Study On The Incompressible Flow Problem Based On Smoothed Finite Element Method And Application In Vehicle Aerodynamics

Smoothed finite element method(S-FEM)has been widely used in computational solid mechanics.However,there has been limited research on applying S-FEM in computational fluid dynamics,particularly in turbulent flow problems.This thesis aims to address this gap by using S-FEM to solve relevant problems.The stability,convergence and accuracy of S-FEM were studied.The present work describes the establishment of an aerodynamic simulation system based on S-FEM,which successfully solved 3D complex unsteady vehicle aerodynamics problems.This marks a significant advancement of S-FEM and enriches the computational fluid dynamics method system.The main contents of the present work are described as follows:(1)A new numerical stability method named SUPG/SPGP/Fractional step method was proposed for solving incompressible laminar flow problems.The proposed method combined pressure gradient projection and numerical correction on streamlines with the Fractional step method to alleviate pressure numerical stability and spatial oscillation caused by convective terms.The weak-weak form of N-S equation was discretized using S-FEM to achieve second-order accuracy.This study conducted 2D and 3D numerical examples for incompressible laminar flow problems.The results demonstrate that the proposed method effectively preclude the numerical instability issue when solving the Navier-Stokes(N-S)equation using S-FEM and FEM.This study compared the performance of S-FEM and FEM in solving incompressible laminar flows,while also analyzing the differences between several element types using the proposed numerical stability method based on S-FEM.The results suggest that SFEM is more effective than traditional FEM in solving incompressible laminar flow problems due to its superior parameter applicability,higher numerical solution accuracy,greater mesh convergence,and better mesh robustness.(2)The study employed RANS in conjunction with SUPG/SPGP/Fractional step method to develop an incompressible turbulent flow solver based on S-FEM.To overcome the numerical instability caused by strongly convective turbulent flow,an efficient solving method,S-FEM with mixed elements(including tetrahedral,pyramid,wedge,and hexahedral elements),was established.The remarkable numerical stability of the SUPG/SPGP/Fractional step method in solving strongly convective turbulent flow problems was exhibited through 2D and 3D numerical examples.The performance of S-FEM was evaluated using the SA turbulence model and k-ε turbulence model.Compared with traditional FEM,S-FEM shows higher accuracy in nearwall and strongly convective regions,and better mesh robustness in solving incompressible turbulent flow problems.(3)A parallel S-FEM flow solver was developed using Open MP and the behavior of different mixed meshes based on S-FEM was tested.Specifically,a high-precision discretization form of S-FEM with hex-core mixed mesh was established to solve 3D complex flow problems.Additionally,an aerodynamics simulation framework based on S-FEM was established,which can deal with a relatively large-scale aerodynamics problem.The behaviors in time and space of the vortex structure around the Ahmed body and the high-speed train,including generation,development,vortex shedding,reattachment,and dissipation,were replayed.Futhermore,a correlation between unsteady flow and aerodynamic loads is established based on the flow field.The velocity and pressure distributions around vehicle bodies obtained by S-FEM are basically consistent with those obtained by FVM.When compared to experimental results,the results show that the prediction errors of the air drag coefficients of the Ahmed body and the high-speed train are 3% and5%,respectively.The SUPG/SPGP/Fractional step method offers reliable numerical stability for complex 3D high Reynolds number problems.