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首页> 外文期刊>Computer physics communications >A non-staggered, conservative, del center dot(B)over right arrow=0, finite-volume scheme for 3D implicit extended magnetohydrodynamics in curvilinear geometries
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A non-staggered, conservative, del center dot(B)over right arrow=0, finite-volume scheme for 3D implicit extended magnetohydrodynamics in curvilinear geometries

机译：曲线几何中3D隐式扩展磁流体动力学的右箭头= 0上的非交错，保守的del中心点（B）

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摘要

In the development of spatial difference schemes for magnetohydrodynamics (MHD), the preservation of continuum proper ties such as conservation of mass, momentum, and energy, as well as required electromagnetic constraints (del (.) b = del (.) j = 0, where j = del x B is the electrical current), is desirable to preserve numerical accuracy. Moreover, simplicity of the scheme is also a desirable feature, particularly when an implicit implementation is considered (the focus of this paper). We propose here a finite-volume, cell-centered (non-staggered) scheme for the extended MHD formulation that: (1) is suitable for implicit implementations in arbitrary curvilinear geometries, (2) is conservative, (3) preserves both the magnetic field and the electrical current solenoidal to machine precision, and (4) is linearly and nonlinearly stable in the absence of numerical and physical dissipation. Crucial to the viability of the scheme is the use of a clever interpolation scheme (ZIP [Hirt, J. Comput. Phys. 2 (1968) 339-355]), the proper treatment of boundary conditions in curvilinear geometry, and a novel treatment of geometric source terms in the momentum equation that ensures their exact cancellation in the absence of pressure forces. (C) 2004, Elsevier B.V. All rights reserved.
机译：在开发磁流体动力学（MHD）的空间差异方案时，要保持连续性，例如质量，动量和能量的守恒，以及所需的电磁约束（del（。）b = del（。）j = 0 ，其中j = del x B是电流）是保持数值精度所希望的。而且，该方案的简单性也是一个理想的功能，特别是在考虑隐式实现时（本文重点）。我们在这里为扩展的MHD公式提出一个有限体积，以单元为中心的方案（非交错）：（1）适用于任意曲线几何中的隐式实现，（2）是保守的，（3）保留了磁性（4）在没有数值和物理耗散的情况下线性和非线性稳定。对于该方案的可行性至关重要的是使用聪明的插值方案（ZIP [Hirt，J. Comput。Phys。2（1968）339-355]），对曲线几何中的边界条件进行适当的处​​理以及一种新颖的处理方法。动量方程中的几何源项的集合可确保在没有压力的情况下将其精确抵消。 （C）2004，Elsevier B.V.保留所有权利。

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