论文标题
结构保存传输稳定的兼容兼容有限元方法用于磁性水力学
Structure preserving transport stabilized compatible finite element methods for magnetohydrodynamics
论文作者
论文摘要
我们为理想的可压缩磁性流体动力方程式提供了兼容的有限元空间离散。磁场在div和弯曲的空间中均被考虑，分别导致强烈或弱保存的零差异条件。这些方程在空间中被离散化，因此动力学，内部和磁能之间的转移是一致的，从而导致总能量。我们还讨论了对实现磁性螺旋性保存所需的离散化的进一步调整。最后，我们描述了磁场方程的新运输稳定方法，该方法维持零差异和能量保护特性，包括一种还保留磁性螺旋性的方法。使用稳态和磁力测试案例，通过数值确认了方法的保存和改善的稳定性。
We present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved zero-divergence condition, respectively. The equations are discretized in space such that transfers between the kinetic, internal, and magnetic energies are consistent, leading to a preserved total energy. We also discuss further adjustments to the discretization required to additionally achieve magnetic helicity preservation. Finally, we describe new transport stabilization methods for the magnetic field equation which maintain the zero-divergence and energy conservation properties, including one method which also preserves magnetic helicity. The methods' preservation and improved stability properties are confirmed numerically using a steady state and a magnetic dynamo test case.
