Computationally efficient GPU based NS solver for two dimensional high-speed inviscid and viscous compressible flows

Abstract

In this study, we proposed a novel GPU-based solution for modelling two-dimensional inviscid and viscous compressible supersonic/hypersonic flows. Texture and surface pointers are used to access GPU memory locations. For effective and efficient use of surface pointers, we grouped multiple 2D arrays referenced and indexed by a single 3D surface pointer. To enable the proposed solver for double-precision calculations, two consecutive 32-bit memory locations were grouped to maintain the efficiency of surface pointers while taking advantage/accuracy of 64-bit calculations. Resolving data and computation dependencies for parallel applications is another complex task that is the focus of this study. Computation dependencies have been solved by using multiple mutually synchronized GPU kernels and executing them sequentially using the GPU default stream to ensure that all relevant data is available to the threads or computed before they actually use it. Consequently, there is no intra-core data dependency in our proposed approach, while inter-core data dependency is successfully solved by stringing multiple kernels together. Using NVIDIA GTX 660 GPUs, we achieved 20x speedup compared to traditional Core i5[Formula: see text] computers. This speedup is the result of the Surface Pointer's GPU capabilities for double precision computations. The simulation results are also consistent with the experimental and numerical results of this study.

Keywords

• Computational mathematics
• computational complexity
• Navier-Stokes equations
• graphic processing unit
• shock wave
• surface pointers