Abstract
A GPU-accelerated ADI method for solutions of compressible Navier-Stokes equations is developed to reduce the computational cost of simulating turbomachinery flow. Despite the advantages of implicit time advancement in stability and convergence speed, implicit schemes tend to rely on linear systems of equations which benefit less from parallel computing than explicit schemes. In particular, the Alternating Direction Implicit (ADI) method applied to compressible Navier-Stokes equations on a multi-block grid requires the solution of block-tridiagonal systems, which are challenging to accelerate on GPUs. The present study suggests an algorithm for GPU-acceleration of the ADI method in the context of compressible flows. A divide-and-conquer-type algorithm is recursively applied to block-tridiagonal matrices to reduce it into a number of smaller sub-matrices well suited for GPU acceleration. Using a single NVIDIA Titan V GPU, a speedup of 26 ⨯ compared to a single-core Intel i7-9800X CPU is achieved on 4.6 million grid points.
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