Chapter 17 - CUDA Implementation of Vertex-Centered, Finite Volume CFD Methods on Unstructured Grids with Flow Control Applications

Abstract

This chapter presents the graphical processing unit (GPU) implementation of a Navier-Stokes equations solver for steady and unsteady flows that is used for the analysis and optimization of flow control problems based on active control mechanisms. An important issue that affects the GPU performance is related to the memory access. Structured grids are associated with organized memory accesses and, thus, high speed-ups. On the other hand, unstructured grid solvers running on GPUs achieve inevitably lower speed-ups depending, among others, on the discretization scheme used. In contrast, in vertex-centered finite volume (VCFV) schemes, the number of neighbors to each finite volume is variable and, therefore, the corresponding software requires delicate memory management owing to highly noncoalesced memory accesses. For the analysis of flow control problems, a steady Navier-Stokes equations solver for turbulent compressible flows, coupled with a turbulence model, is used. Steady-state solvers are concerned with the numerical modeling of flows with properties that do not change in time. The solver employs a VCFV technique with a second-order upwind scheme for the spatial discretization on unstructured grids. For the more accurate prediction of the viscous layers developed in the vicinity of solid walls, unstructured/hybrid grids with structured layers of quadrilaterals close to the wall and triangular elements elsewhere are generated and used. The solution is based on the time-marching method with dual-time stepping for time-accurate computations. A typical way of programming the iterative part of a Navier-Stokes solver for unstructured grids is by looping over grid edges, computing the associated fluxes and scattering-adding flux contributions to their two end nodes within the same loop.