Parallel Implementation of the Immersed Boundary Conditions Method for Three Dimensional Heat Conduction in a Medium with Moving Boundaries

摘要

This paper describes a grid-less fully implicit spectral method for solving both stationary and moving boundary problems. The algorithm is based on the concept of immersed boundary conditions (IBC), where the physical domain is immersed within the computational domain; in other words, the boundary conditions become internal constraints. The algorithm is applied to the diffusion problem in a three dimensional domain bounded by moving rough surfaces. This method is advantageous as it does not require adaptive grid generation, and hence less computational effort is needed, while sharp resolution of the location of the boundary is maintained. The algorithm is spectrally accurate in space while first and second order accurate in time. Given the immense size of the resultant system of discretized algebraic equations, various methods for reducing the computational costs are explored, including parallelization of the solution process.