论文标题
不可压缩的磁性流体动力学方程式的差异融合杂交杂交方法
A Divergence-Conforming Hybridized Discontinuous Galerkin Method for the Incompressible Magnetohydrodynamics Equations
论文作者
论文摘要
我们介绍了一种新的杂交不连续的盖尔金方法，用于不可压缩的磁性水力动力学方程。如果用于元素和痕量溶液场都采用了特定的速度，压力，磁场和磁压空间，我们得出了一种能量稳定的方法，该方法可以返回无差异的速度场和磁场，并适当平衡线性动量。我们使用二阶通用 - $α$方法随时间离散，并提出了一个块迭代方法，用于在每个时间步骤求解所得的非线性方程系统。我们使用制造溶液来数值检查我们方法的有效性，并观察我们的方法在速度场，压力场，磁场和磁性压力场的$ L_2 $ NORM中产生最佳收敛速率。我们进一步发现我们的方法是强大的。然后，我们将方法应用于选择基准问题，并在数值上确认我们的方法是能量稳定的。
We introduce a new hybridized discontinuous Galerkin method for the incompressible magnetohydrodynamics equations. If particular velocity, pressure, magnetic field, and magnetic pressure spaces are employed for both element and trace solution fields, we arrive at an energy stable method which returns pointwise divergence-free velocity fields and magnetic fields and properly balances linear momentum. We discretize in time using a second-order-in-time generalized-$α$ method, and we present a block iterative method for solving the resulting nonlinear system of equations at each time step. We numerically examine the effectiveness of our method using a manufactured solution and observe our method yields optimal convergence rates in the $L_2$ norm for the velocity field, pressure field, magnetic field, and magnetic pressure field. We further find our method is pressure robust. We then apply our method to a selection of benchmark problems and numerically confirm our method is energy stable.
