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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2020

01-04-2020

On Two-Level Oseen Penalty Iteration Methods for the 2D/3D Stationary Incompressible Magnetohydronamics

Authors: Haiyan Su, Xinlong Feng, Jianping Zhao

Published in: Journal of Scientific Computing | Issue 1/2020

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Abstract

This paper studies several decoupled penalty methods to overcome the saddle point system of the steady state 2D/3D incompressible magnetohydronamics (MHD). These approaches combine the Oseen iteration and two-level technique with strong uniqueness condition \(0<\frac{\sqrt{2}C_{0}^{2}\max \{1,\sqrt{2}S_{c}\}\Vert {\mathbf{F }}\Vert _{-1}}{(\min \{R_{e}^{-1},S_{c}C_{1}R_{m}^{-1}\})^2}\le 1-\left( \frac{\Vert \mathbf{F }\Vert |_{-1}}{\Vert |\mathbf{F }\Vert _{0}}\right) ^{\frac{1}{2}}<1\) satisfied. For the convenience of implementation, we employ two different simple Lagrange finite element pairs \(P_{1}b-P_{1}-P_{1}b\) and \(P_{1}-P_{0}-P_{1}\) for velocity field, pressure and magnetic field, respectively. Rigorous analysis of the optimal error estimate and stability are provided. We present comprehensive numerical experiments, which indicate the effectiveness of the proposed methods for both two dimensional and three-dimensional problems.
previous article A Preconditioning Technique for All-at-Once System from the Nonlinear Tempered Fractional Diffusion Equation
next article Computation of Design Sensitivities in Steady-State Incompressible Laminar Flows Based on New Semi-Analytical Method

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Metadata
Title
On Two-Level Oseen Penalty Iteration Methods for the 2D/3D Stationary Incompressible Magnetohydronamics
Authors
Haiyan Su
Xinlong Feng
Jianping Zhao
Publication date
01-04-2020
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2020
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-020-01186-0

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