Discontinuous Galerkin Two-Grid Method for the Transient Navier–Stokes Equations

IF 1 4区数学 Q3 MATHEMATICS, APPLIED

Computational Methods in Applied Mathematics Pub Date : 2023-11-24 DOI:10.1515/cmam-2023-0035

Kallol Ray, Deepjyoti Goswami, Saumya Bajpai

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引用次数: 0

Abstract

In this paper, we apply a two-grid scheme to the DG formulation of the 2D transient Navier–Stokes model. The two-grid algorithm consists of the following steps: Step 1 involves solving the nonlinear system on a coarse mesh with mesh size 𝐻, and Step 2 involves linearizing the nonlinear system by using the coarse grid solution on a fine mesh of mesh size ℎ and solving the resulting system to produce an approximate solution with desired accuracy. We establish optimal error estimates of the two-grid DG approximations for the velocity and pressure in energy and L 2

L^{2}

-norms, respectively, for an appropriate choice of coarse and fine mesh parameters. We further discretize the two-grid DG model in time, using the backward Euler method, and derive the fully discrete error estimates. Finally, numerical results are presented to confirm the efficiency of the proposed scheme.

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瞬态Navier-Stokes方程的不连续Galerkin双网格法

本文将两网格格式应用于二维瞬态Navier-Stokes模型的DG表达式。两网格算法包括以下步骤:步骤1涉及在网格尺寸为𝐻的粗网格上求解非线性系统，步骤2涉及通过在网格尺寸为的细网格上使用粗网格解对非线性系统进行线性化，并求解结果系统以产生所需精度的近似解。我们分别在能量范数和l2 L^{2}范数中建立了速度和压力的两网格DG近似的最佳误差估计，以适当选择粗网格和细网格参数。利用后向欧拉方法对两网格DG模型进行离散化，得到了完全离散的误差估计。最后给出了数值结果，验证了所提方案的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computational Methods in Applied Mathematics MATHEMATICS, APPLIED-

CiteScore

2.40

自引率

7.70%

发文量

期刊介绍： The highly selective international mathematical journal Computational Methods in Applied Mathematics　(CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.