Lagrangian magneto-hydrodynamics simulation for underwater electrical wire explosion
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摘要: 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。Abstract: 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.
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图 2 多介质磁扩散问题模拟结果
Figure 2. Numerical results of the multi-material magnetic diffusion problem
图 3 一维柱形Sod激波管模拟结果
Figure 3. Numerical results of one-dimensional cylindrical Sod shock tube
图 4 直径0.2 mm铜丝水中电爆炸数值模拟结果
Figure 4. Simulation results of underwater electrical explosion of a copper wire with 0.2 mm diameter
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