A fully decoupled linearized and second-order accurate numerical scheme for two-phase magnetohydrodynamic flows

IF 1.7 4区工程技术 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

International Journal for Numerical Methods in Fluids Pub Date : 2023-12-17 DOI:10.1002/fld.5253

Danxia Wang, Yuan Guo, Fang Liu, Hongen Jia, Chenhui Zhang

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Abstract

In this paper, we analyze the numerical approximation of two-phase magnetohydrodynamic flows. Firstly, an equivalent new system is designed by introducing two scalar auxiliary variables. One of variables is used to linearize the phase field function and the other is used to deal with the highly coupled and nonlinear terms. Secondly, by combining with a novel decoupling technique based on the “zero-energy-contribution” feature and the pressure correction method, the linearized second order BDF numerical scheme, which has the advantage of fully decoupled structure, is constructed. Furthermore, we strictly prove the unconditional energy stability and error analysis of the scheme, and give a detailed implementation procedure that only requires to calculate several linear elliptic equations with constant coefficients. Finally, the results of numerical simulations are presented to validate the rates of convergence and energy stability.

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两相磁流体动力学流的完全解耦线性化二阶精确数值方案

本文分析了两相磁流体动力学流的数值近似。首先，通过引入两个标量辅助变量，设计了一个等效的新系统。其中一个变量用于使相场函数线性化，另一个变量用于处理高度耦合的非线性项。其次，结合基于 "零能量贡献 "特征的新型解耦技术和压力校正方法，构建了线性化二阶 BDF 数值方案，该方案具有完全解耦结构的优点。此外，我们严格证明了该方案的无条件能量稳定性和误差分析，并给出了详细的实现步骤，只需计算几个常数系数的线性椭圆方程即可。最后，我们给出了数值模拟结果，以验证收敛速度和能量稳定性。

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来源期刊

International Journal for Numerical Methods in Fluids 物理-计算机：跨学科应用

CiteScore

3.70

自引率

5.60%

发文量

111

审稿时长

8 months

期刊介绍： The International Journal for Numerical Methods in Fluids publishes refereed papers describing significant developments in computational methods that are applicable to scientific and engineering problems in fluid mechanics, fluid dynamics, micro and bio fluidics, and fluid-structure interaction. Numerical methods for solving ancillary equations, such as transport and advection and diffusion, are also relevant. The Editors encourage contributions in the areas of multi-physics, multi-disciplinary and multi-scale problems involving fluid subsystems, verification and validation, uncertainty quantification, and model reduction. Numerical examples that illustrate the described methods or their accuracy are in general expected. Discussions of papers already in print are also considered. However, papers dealing strictly with applications of existing methods or dealing with areas of research that are not deemed to be cutting edge by the Editors will not be considered for review. The journal publishes full-length papers, which should normally be less than 25 journal pages in length. Two-part papers are discouraged unless considered necessary by the Editors.