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An efficient iterative penalization method using recycled Krylov subspaces and its application to impulsively started flows

机译:利用回收的Krylov子空间的高效迭代惩罚方法及其应用冲动开始流动

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摘要

We formulate the penalization problem inside a vortex particle-mesh method as a linear system. This system has to be solved at every wall boundary condition enforcement within a time step. Furthermore, because the underlying problem is a Poisson problem, the solution of this linear system is computationally expensive. For its solution, we here use a recycling iterative solver, rBiCGStab, in order to reduce the number of iterations and therefore decrease the computational cost of the penalization step. For the recycled subspace, we use the orthonormalized previous solutions as only the right hand side changes from the solution at one time to the next. This method is validated against benchmark results: the impulsively started cylinder, with validation at low Reynolds number (Re = 550) and computational savings assessments at moderate Reynolds number (Re = 9500); then on a flat plate benchmark (Re = 1000). By improving the convergence behavior, the approach greatly reduces the computational cost of iterative penalization, at a moderate cost in memory overhead. (C) 2017 Elsevier Inc. All rights reserved.
机译:我们在涡流粒子网格中制定惩罚问题作为线性系统。该系统必须在一步步骤中在每个墙边界条件执行中得到解决。此外,因为潜在的问题是泊松问题,所以该线性系统的解决方案是计算昂贵的。对于其解决方案,我们在这里使用回收迭代求解器RBICGSTAB,以减少迭代的数量,因此降低惩罚步骤的计算成本。对于回收的子空间,我们使用正常化的先前解决方案,只有右手侧一次从解决方案发生变化到下一个。该方法针对基准结果验证:冲动启动圆柱,在低雷诺数(RE = 550)时验证,以及适度雷诺数(RE = 9500)的计算储蓄评估;然后在平板基准(RE = 1000)上。通过提高收敛行为,该方法在记忆开销中的中等成本下大大降低了迭代惩罚的计算成本。 (c)2017年Elsevier Inc.保留所有权利。

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