A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
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DOI：
10.1016/j.jcp.2018.08.025
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发表时间：
2017-11
期刊：
影响因子：
--
通讯作者：
K. Felker;J. Stone
中科院分区：
文献类型：
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作者：
K. Felker;J. Stone
我们提出了一种用于求解理想磁流体动力学（MHD）的四阶精确有限体积方法。该数值方法将双曲守恒定律半离散公式求解中的高阶求积规则与逆风约束输运（UCT）框架相结合，以确保满足磁场的无发散约束。介绍了一种新颖的 UCT 实现，它使用分段抛物线法 (PPM) 来重建二维单元角处的磁场。由此产生的方案可以表示为当前在雅典娜天体物理代码中使用的二阶精确约束输运（CT）戈杜诺夫型方案的扩展。在对一系列流体动力学测试问题验证基本算法后，我们提出了多维 MHD 测试问题的结果，该结果证明了平滑问题的形式四阶收敛性、不连续问题的鲁棒性以及相对于二阶方案的改进精度。
We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation laws with the upwind constrained transport (UCT) framework to ensure that the divergence-free constraint of the magnetic field is satisfied. A novel implementation of UCT that uses the piecewise parabolic method (PPM) for the reconstruction of magnetic fields at cell corners in 2D is introduced. The resulting scheme can be expressed as the extension of the second-order accurate constrained transport (CT) Godunov-type scheme that is currently used in the Athena astrophysics code. After validating the base algorithm on a series of hydrodynamics test problems, we present the results of multidimensional MHD test problems which demonstrate formal fourth-order convergence for smooth problems, robustness for discontinuous problems, and improved accuracy relative to the second-order scheme.