期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 456, 期 -, 页码 -出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2022.111070
关键词
High-order; Flux Reconstruction; Convergence acceleration; Multigrid; Non-modal analysis; Stability
资金
- European Union [813605]
- Marie Curie Actions (MSCA) [813605] Funding Source: Marie Curie Actions (MSCA)
We present a numerical analysis of linear multigrid operators for the high-order Flux Reconstruction method. The non-modal analysis is used to assess the short-term numerical dissipation in the context of 1D and 2D linear convection-diffusion. The effect of several parameters, including the number of coarse-level iterations, the polynomial order, and the combination of h- and p-multigrid, is explored to find the most efficient configurations. V-cycle p-multigrid is shown to be more efficient at higher polynomial orders, and the use of W-cycles and/or hp-multigrid appears to offer additional advantages. Additionally, the influence of high Peclet numbers and high aspect-ratio cells on error dissipation is investigated in the 2D case. Finally, the non-modal dissipation is related to the convergence rate of the multigrid through a series of manufactured solutions.
We present a numerical analysis of linear multigrid operators for the high-order Flux Reconstruction method. The non-modal analysis is used to assess the short-term numerical dissipation in the context of 1D and 2D linear convection-diffusion. The effect of several parameters, namely the number of coarse-level iterations, the polynomial order and the combination of h- and p-multigrid is explored in an effort to identify the most efficient configurations. V-cycle p-multigrid is shown to have increased efficiency at higher polynomial orders, and the use of W-cycles and/or hp-multigrid appear to offer additional advantages. The effect of high Peclet numbers and high aspect-ratio cells is also explored in 2D, and both factors are shown to decrease the error dissipation. Finally, we relate the non-modal dissipation to the convergence rate of the multigrid in a series of manufactured solutions. (c) 2022 The Authors. Published by Elsevier Inc.
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