交错网格下MHD相容守恒格式的发展

Development of a consistent and conservative scheme on a staggered grid for liquid metal MHD flows

在低磁场雷诺数条件下,基于电势泊松方程,发展了交错网格下可以精确计算电流和洛伦兹力（电磁力）的相容守恒格式。采用压力为变量的原始变量法求解不可压缩Navier-Stokes方程,所计算的电流满足电荷守恒定律,所计算的电磁力满足动量守恒定律。对金属流体在Hartmann数50~5000范围内验证了格式的精确性。交错网格下相容守恒格式的发展为后续MHD稳定性分析、湍流的大涡模拟及直接数值模拟提供很好的选择。

A consistent and conservative scheme has been extended and developed on a staggered grid system for liquid metal MHD flow at a low magnetic Reynolds number by solving electrical potential Poisson equation based on the Ohm＇s law and the charge conservation law.The consistent scheme is used to ensure the calculated current density conserves the charge,and the divergence formula of the Lorentz force is used to ensure the momentum conservation.Simulation of liquid metal flows in a three-dimensional straight channel is conducted and compared with the analytical solutions from Shercliff＇s and Hunt＇s.The numerical results are in good agreement with analytical solutions for the Hartmann numbers from 50 to 5000.A fully conservative scheme on a staggered grid,which can conserve mass,momentum and kinetic energy and charge,is then developed with the central-symmetrical scheme for the convective term and the pressure term and with the consistent and conservative scheme for the calculation of the current density and the Lorentz force.A fully conservative scheme can be a good tool for numerical analysis of MHD flow instability,large eddy simulation（LES） and direct numerical simulation（DNS） of MHD turbulence.