CFD-based analysis and two-level aerodynamic optimization on graphics processing units

This paper presents the porting of 2D and 3D Navier–Stokes equations solvers for unstructured grids, from the CPU to the graphics processing unit (GPU; NVIDIA’s Ge-Force GTX 280 and 285), using the CUDA language. The performance of the GPU implementations, with single, double or mixed precision arithmetic operations, is compared to that of the CPU code. regarding the optimal handling of the unstructured grid topology on the GPU, particularly for vertex-centered CFD algorithms, are discussed. Restructuring the existing codes was necessary in order to maximize the parallel efficiency of the GPU implementations. The mixed precision implementation, in which the left-hand-side operators are computed with single precision, was shown to bridge the gap between the single and double precision speed-ups. Based on the different speed-ups and prediction accuracy of the aforementioned GPU implementations of the Navier–Stokes equations solver, a hierarchical optimization method which is suitable for GPUs is proposed and demonstrated in inviscid and turbulent 2D flow problems. The search for the optimal solution(s) splits into two levels, both relying upon evolutionary algorithms (EAs) though with different evaluation tools each. The low level EA uses the very fast single precision GPU implementation with relaxed convergence criteria for the inexpensive evaluation of candidate solutions. Promising solutions are regularly broadcast to the high level EA which uses the mixed precision GPU implementation of the same flow solver. Single- and two-objective aerodynamic shape optimization problems are solved using the developed software.