OpenACC directive-based GPU acceleration of an implicit reconstructed discontinuous Galerkin method for compressible flows on 3D unstructured grids

Despite of the increasing popularity of Open ACC directive-based acceleration for com- putational Fluid dynamics (CFD) codes using the general-purpose graphics processing units (GPGPUs), an efficient implicit algorithm for high-order method on unstructured grids is still a relatively unexplored area. This is mainly due to the fact that, the capacity of local cache memory of a top-notch GPGPU is still far behind a common CPU. Thus many state-of-the-art preconditioning algorithms (e.g. the Symmetric Gauss-Seidel (SGS) and Lower Upper-Symmetric Gauss-Seidel (LU-SGS)), in which the matrix and strongly inherent data dependent operations are heavily involved, become extremely inefficient because of the local cache memory bound, when simply ported onto GPGPUs. In the present study, an efficient implicit algorithm for a GPGPU accelerated reconstructed discontinuous Galerkin (DG) CFD code is introduced and assessed for the solution of the Euler equations on unstructured grids. The block matrix operations are refined to element level. A Gauss-Jordan elimination based matrix inversion algorithm is adopted to optimize the performance on GPU platform. For SGS-type linear solver/preconditioner, a straight forward element reordering algorithm is employed to eliminate data dependency. As a result, the developed algorithm is implemented on GPGPU to accelerate a high-order implicit reconstructed discontinuous Galerkin (rDG) method as a compressible ow solver on 3D unstructured grids. Several numerical tests are carried out to obtain the speed up factor as well as the parallel efficiency, which indicates that the presented algorithm is able to offer low-overhead concurrent CFD simulation on unstructured grids on NVIDIA GPGPUs.