“…A third direction of improvement which needs to be pursued is the integration of multigrid solution strategies with procedures for automatic grid refinement. Results which have already been obtained in two dimensional calculations clearly show the potential advantages of such an approach, which could be the key to better resolution of both shock waves and boundary layers [49,50].…”
“…A third direction of improvement which needs to be pursued is the integration of multigrid solution strategies with procedures for automatic grid refinement. Results which have already been obtained in two dimensional calculations clearly show the potential advantages of such an approach, which could be the key to better resolution of both shock waves and boundary layers [49,50].…”
“…The first step of the multiple grid procedure is to transport the fine grid residuals to the coarse grid. The first-order change at the center of a cell A is [10,27] 1 The contributions to the change at node 1 from the cells with centers at B,C,...,H are computed in a similar way. After the changes are computed, boundarj'^ conditions in the near field are applied.…”
“…(1)- (3), (9), and (10) are solved using a Lax-Wendroff control-volume, time-marching scheme as developed by Ni 17 , Dannenhoffer 18 , and Davis 19,20 . Numerical solution of unsteady flows is performed with a dual time-step procedure 21 , allowing for use of multiple-grid and local time-stepping convergence acceleration.…”
This paper describes the GPU accelerated MBFLO2 multi-block turbulent flow solver completely in double precision using CUDA and the latest generation of GPU processors. On a cluster of 8 Tesla C2050 "Fermi" GPUs and Intel Xeon X5550 "Nehalem" quad-core CPUs, we achieve 9x speedup over the parallel CPU solver or 70x speedup over the serial solver. High performance is obtained by optimizing the data layout on the GPU, optimizing data transfers and using asynchronous memory copies to overlap GPU execution with communications. We test the solver on a turbulent flat plate and an unsteady turbulent cylinder with 3.2 million grid points. We confirm the GPU results are in agreement with turbulent flow theory. We discuss the GPU optimization techniques used to reach this level of performance. Nomenclature E = total energy g = acceleration due to gravity H = total enthalpy h = static enthalpy I = rothalpy k = turbulent kinetic energy p = pressure Pr = Prandtl number Pr t = turbulent Prandtl number R = radius from specified axis of rotation S ij = mean strain-rate tensor u = axial velocity component û = internal energy v = tangential velocity component V = velocity magnitude z = elevation = coefficient of viscosity = turbulent coefficient of viscosity = turbulent dissipation rate divided by turbulent kinetic energy = rotational velocity about specified axis of rotation (rads/s) ij = shear stress tensor = density
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