Compressible density-based solvers are widely used in OpenFOAM, and the parallel scalability of these solvers is crucial for large-scale simulations. In this paper, we report our experiences with the scalability of OpenFOAM’s native rhoCentralFoam solver, and by making a small number of modifications to it, we show the degree to which the scalability of the solver can be improved. The main modification made is to replace the first-order accurate Euler scheme in rhoCentralFoam with a third-order accurate, four-stage Runge-Kutta or RK4 scheme for the time integration. The scaling test we used is the transonic flow over the ONERA M6 wing. This is a common validation test for compressible flows solvers in aerospace and other engineering applications. Numerical experiments show that our modified solver, referred to as rhoCentralRK4Foam, for the same spatial discretization, achieves as much as a 123.2% improvement in scalability over the rhoCentralFoam solver. As expected, the better time resolution of the Runge–Kutta scheme makes it more suitable for unsteady problems such as the Taylor–Green vortex decay where the new solver showed a 50% decrease in the overall time-to-solution compared to rhoCentralFoam to get to the final solution with the same numerical accuracy. Finally, the improved scalability can be traced to the improvement of the computation to communication ratio obtained by substituting the RK4 scheme in place of the Euler scheme. All numerical tests were conducted on a Cray XC40 parallel system, Theta, at Argonne National Laboratory.

中文翻译：

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具有 Runge-Kutta 时间离散化方案的基于 OpenFOAM 密度的求解器的可扩展性

OpenFOAM 中广泛使用了基于可压缩密度的求解器，这些求解器的并行可扩展性对于大规模模拟至关重要。在本文中，我们报告了我们在 OpenFOAM 的原生 rhoCentralFoam 求解器可扩展性方面的经验，并通过对其进行少量修改，展示了求解器可扩展性的改进程度。所做的主要修改是将 rhoCentralFoam 中的一阶精确 Euler 格式替换为用于时间积分的三阶精确、四阶段 Runge-Kutta 或 RK4 格式。我们使用的缩放测试是在 ONERA M6 机翼上的跨音速流。这是航空航天和其他工程应用中可压缩流动求解器的常见验证测试。数值实验表明，我们改进的求解器，称为 rhoCentralRK4Foam，对于相同的空间离散化，与 rhoCentralFoam 求解器相比，可扩展性提高了 123.2%。正如预期的那样，Runge-Kutta 方案更好的时间分辨率使其更适合非定常问题，例如 Taylor-Green 涡流衰减，其中与 rhoCentralFoam 相比，新求解器的整体求解时间减少了 50%，以获得到具有相同数值精度的最终解。最后，改进的可扩展性可以追溯到通过用 RK4 方案代替欧拉方案获得的计算与通信比的改进。所有数值测试均在阿贡国家实验室的 Cray XC40 并行系统 Theta 上进行。Runge-Kutta 方案更好的时间分辨率使其更适合非定常问题，例如 Taylor-Green 涡流衰减，其中与 rhoCentralFoam 相比，新求解器的整体求解时间减少了 50%具有相同数值精度的解。最后，改进的可扩展性可以追溯到通过用 RK4 方案代替欧拉方案获得的计算通信比的改进。所有数值测试均在阿贡国家实验室的 Cray XC40 并行系统 Theta 上进行。Runge-Kutta 方案更好的时间分辨率使其更适合非定常问题，例如 Taylor-Green 涡流衰减，其中与 rhoCentralFoam 相比，新求解器的整体求解时间减少了 50%具有相同数值精度的解。最后，改进的可扩展性可以追溯到通过用 RK4 方案代替欧拉方案获得的计算通信比的改进。所有数值测试均在阿贡国家实验室的 Cray XC40 并行系统 Theta 上进行。