed boundary method to address the velocity and temperature jump conditions at the fluid--structure interface in rarefied gas flow within slip regime. In this method, the compressible flow governed by Navier-Stokes equations are solved by using high-order finite difference method; the elastic solid is solved by using finite element method; the fluid and solid are solved independently and the fluid--structure--thermal interaction are achieved by using a penalty method in a partitioned way. Several validations are conducted including Poiseuille flow in a 2D pipe, flow around a 2D NACA airfoil, moving square cylinder in a 2D pipe, flow around a sphere and moving sphere in quiescent flow. The numerical results from present method show good agreement with the previous published data obtained by other methods, and it confirms the the good ability of the proposed method in handling fluid--structure--thermal interaction for both weakly compressible and highly compressible rarefied gas flow. To overcome the incapability of Navier-Stokes equations at high local Knudsen numbers in supersonic flow, an artificial viscosity is introduced to ease the sharp transition at the shock wave front. Inspired by Martian exploration, the application of proposed method to study the aerodynamics of flapping wing in rarefied gas flow is conducted in both 2D and 3D domains, to obtain some insights for the flapping-wing aerial vehicles operating in Martian environment