Research On The Key Technology Of HopeFOAM:A Discontinuous Finite Element Based High Order Parallel Computing Framework

With the continuous development of high-performance computing and the maturity of computational theory,Computational Fluid Dynamics(CFD)plays an increasingly important role in scientific research and industrial applications,which can effectively reduce R&D costs,shorten development cycles,Optimize the design and provide reliable guarantees.Surely,CFD will become a pivotal part of China's economic transformation and”smart manufacturing 2025” plan.CFD has been widely used in practical engineering.However,to accurately describe the complex turbulence at the adjacent boundary in engineering,high-precision numerical simulation is necessary and becoming the trend of future CFD development.High-order precision format is one of the important directions,among which Discontinuous Galerkin Finite Element Method(DG-FEM)is one of the most potential one.DG-FEM has the advantages of conservation,high-order,supporing unstructured mesh and stability.Developing parallel CFD application covers multiple fields such as physical models,numerical calculations,and computer science.But,the current development framework for high-order methods is lacking,which restricts the development and application of high-order methods.To this end,this PhD project tries to design and implement the discontinuous finite element high-order computation framework named HopeFOAM,based on the open source software OpenFOAM.Besides,We carry out several related key technologies such as frame-based incompressible fluid simulation stability,compressible fluid limiter,and high-order parallel computing performance optimization.The main work and innovations are as follows:The designs and implements of HopeFOAM,a high-order discontinuous finite element parallel computing framework(Chapter 2).The relationship between finite volume method,finite element method and discontinuous finite element method is deeply excavated.We proposed to develop discontinuous finite element schemes based on OpenFOAM,an open source finite volume CFD software.The hierarchical architecture is utilized to support features such as high order,high performance,and high scalability.We design and implement the high-order discrete core layer,scalable discrete system description layer,pre-and post-processing tools and other important components.HopeFOAM successfully supports the high-order discrete and operations covering the whole CFD process.By inheriting and extending the user interface in OpenFOAM,HopeFOAM allows users to approach ”zero programming” for high-order application development.The temporal and spatial stability of the incompressible fluid solved by continuous pressure and discontinuous velocity are studied(Chapter 3).For the first time,this paper discusses the temporal-spatial stability of the DG-CG based INS solver under small time steps and high Reynolds number.With the Pearson Vortex case,the small time step instability under Pure DG is successfully reproduced,and the behavior of DG-CG is also tested.The temporal stability of DG-CG is further illustrated by the eigenvalue spectrum method.Finally,the Poiseuille case is used to analyze the spatial stability of DG-CG method under high Reynolds number,concluding that the viscosity coefficient,discretization order,and mesh scale are important to the numerical stability.High-order limiter-detector design based on HopeFOAM(Chapter 4).The limiterdetector is critical to maintaining the stability of higher order methods in problems with shocks.However various types are suitable for different situations,making the limiterdetector difficult to implement and use.This paper analyzes the mainstream limiters including slope,moment and WENO limiter,as well as the minmod and KXRCF detectors.Through the abstraction of the calculation process,a unified limiter-detector interface based on HopeFOAM is designed and implemented.In a series of case tests with shock discontinuities,HopeFOAM exhibits high-order convergence accuracy and numerical stability.Matrix-free based performance optimization on HopeFOAM(Chapter 5).The Matrixfree method is introduced into HopeFOAM to extend the current PETSc-based linear system.The member classes for the matrix-free method are added,keeping consistent with the front user interfaces.Based on the Kronecker product,we implemente an efficient Matrix-Vector multiplication,which significantly remit memory access restrictions.Explicit vectorization operations based on matrix partitioning are utilized to fully explore the capability of modern processors.In the test cases,the Matrix-Free method shows good scalability.Compared with the traditional implementation,the highest acceleration ratio is 7 times in 2D explicit simulation,and 32 times in 3D.