Strategies for parallel and numerical scalability of CFD codes

Abstract

In this article we discuss a strategy for speeding up the solution of the Navier—Stokes equations on highly complex solution domains such as complete aircraft, spacecraft, or turbomachinery equipment. We have used a finite-volume code for the (non-turbulent) Navier—Stokes equations as a testbed for implementation of linked numerical and parallel processing techniques. Speedup is achieved by the Tangled Web of advanced grid topology generation, adaptive coupling, and sophisticated parallel computing techniques. An optimized grid topology is used to generate an optimized grid: on the block level such a grid is unstructured whereas within a block a structured mesh is constructed, thus retaining the geometrical flexibility of the finite element method while maintaining the numerical efficiency of the finite difference technique. To achieve a steady state solution, we use grid-sequencing: proceeding from coarse to finer grids, where the scheme is explicit in time. Adaptive coupling is derived from the observation that numerical schemes have differing efficiency during the solution process. Coupling strength between grid points is increased by using an implicit scheme at the sub-block level, then at the block level, ultimately fully implicit across the whole computational domain. Other techniques include switching numerical schemes and the physics model during the solution, and dynamic deactivation of blocks. Because the computational work per block is very variable with adaptive coupling, especially for very complex flows, we have implemented parallel dynamic load-balancing to dynamically transfer blocks between processors. Several 2D and 3D examples illustrate the functioning of the Tangled Web approach on different parallel architectures.