The Application Of DGM In Electromagnetism And Fluid Dynamics Based On GPU Acceleration

Discontinuous Galerkin Method?DGM?is a novel kind of numerical simulation method with high precision.DGM can be seen as the combination of Finite Volume Method which uses independent elements,and traditional Finite Element Method which uses arbitrary hign-order basis function,so it has the the advantages of high-accuracy and high degree of parallelism.In order to release the potential of high degree of parallelism of DGM and improve the practical value,this thesis focuses on the research of GPU parallel of DGM in the domain of Time-Domain Electronmegnetism and Fluid Dynamics,and develop corresponding solver.As the first step,this thesis researched the general conservation law equation,derives the semi-discrete formulation of DGM,then derives the partial differential,integration and numerical integration of volume coordinate on tetrahedron unstructured mesh,also derives two kind of basis function based on tetrahedron volume coordinate.The CUDA GPU parallel programming model is adopted,then the Structure of Arrays?AOS?and a general framework of GPU parallel DGM is designed.This thesis uses the framework above and adittional mesh generator,mesh importer and results outputter to develop the GPU parallel DGM solver of Electronmegnetism in Time Domain and Fluid Dynamics,which based on formulation method and numerical integration method,respectively.The Electronmegnetism solver with 1^st order and 2^nd order basis function can be used in the simulation with PEC and ABC.Fluid Dynamics solver with Roe convection flux and novel DDG viscosity flux which is well researched recently,can be used in the simulation of inviscid flow,viscous steady flow and viscous unsteady flow.The Electronmegnetism solver is validated by resonant cavity example and plane wave example,then a maximum speedup of 19 and 148 for 1^st order and 2^nd order is obvserved,respectively.The Fluid Dynamics solver is validated by the examples of cylinder,sphere,NACA0012 airfoil,ONERA M6 airfoil,and DLR-F6 wing-body,then a maximum speedup of 100 and 148 is observed in the simulation of inviscid flow and viscous flow respectively.