三维理想MHD约束迁移的不分裂Goddom方法
An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
摘要：
我们提出了一个单步的，二阶精度的理想MHD的Goddom格式，这是一个扩展的方法由Gardiner和Stone（2005年）描述的三维。该算法结合了Colella的用于多维积分的角点传输迎风（CTU）方法和用于保持磁场上的无发散约束的约束传输（CT）算法。我们描述了三维理想MHD的PPM界面态的计算，它必须包括多维的“MHD源项”，并自然地尊重隐含在这些项中的平衡的${\bf\nabla\cdot B}=0$条件。我们比较了两种不同形式的CTU集成算法，需要6-或12-解决方案的黎曼问题，每细胞每时间步，并提出了详细的描述6-解决算法。最后，我们提出了解决方案的测试问题，以证明该算法的准确性和鲁棒性。
英文摘要：
We present a single step, second-order accurate Godunov scheme for ideal MHD which is an extension of the method described by Gardiner & Stone (2005) to three dimensions. This algorithm combines the corner transport upwind (CTU) method of Colella for multidimensional integration, and the constrained transport (CT) algorithm for preserving the divergence-free constraint on the magnetic field. We describe the calculation of the PPM interface states for 3D ideal MHD which must include multidimensional ``MHD source terms'' and naturally respect the balance implicit in these terms by the ${\bf\nabla\cdot B}=0$ condition. We compare two different forms for the CTU integration algorithm which require either 6- or 12-solutions of the Riemann problem per cell per time-step, and present a detailed description of the 6-solve algorithm. Finally, we present solutions for test problems to demonstrate the accuracy and robustness of the algorithm.
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