The Efficient Implementation of Correction Procedure via Reconstruction with GPU Computing

Abstract

<p>Computational fluid dynamics (CFD) has long been a useful tool to model fluid flow problems across many engineering disciplines, and while problem size, complexity, and difficulty continue to expand, the demands for robustness and accuracy grow. Furthermore, generating high-order accurate solutions has escalated the required computational resources, and as problems continue to increase in complexity, so will computational needs such as memory requirements and calculation time for accurate flow field prediction. To improve upon computational time, vast amounts of computational power and resources are employed, but even over dozens to hundreds of central processing units (CPUs), the required computational time to formulate solutions can be weeks, months, or longer, which is particularly true when generating high-order accurate solutions over large computational domains. One response to lower the computational time for CFD problems is to implement graphical processing units (GPUs) with current CFD solvers. GPUs have illustrated the ability to solve problems orders of magnitude faster than their CPU counterparts with identical accuracy. The goal of the presented work is to combine a CFD solver and GPU computing with the intent to solve complex problems at a high-order of accuracy while lowering the computational time required to generate the solution. The CFD solver should have high-order spacial capabilities to evaluate small fluctuations and fluid structures not generally captured by lower-order methods and be efficient for the GPU architecture. This research combines the high-order Correction Procedure via Reconstruction (CPR) method with compute unified device architecture (CUDA) from NVIDIA to reach these goals. In addition, the study demonstrates accuracy of the developed solver by comparing results with other solvers and exact solutions. Solving CFD problems accurately and quickly are two factors to consider for the next generation of solvers. GPU computing is a step forward for the CFD community in solving both current and up-coming problems fast and with high accuracy.</p>