Houba Tomas, Dasgupta Arnob, Gopalakrishnan Shivasubramanian, Gosse Ryan, Roy Subrata
SurfPlasma Inc, Gainesville, FL, 32601, USA.
Applied Physics Research Group, Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32601, USA.
Sci Rep. 2019 Oct 8;9(1):14442. doi: 10.1038/s41598-019-50546-w.
The scalability and efficiency of numerical methods on parallel computer architectures is of prime importance as we march towards exascale computing. Classical methods like finite difference schemes and finite volume methods have inherent roadblocks in their mathematical construction to achieve good scalability. These methods are popularly used to solve the Navier-Stokes equations for fluid flow simulations. The discontinuous Galerkin family of methods for solving continuum partial differential equations has shown promise in realizing parallel efficiency and scalability when approaching petascale computations. In this paper an explicit modal discontinuous Galerkin (DG) method utilizing Implicit Large Eddy Simulation (ILES) is proposed for unsteady turbulent flow simulations involving the three-dimensional Navier-Stokes equations. A study of the method was performed for the Taylor-Green vortex case at a Reynolds number ranging from 100 to 1600. The polynomial order P = 2 (third order accurate) was found to closely match the Direct Navier-Stokes (DNS) results for all Reynolds numbers tested outside of Re = 1600, which had a normalized RMS error of 3.43 × 10 in the dissipation rate for a 60 element mesh. The scalability and performance study of the method was then conducted for a Reynolds number of 1600 for polynomials orders from P = 2 to P = 6. The highest order polynomial that was tested (P = 6) was found to have the most efficient scalability using both the MPI and OpenMP implementations.
随着我们迈向百亿亿次计算，数值方法在并行计算机架构上的可扩展性和效率至关重要。像有限差分格式和有限体积法这样的经典方法在其数学构造上存在固有的障碍，难以实现良好的可扩展性。这些方法广泛用于求解流体流动模拟中的纳维 - 斯托克斯方程。求解连续偏微分方程的间断伽辽金方法家族在接近千万亿次计算时，已显示出实现并行效率和可扩展性的潜力。本文提出了一种利用隐式大涡模拟（ILES）的显式模态间断伽辽金（DG）方法，用于涉及三维纳维 - 斯托克斯方程的非定常湍流模拟。针对泰勒 - 格林涡案例，在雷诺数范围为100至1600的情况下对该方法进行了研究。发现多项式阶数P = 2（三阶精度）在所有测试的雷诺数（除Re = 1600外）下都与直接纳维 - 斯托克斯（DNS）结果紧密匹配，对于一个60单元网格，在耗散率方面的归一化均方根误差为3.43×10。然后针对雷诺数为1600，对多项式阶数从P = 2到P = 6的情况进行了该方法的可扩展性和性能研究。发现测试的最高阶多项式（P = 6）在使用MPI和OpenMP实现时具有最有效的可扩展性。
