Numerical Studies Of Unsteady Euler Equations Based On GPU Parallel Computing

In CFD field, Computing times increased greatly with more complex problems and highcalculation needed. The excellent performance of GPU was taken by many foreign scholars to solvefluid problems in parallel, And dozens of times speedup ware get in single piece of GPU. Accordingto the situation, Research on dynamic grid and GPU parallel algorithm of solving unsteady Eulerequation on CUDA Fortran parallel environment were carried out in this paper.In the front half part,a new dynamic grid generation technique based on unstructured backgroundgrid was given in this paper, to deal with moving boundary problems. Firstly, a relatively coarseunstructured background grid was generated by small amount of surface nodes; secondly, springanalogy method was used to calculate the movement of background mesh nodes caused by boundarymovement; thirdly, the movement of computing mesh nodes were interpolated using their position inthe background mesh; finally, the movement of surface nodes and thick nodes near them are correctedwhen the surface is curly. Compared with directly spring analogy, The proposed method improves theefficiency of mesh deformation effectively by reducing the solving scale of the spring analogy.Additionally, using improved spring analogy method and unstructured background mesh can transferthe movement to internal nodes more evenly, make the grid more smooth, and improve the quality ofthe dynamic mesh. The2D and3D dynamic meshing examples are given in this paper to show thefeasibility and efficiency of this method.Then, GPU parallel computing programs based on the finite volume method were developed andresearched to solve the unsteady Euler equation. Classical methods were used in the programs,including Jameson spatial discretization scheme, dual Time-stepping temporal discretization scheme,TVD Runge-Kutta scheme and etc. The2D and3D representative flow examples were given at theend of this paper. Compared with the experimental data and the related literature results, the GPUparallel computing results were reliable. At last, an example of3D M6wing unsteady flow was givento show the application prospect of the proposed dynamic grid method and GPU parallel computingtechnology.