标题： 基于保结构有限元的粘性和耗散磁流体力学变分离散化 显示英文标题

标题： Variational discretizations of viscous and resistive magnetohydrodynamics using structure-preserving finite elements

摘要： 我们提出了一种新的保结构离散化方法，用于粘性及电阻磁流体力学。 我们遵循最近关于流体和等离子体方程的离散最小作用量原理的研究方向，结合最近在通过广义拉格朗日-达朗贝尔约束变分原理建模耗散现象方面的进展。 我们证明了我们的半离散格式等价于一个度量泊松系统，并利用这一性质提出了一种泊松分裂时间积分方法。 由此得到的近似解保留了质量、能量以及磁场的散度约束。 然后，我们展示了一些使用该方法获得的数值结果。 我们首先在一个简单的学术测试中检验我们的格式，以与已建立的方法进行比较，然后重点关注等离子体不稳定性模拟，同时对非笛卡尔几何进行一些测试，以验证我们在托卡马克不稳定性范围内的离散化方案。 显示英文摘要

摘要： We propose a novel structure preserving discretization for viscous and resistive magnetohydrodynamics. We follow the recent line of work on discrete least action principle for fluid and plasma equation, incorporating the recent advances to model dissipative phenomena through a generalized Lagrange-d Alembert constrained variational principle. We prove that our semi-discrete scheme is equivalent to a metriplectic system and use this property to propose a Poisson splitting time integration. The resulting approximation preserves mass, energy and the divergence constraint of the magnetic field. We then show some numerical results obtained with our approach. We first test our scheme on simple academic test to compare the results with established methodologies, and then focus specifically on the simulation of plasma instabilities, with some tests on non Cartesian geometries to validate our discretization in the scope of tokamak instabilities.