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首页> 外文期刊>Journal of Computational Physics >Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD
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Increasing the accuracy in locally divergence-preserving finite volume schemes for MHD

机译：提高用于MHD的局部保留有限体积方案的准确性

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摘要

It is of utmost interest to control the divergence of the magnetic flux in simulations of the ideal magnetohydrodynamic equations since, in general, divergence errors tend to accumulate and render the schemes unstable. This paper presents a higher-order extension of the locally divergence-preserving procedure developed in Torrilhon [M. Torrilhon, Locally divergence-preserving upwind finite volume schemes for magnetohydrodynamic equations, SIAM J. Sci. Comput. 26 (2005) 1166-1191]; a fourth-order accurate local redistribution of the numerical magnetic field fluxes of a finite volume base scheme is introduced. The redistribution ensures that a fourth-order accurate discrete divergence operator is preserved to round off errors when applied to the cell averages of the magnetic flux density. The developed procedure is applicable to generic semi-discrete finite volume schemes and its purpose is to stabilize the schemes using a local procedure that respects the accuracy of the base scheme to a greater extent than the previous second-order achievements. Numerical experiments that demonstrate the properties of the new procedure are also presented. (C) 2007 Elsevier Inc. All rights reserved.
机译：在理想的磁流体动力学方程式的仿真中，控制磁通量的发散是最重要的，因为通常，发散误差往往会累积并使方案不稳定。本文提出了在Torrilhon [M。 Torrilhon，磁流体动力学方程的局部保持发散的迎风有限体积方案，SIAM J. Sci。计算26（2005）1166-1191];引入了有限体积基方案的数字磁场通量的四阶精确局部重新分布。重新分配可确保保留四阶精确离散散度算子，以将其应用于磁通量密度的单元平均值时，可以消除误差。所开发的过程适用于一般的半离散有限体积方案，其目的是使用局部过程来稳定方案，该过程比以前的二阶成就更大程度地尊重了基础方案的准确性。数值实验也证明了新程序的性质。 （C）2007 Elsevier Inc.保留所有权利。

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