A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

Yalim M.S.; Vanden Abeele D.; Lani A.; Quintino T.; Deconinck H.

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A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

机译：解双曲线发散清洗方法理想磁流体动力学方程的有限体积隐式时间积分方法

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A finite volume numerical technique is proposed to solve the compressible ideal MHD equations for steady and unsteady problems based on a quasi-Newton implicit time integration strategy. The solenoidal constraint is handled by a hyperbolic divergence cleaning approach allowing its satisfaction up to machine accuracy. The conservation of the magnetic flux is computed in a consistent way using the numerical flux of the finite volume discretization. For the unsteady problem, the time accuracy is obtained by a Newton subiteration at each physical timestep thereby converging the solenoidal constraint to steady state. We perform extensive numerical experiments to validate and demonstrate the capabilities of the proposed numerical technique.

机译：提出了一种基于拟牛顿隐式时间积分策略的有限体积数值技术，用于求解稳态和非稳态问题的可压缩理想MHD方程。螺线管约束由双曲线发散清洗方法处理，从而使其满足机器精度要求。使用有限体积离散化的数值磁通量以一致的方式计算磁通量的守恒。对于不稳定问题，通过在每个物理时间步上进行牛顿迭代来获得时间精度，从而将螺线管约束收敛到稳态。我们进行了广泛的数值实验，以验证和证明所提出的数值技术的功能。

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来源
《Journal of Computational Physics》 |2011年第15期|共19页
作者
Yalim M.S.; Vanden Abeele D.; Lani A.; Quintino T.; Deconinck H.;
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正文语种 eng
中图分类数学物理方法;
关键词
Artificial compressibility; Hyperbolic divergence cleaning; Ideal magnetohydrodynamics; Implicit time integration strategy; Time-accurate;

机译：人工可压缩性;双曲散度清洁;理想的磁流体动力学;隐式时间积分策略;时间精确;

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1. A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach [J] . Yalim M.S., Vanden Abeele D., Lani A., Journal of Computational Physics . 2011,第15期

机译：解双曲线发散清洗方法理想磁流体动力学方程的有限体积隐式时间积分方法
2. A divergence-free semi-implicit finite volume scheme for ideal, viscous, and resistive magnetohydrodynamics [J] . Dumbser M., Balsara D. S., Tavelli M., International Journal for Numerical Methods in Fluids . 2019,第1a2期

机译：一种无差异的半隐式有限体积方案，可用于理想，粘性和电阻磁力流体动力学
3. An adaptive multiresolution method for ideal magnetohydrodynamics using divergence cleaning with parabolic-hyperbolic correction [J] . Anna Karina Fontes Gomes, Margarete Oliveira Domingues, Kai Schneider, Applied numerical mathematics . 2015,第sepa期

机译：带有抛物线-双曲线校正的发散清洗的理想磁流体动力学自适应多分辨率方法
4. Central Finite Volume Methods for one and two-dimensional ideal magnetohydrodynamics [C] . P.Arminjon, R.Touma 12th annual conference of the CFD Society of Canada (CFD 2004) . 2004

机译：一维和二维理想磁流体动力学的中央有限体积方法
5. Simulation of Rapidly Varying and Dry Bed Flow Using the Serre Equations Solved by a Finite Element Volume Method [D] . Pitt, Jordan Peter Anthony. 2019

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6. A divergence‐free semi‐implicit finite volume scheme for ideal viscous and resistive magnetohydrodynamics [O] . M. Dumbser, D.S. Balsara, M. Tavelli, -1

机译：无散度的半隐式有限体积方案用于理想粘性和电阻性磁流体动力学
7. Implicit-Explicit Time Integration of a High-Order Particle-in-Cell Method with Hyperbolic Divergence Cleaning [O] . G. B. Jacobs, J. S. Hesthaven 2014

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8. Using Diagonally Implicit Multistage Integration Methods for Solving OrdinaryDifferential Equations. Part 2: Implicit Methods [R] . VanWieren, J. 1997

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A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach

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