Abstract In the world of computational fluid dynamics (CFD), solving the governing equations of incompressible, turbulent, single-phase fluid flow still represents the basis of many industrial and academic applications. The implicitly coupled (monolithic) solution approach is still being developed and investigated for industrial-size applications. A parallel selection algebraic multigrid algorithm (AMG) based on the domain decomposition method is presented, applied for the solution of the linearised implicitly coupled pressure–velocity system discretised by the finite volume method, implemented in OpenFOAM. Since the setup phase of the selection AMG, i.e. sorting the equations into coarse and fine subsets is inherently sequential, it was decided to perform the setup phase locally on each processing unit. The prolongation matrix for transferring the correction from coarse to fine level and restriction matrix for transferring the residual from fine to coarse level are assembled locally as well. Parallel communication is necessary only for the calculation of the coarse level matrix, i.e. the matrix elements which describe the cross-coupling of equations located on different processing units. A localised version of the ILU factorisation based on Crout’s algorithm is used as a smoother in the multigrid cycle. A detailed analysis of the coarse level matrix complexity is conducted in the context of the finite volume method in domain decomposition mode. The performance and scaling of our parallel implementation is investigated for two test cases and the possible drawbacks of the method are given.

中文翻译：

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OpenFOAM中块-压力-速度系统的选择性代数多重网格的并行化

摘要 在计算流体动力学 (CFD) 领域，求解不可压缩、湍流、单相流体流动的控制方程仍然是许多工业和学术应用的基础。隐式耦合（单片）解决方案方法仍在为工业规模的应用开发和研究。提出了一种基于域分解方法的并行选择代数多重网格算法 (AMG)，用于求解有限体积法离散化的线性隐式耦合压力-速度系统，在 OpenFOAM 中实现。由于选择 AMG 的设置阶段，即将方程分类为粗细子集是固有顺序的，因此决定在每个处理单元上本地执行设置阶段。将校正从粗级转移到精细级的扩展矩阵和将残差从精细级转移到粗级的限制矩阵也在局部组装。并行通信仅对于粗略矩阵的计算是必要的，即描述位于不同处理单元上的方程的交叉耦合的矩阵元素。基于克劳特算法的 ILU 分解的局部版本用作多重网格循环中的平滑器。在域分解模式下的有限体积方法的上下文中，对粗级矩阵复杂度进行了详细分析。我们针对两个测试用例研究了我们并行实现的性能和扩展性，并给出了该方法的可能缺点。