High-Order Flux Reconstruction Numerical Simulation Method Research Based On Adaptive Grid

With the improvement of computer computing capabilities,computational fluid dynamics(CFD)high-order numerical simulation methods have attracted widespread attention from industry and researchers.The Flux Reconstruction(FR)method has become one of the research highlight in CFD for its high-order accuracy and simplicity for parallel computing.However,the FR method is still in the development stage,some key problems still need to be solved and improved,such as the shock capture,reduce the simulation amount on the premise of ensuring the high-order accuracy.Aiming at these problems,this thesis develops a high-order FR method based on adaptive grid to obtain high-order numerical results with as few grids as possible.First,high-order FR flow field solvers are developed for one-dimensional and two-dimensional flow simulation.To ensure the high-order accuracy of the numerical results,a curved mesh generation method on two-dimensional quadrilateral mesh is developed.To realize the shock capture,a shock detector based on the series expansion is introduced,and two kinds of shock capture methods are given: artificial viscosity and in-cell piecewise integrated solutions.At the same time,a positive limiter is adopted for simulation robustness.Secondly,a grid adaption high-order FR flow field solver is developed for two-dimensional parallel computing.The p4 est grid adaption library based on the tree data structure is used to realize grid information storage and MPI parallelism.The vorticity and the smooth indicator in the shock detector are used as the criteria for grid adaption.Based on the idea of least squares,the data projection of non-uniform faces and the conserved quantity interpolation in grid adaption process is realized.Finally,the grid adaption high-order FR method developed was verified by various numerical cases.The numerical results show that the grid adaption FR method developed in the thesis can greatly improve the simulation efficiency while ensuring high-order accuracy.