三维无感应磁流体动力学模型的虚拟单元法
The virtual element method for the three dimensional inductionless magnetohydrodynamic model
AI总结：
针对三维无感应磁流体动力学问题，提出基于标量辅助变量法的一、二阶全离散虚拟单元格式，兼具守恒性、解耦特性与无条件稳定性，经数值实验验证有效。
摘要：
本文针对三维无感应磁流体动力学问题，基于标量辅助变量法提出了一种新的一阶和一种新的二阶全离散虚拟单元格式。时间离散采用向后欧拉公式和向后微分公式，空间离散采用两类守恒型虚拟单元列式。该方法的主要优势包括：利用虚拟单元法离散复结构的特性，保持了速度场的质量守恒与电流密度场的电荷守恒；通过标量辅助变量法显式处理非线性项；电流密度场与动量方程解耦，速度场与欧姆定律解耦。本文证明了两种全离散格式的无条件稳定性。最后，我们通过数值实验验证了所提格式的有效性。
英文摘要：
This paper proposes a novel first-order and a novel second-order fully discrete virtual element schemes based on the scalar auxiliary variable method for the three dimensional inductionless magnetohydrodynamics problem. The backward Eular formula and the backward differential formula are used for the time discretization and two types conservation virtual element formulations are employed for spatial discretization. The main advantages include that the mass conservation in the velocity field and the charge conservation in the current density field are kept by taking characteristics of the virtual element method's discrete complex structures, the nonlinear term is handled explicitly by applying the scalar auxiliary variable method, the current density field is decoupled from the momentum equation, and the velocity field is decoupled from the Ohm's law. The unconditionally stable of the two fully discrete schemes are demonstrated. Finally, we present numerical experiment to verify the valid of the proposed schemes.
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