Immersed Boundary Method for Boltzmann and Navier-Stokes Solvers with Adaptive Cartesian Mesh

Abstract

Adaptive Cartesian mesh methods have demonstrated unique abilities for automated mesh generation and dynamic mesh adaptation to flow solution and moving boundaries. However Navier‐Stokes (NS) solvers with Cartesian mesh often produce large fluctuations of surface quantities (pressure, skin friction, and heat flux) at solid boundaries. We show that the Immersed Boundary Method (IBM) with adaptive octree Cartesian mesh allows one to eliminate unphysical fluctuations of skin friction and heat flux at solid boundaries for viscous flow simulations. Implementation of IBM for deterministic Boltzmann solvers with adaptive Cartesian mesh is described.