非定常不可压磁流体力学方程组的显式算法及其应用研究

项目名称： 非定常不可压磁流体力学方程组的显式算法及其应用研究

项目编号： No.91330112

项目类型： 重大研究计划

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 田振夫

作者单位： 复旦大学

项目金额： 70万元

中文摘要： “非定常磁流力学方程组的高效算法”已被列为“高性能科学计算的基础算法与可计算建模”重大研究计划中培育项目拟资助的方向之一。非定常磁流体力学(MHD)流动的数值模拟或要求准而快，或要求稳而长。构建MHD方程组具有并行本性的高分辨率、高精度数值算法是精确、高效、稳健的模拟、预测非定常MHD问题的一个核心和关键。基于高性能计算非定常MHD流动问题的目标,本项目拟完善已发展的空间导数任意阶的三点显式紧致格式,发展时间方向低色散、低耗散的高阶显格式,给出非定常不可压MHD易于构造显式算法的方程组形式,建立非定常不可压MHD方程组具有并行秉性的显式差分算法,编制串、并行计算程序,对磁场环境下液态金属磁流体双扩散对流特性进行数值模拟研究。本项目将有助于丰富MHD的研究方法,促进计算磁流体力学新方法和新理论的发展,也将有助于高性能科学计算的应用,推动高性能计算技术的发展。

中文关键词： 磁流体力学；非定常；显式差分算法；双扩散对流；液态金属

英文摘要： Magnetohydrodynamics(MHD) is an academic discipline combined with electromagnetics and fluid mechanics that studies the motion of electrically conducting fluids in the presence of magnetic fields.High efficient algorithm for unsteady MHD equations is one of important developing directions in“Basic algorithm of high performance scientific computing and computable modeling”which has been listed as a major program by the National Natural Science Foundation.The numerical simulations of the unsteady MHD flow and heat and mass transfer must be accurate, fast,robust and long time.The establishment of high resolution and high accuracy algorithms with inherent parallelism for MHD equations is a core and key for simulating and forecasting unsteady MHD problems. Motivated by objective from the high performance of parallel computation of the unsteady MHD flow and heat and mass transfer problems,this project is focused on the numerical methods for the simulation of the viscous incompressible MHD flows with multi-physics fields and strongly nonlinear coupling effects,the improvement of the arbitrary order three-point explicit compact schemes established by the research group for spatial derivatives,the development of low-dissipation and low-dispersion high order explicit difference scheme for temporal direction,the suggestion

英文关键词： magnetohydrodynamics；unsteady；explicit difference algorithm；double-diffusive convection；liquid metal