scholarly journals On the Full Space-Time Discretization of the Generalized Stokes Equations: The Dirichlet Case

2018 ◽  
Vol 56 (4) ◽  
pp. 2234-2261 ◽  
Author(s):  
Sarah Eckstein ◽  
Michael Růžička
Keyword(s):  
Stokes Equations ◽  
Time Discretization ◽  
Space Time ◽  
Generalized Stokes Equations

scholarly journals A Multi-GPU Parallel Algorithm in Hypersonic Flow Computations

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Jianqi Lai ◽  
Hua Li ◽  
Zhengyu Tian ◽  
Ye Zhang
Keyword(s):  
Parallel Algorithm ◽  
Hypersonic Flow ◽  
Stokes Equations ◽  
Programming Model ◽  
Graphics Processing Unit ◽  
Three Dimensional ◽  
Flow Characteristics ◽  
Time Discretization ◽  
Processing Unit ◽  
Complex Flow

Computational fluid dynamics (CFD) plays an important role in the optimal design of aircraft and the analysis of complex flow mechanisms in the aerospace domain. The graphics processing unit (GPU) has a strong floating-point operation capability and a high memory bandwidth in data parallelism, which brings great opportunities for CFD. A cell-centred finite volume method is applied to solve three-dimensional compressible Navier–Stokes equations on structured meshes with an upwind AUSM+UP numerical scheme for space discretization, and four-stage Runge–Kutta method is used for time discretization. Compute unified device architecture (CUDA) is used as a parallel computing platform and programming model for GPUs, which reduces the complexity of programming. The main purpose of this paper is to design an extremely efficient multi-GPU parallel algorithm based on MPI+CUDA to study the hypersonic flow characteristics. Solutions of hypersonic flow over an aerospace plane model are provided at different Mach numbers. The agreement between numerical computations and experimental measurements is favourable. Acceleration performance of the parallel platform is studied with single GPU, two GPUs, and four GPUs. For single GPU implementation, the speedup reaches 63 for the coarser mesh and 78 for the finest mesh. GPUs are better suited for compute-intensive tasks than traditional CPUs. For multi-GPU parallelization, the speedup of four GPUs reaches 77 for the coarser mesh and 147 for the finest mesh; this is far greater than the acceleration achieved by single GPU and two GPUs. It is prospective to apply the multi-GPU parallel algorithm to hypersonic flow computations.

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