A numerical method for multiphysics simulations based on hierarchical Cartesian grids

Abstract

We present a numerical method based on hierarchical Cartesian grids for the simulation of multiphysics problems, here in particular for the conjugate heat transfer between a fluid and a solid. The data structures developed for this simulation method allow to account for moving objects and are especially well suited for massive parallelization. The major problem of a suitable domain decomposition for a coupled fluid and heat conducting domain is solved by discretizing both domains on a joint hierarchical Cartesian mesh, where the individual cells can be marked according to the underlying physics, i.e. to be a fluid cell, a heat conducting cell or both. Individual solvers for the Navier-Stokes equations and the heat conduction equation are implemented which only operate on the Cartesian cells belonging to the fluid or solid subset of the joint hierarchical mesh. The solution strategy is validated against the analytical solution of the convective heat transfer between a heat-conducting solid flat plate and a laminar incompressible boundary layer. The applicability of the method for moving objects is then demonstrated by solving a conjugate heat transfer problem for a heated and moving cylinder in a laminar flow.

Keywords

• resolved particle simulation
• multi-physics problems
• conjugate heat transfer
• hierarchical cartesian grids
• moving boundaries
• immersed boundary method