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Mathematics > Numerical Analysis

arXiv:2204.01237 (math)
[Submitted on 4 Apr 2022]

Title:A Vanka-based parameter-robust multigrid relaxation for the Stokes-Darcy Brinkman problems

Authors:Yunhui He
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Abstract:We propose a block-structured multigrid relaxation scheme for solving the Stokes-Darcy Brinkman equations discretized by the marker and cell scheme. An element-based additive Vanka smoother is used to solve the corresponding shifted Laplacian operator. Using local Fourier analysis, we present the stencil for the additive Vanka smoother and derive an optimal smoothing factor for Vanka-based Braess-Sarazin relaxation for the Stokes-Darcy Brinkman equations. Although the optimal damping parameter is dependent on meshsize and physical parameter, it is very close to one. Numerical results of two-grid and V(1,1)-cycle are presented, which show high efficiency of the proposed relaxation scheme and its robustness to physical parameters and the meshsize. Using a damping parameter equal to one gives almost the same results as these for the optimal damping parameter at a lower computational overhead.
Comments: 24 pages, 12 figures, 4 tables
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2204.01237 [math.NA]
  (or arXiv:2204.01237v1 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2204.01237

Submission history

From: Yunhui He [view email]
[v1] Mon, 4 Apr 2022 04:53:48 UTC (702 KB)
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