Research And Application Of Unstructured Finite Volume Gradient Reconstruction Algorithms

Computational Fluid Dynamics(CFD)is one of the important methods to research and predict Fluid motion patterns and reveal flow phenomena,and now is widely used in the fields of scientific research and engineering,such as aerospace,meteorology,weapon design and shipbuilding.Since for unstructured meshes,it is possible to achieve automatic and rapid generation compared with structural meshes,the unstructured finite volume method is a common discrete method for solving CFD problems.However,unstructured meshes is not able to achieve regularity and efficiency as structured meshes,and it is difficult for the finite volume method to reach high order accuracy as finite difference method.This paper applies the characteristics of the finite difference method to the gradient reconstruction of the finite volume method,generates the local directions for the unstructured meshes,and generates the stencil along regulated directions.In this way,the procedure of the gradient reconstruction is able to utilize much information along the normal direction of the way,and improve the performance of the computational efficiency,the convergence efficiency,and the load balancing.Specifically,the main work and innovation of this paper are as follows:1)We proposed a local direction searching method based on advancing front(LDSMAF)for unstructured grid.The local directions of two-dimensional triangle,quadrilateral and mixed unstructured meshes are redefined,and the redefined local directions are calculated by the advancing front technique.LDSMAF considers not only the topology but also the information of the normal direction of the wall.Compared to the curvilinear reconstruction method,LDSMAF is able to reduce 47% angle deviation between the local direction and the normal direction of the wall in the regions near the wall boundary.Moreover,LDSMAF is able to increase 14% orthogonality in the whole computational region.2)We proposed a stencil selection method based on local direction(SSMLD)and a structured least squares reconstruction method(struLSQR).Based on the local direction of LDSMAF,SSMLD is proposed to generate the stencil for each control volume.SSMLD utilizes a recursive function to select the stencil cell and optimizes the recursive procedure in two aspects.Then,SSMLD is combined with the least squares gradient reconstruction method,and struLSQR is proposed and parallelized.struLSQR is able to obtain controllable and constant stencil.Compared to the extended least squares gradient reconstruction method(extLSQR),struLSQR with 8 stencil cells is able to reduce 35%computational amounts and improve the computational and communicational load balancing performance for at most 41% and 36% respectively,in the case of flow around a two-dimensional circular cylinder.3)We designed the test function and use it for the verification of struLSQR.Based on the key points of verification and the features of gradient reconstruction,the test function is designed to verify the code of struLSQR.The code verification procedure tests and analyzes the distribution of the gradient order of accuracy for a single grid unit,global gradient error and convergence order of accuracy,as well as the error and order of accuracy for different grid types.For the tested four types of quadrilateral grids and five types of triangular grids,struLSQR is able to achieve the order of accuracy of more than0.9992.Moreover,the order of accuracy along y direction is higher than those in the other three gradient reconstruction methods.4)We applied struLSQR to the realistic applications and analyzed its performance.struLSQR is applied in the inviscid flow,laminar flow and turbulence flow,and has been compared with the two least squares gradient reconstruction algorithms in OpenFOAM.Test cases cover inviscid flow,viscous flow and turbulence flow,the test of performance are the serial and parallel performance criteria,including the serial performance of error,order of accuracy,computational efficiency and convergence efficiency,and the parallel performance of wall time,scalability,communication overhead,and load balancing.The test could comprehensively reflect the performance of struLSQR in the unstructured finite volume applications.Compared to extLSQR,struLSQR is able to reduce 35% overall time and increase 21% computational efficiency and 160% convergence efficiency at the same time.And struLSQR is able to obtain more accurate normal velocity profile and 1.64 x parallel communication efficiency.