水中金属丝电爆炸拉氏磁流体动力学模拟方法

Lagrangian magneto-hydrodynamics simulation for underwater electrical wire explosion

基于拉格朗日描述,建立了水中金属丝电爆炸的单温磁流体动力学模型,并给出一种高阶混合有限元离散求解方法。拉氏可压缩流体方程组中,速度定义在H1连续有限元空间,内能定义在L2间断有限元空间实现物质界面的精确捕捉,存在激波的区域引入张量人工粘性抑制数值振荡。磁扩散方程仅考虑周向磁通量密度,简化为标量方程,使用H1连续有限元方法离散求解。焦耳热和洛伦兹力作为源项引入实现磁流体方程的耦合。数值算例表明:磁扩散求解器能够求解存在不同电导率的多介质磁扩散问题;拉氏流体求解器能够精确追踪物质界面,具有较好的激波分辨能力;耦合RLC电路的磁流体求解器能够复现水中金属丝电爆炸加热相变、冲击波的产生与传播、放电模式转变等物理过程。

Based on the Lagrangian description,a single temperature magneto-hydrodynamics model of underwater electrical wire explosion is established,and a high-order mixed finite element method is used to solve this model.For the Lagrangian compressible fluid equations,velocity is discretized using the continuous high-order basis function in the H1 space,and internal energy is discretized using a L2 piecewise discontinuous high-order basis function for the precise capture of the material interface.A tensor artificial viscosity is introduced to suppress the numerical oscillation.Only the azimuthal magnetic flux density is contained in the magnetic diffusion equation,which is simplified to a scalar equation,and is discretized using continuous basis function.Joule heating and Lorenz force are introduced to couple hydrodynamics equations with magnetic field.Numerical results show that the magneto-diffusion solver can solve a multi-material magnetic diffusion problem,and the hydrodynamics solver can track the material interface and shock wave.Underwater electrical wire explosion is simulated based on the magneto-hydrodynamics solver coupled with RLC circuit,including phase transition,shock wave and different discharge modes.