Parallel3D Numerical Simulation Of MHD With High Hartmann Number On CPU+GPU Cluster

Magnetohydrodynamics (MHD) is a comprehensive discipline whose researchtargets are Electrodynamics characteristics and CFD characteristics of conductivefluid. Because of its comprehensive background of both Electrodynamics and CFD, ithas been widely studied and applied in many fields, such as space weather, theinteraction between solar wind and Earth’s magnetosphere, plasmaconfinement mechanism in controlled thermonuclear reaction, MHD powergeneration. However, MHD related governing equations are too complex to get theanalytical solution, so we commonly use numerical simulation to get the numericalsolution. While, complex simulation procedure and large scale of gird make it slow tosolve them, especially for the MHD with high Hartmann number, it is very difficult toget converged solution. Therefore, the research of parallel3D numerical simulation ofMHD with high Hartmann number has great research value and significance.On the base of many works related with MHD numerical simulation and highperformance computing, this paper studies the parallel numerical simulation of MHDwith high Hartmann number on multi-core cluster and on GPU cluster respectively.The main work and contribution of this paper are summarized as follows:(1)This paper details the theoretical description and analyses the procedure ofMHD numerical simulation. Firstly, this paper introduces the physical andmathematical meaning of MHD numerical simulation and introduces the relatedparameters and governing equations at the same time. Secondly, this paper introducesthe equation discreting, numerical method, convergence criteria, boundary conditionin MHD numerical simulation. Thirdly, this paper draws a detailed flow chart, andanalyses the difficulty compared with CFD numerical simulation. Finally, this papergives a parallel analysis of MHD numerical simulation according to the procedure ofparallel computing.(2)This paper proposes and implements a two-level hybrid parallel MHDnumerical simulation for multi-core cluster. First of all, this paper proposes the workpartition and data communication strategy according to the result of meshing andvariable discreting, and implements a MPI based parallel algorithm bases on domaindecomposition in one direction. Secondly, on this basis, this paper implements aMHD numerical simulation based on MPI+OpenMP according to the thread-level parallelism analysis of MPI parallel algorithm. Finally, this paper performsexperiments on Lenovo DeepComp7000high performance computing cluster.Experiments’ results show that: compared with the serial algorithm, the two-levelparallel MHD numerical simulation on multi-core cluster improves the performancenearly by62%.(3)This paper proposes and implements a three-level hybrid parallel MHDnumerical simulation for GPU cluster. First of all, this paper studies and analyses thethree-level hybrid parallel programming model. Secondly, this paper moves parts ofthe procedure in the two-level hybrid parallel algorithm to GPU cluster according toits portability to implements a parallel MHD numerical simulation based on MPI+OpenMP+CUDA. Finally, this paper performs experiments through PGI AcceleratorFortran Station to verify the performance of the algorithm. Experiments’ results showthat: the three-level parallel MHD numerical simulation on GPU cluster achieves aspeed up of6.89times over the serial algorithm.Through MPI, OpenMP and CUDA, this paper implements3D numericalsimulation of MHD with high Hartmann number on multi-core cluster and on GPUcluster respectively. Importantly, this paper tests the performance of the abovealgorithms through many experiments.The results show that: the three-level hybridparallel algorithm for GPU cluster can significantly improve the numerical simulationperformance of MHD with high Hartmann number. In addition, because of its highportability, this algorithm can be applied into many related fields.