Research On Optimization Technology Of The Parallel Solution Of Euler Equations With Discontinuous Finite Element Method Based On HopeFOAM

With the development of CFD,high-order methods such as DG are widely used in many fields,one of which is the Euler equations discretized by RKDG.HopeFOAM is an open source CFD framework based on OpenFOAM,which supports DG high-order simulation.However,due to the lack of curve boundary,high-order numerical accuracy can not be achieved from HopeFOAM.Morever,the way of solving linear equations greatly limits the performance of DG simulation.This paper is focused on the above problems and the accuracy and performance optimization of Euler equations DG simulation is carried out based on HopeFOAM.The major work and innovations are listed as follow:(1)The paper elaborates the numerical theory of DG based on the Euler equations,and analyze the shortcomings of HopeFOAM in terms of accuracy and performance.The requirements of curve boundary and performance optimization are presented.(2)For the problem of accuracy,this paper designs and implements the curve boundary.The paper completes the curve boundary interface and configuration code processing module,and the iterative search mapping algorithm is designed to complete the points movement.The curve boundary function is pre-processed for the parallel solution.(3)For the problem of performance,this paper designs and implements the MatrixFree and SIMD vectorization architecture on HopeFOAM.Combined with the numerical theories of DG and Matrix-Free,Matrix-Free optimization solution is achieved by the high-efficiency matrix data structure.Based on the data structure of SIMD,the SIMD vectorization is completed.(4)According to the test results of classic benchmark problems,the paper verifies the effects of accuracy and performance optimization.Based on the cylindrical flow,the correctness and necessity of the curve boundary are verified,and the high-efficiency characteristics of high-order simulations are proved.Based on the two-and three-dimensional isentropic vortex,the obvious performance optimization is verified and the maximum speed-up ratios are 7.75 and 32.02 in tow-and three-dimensional space respectively.Moreover,our implementation does not affect the parallel scalability of HopeFOAM.