数值模拟中点值-精确divB =0向量场的无发散插值
Divergence-free Interpolation of Vector Fields From Point Values - Exact divB=0 in Numerical Simulations
摘要：
在天体物理磁流体动力学（MHD）和电动力学模拟中，数值上对磁场施加divB=0的约束一直是困难的。我们观察到，对于基于点的离散化，如在有限差分类型和伪谱方法中所使用的，divB=0的约束可以通过选择用于定义B的导数的插值来完全满足。作为一个例子，我们证明了一类新的有限差分型微分算子的规则网格具有divB=0的性质。这个原则澄清了divB的性质！= 0个错误。本文所展示的原理和技术对磁场特别有用，但也可应用于任何矢量场。本文作为一个简要介绍的方法，并演示了一个实现显示收敛。
英文摘要：
In astrophysical magnetohydrodynamics (MHD) and electrodynamics simulations, numerically enforcing the divB=0 constraint on the magnetic field has been difficult. We observe that for point-based discretization, as used in finite-difference type and pseudo-spectral methods, the divB=0 constraint can be satisfied entirely by a choice of interpolation used to define the derivatives of B. As an example we demonstrate a new class of finite-difference type derivative operators on a regular grid which has the divB=0 property. This principle clarifies the nature of divB != 0 errors. The principles and techniques demonstrated in this paper are particularly useful for the magnetic field, but can be applied to any vector field. This paper serves as a brief introduction to the method and demonstrates an implementation showing convergence.
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