An FCT finite element scheme for ideal MHD equations in 1D and 2D
An FCT finite element scheme for ideal MHD equations in 1D and 2D
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DOI：
10.1016/j.jcp.2017.02.051
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Steffen Basting;D. Kuzmin
中科院分区：
文献类型：
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作者：
Steffen Basting;D. Kuzmin
本文提出了一种求解理想磁流体动力学方程的隐式有限元格式。连续Galerkin近似约束使用通量校正传输（FCT）算法。底层的低阶格式构造使用Rusanov型人工粘性算子的基础上标量耗散成比例的快波速度。低阶解的精度可以使用冲击检测器来提高，该冲击检测器使得可以在单调性保持迭代方式中预先限制附加粘度。在FCT校正步骤中，守恒量的变化以保证密度和热压的正性保持的方式被限制。使用FCT预测器到交错有限元空间的投影来提取无发散磁场，从而形成精确序列。在二维情况下，磁场被投影到Raviart-Thomas有限元空间中。标准的测试问题的数值研究进行验证所提出的算法的能力，以执行相关的限制在应用程序中的理想MHD流。
This paper presents an implicit finite element (FE) scheme for solving the equations of ideal magnetohydrodynamics in 1D and 2D. The continuous Galerkin approximation is constrained using a flux-corrected transport (FCT) algorithm. The underlying low-order scheme is constructed using a Rusanov-type artificial viscosity operator based on scalar dissipation proportional to the fast wave speed. The accuracy of the low-order solution can be improved using a shock detector which makes it possible to prelimit the added viscosity in a monotonicity-preserving iterative manner. At the FCT correction step, the changes of conserved quantities are limited in a way which guarantees positivity preservation for the density and thermal pressure. Divergence-free magnetic fields are extracted using projections of the FCT predictor into staggered finite element spaces forming exact sequences. In the 2D case, the magnetic field is projected into the space of Raviart–Thomas finite elements. Numerical studies for standard test problems are performed to verify the ability of the proposed algorithms to enforce relevant constraints in applications to ideal MHD flows.