Research On OpenFOAM-based Lattice Boltzmann Flux Solvers

At present,the dominating numerical approaches of Computational Fluid Dynamics(CFD)can be roughly classified as the N-S solvers and lattice Boltzmann equation(LBE)solvers,which are respectively based on macroscopic conservation laws and mesoscopic statistical theory of physics.The roots in different theoretical backgrounds result in unique benefits and drawbacks of these two solvers.In the N-S solvers,it is easy to discretize the spatial and temporal terms using various schemes.Moreover,the N-S solvers can be applied on various mesh types including multi-block mesh,adaptive mesh,structured and unstructured body-fitted mesh,which is especially suitable for complex geometries.But they still suffer from the pressure-velocity coupling and complicated computation of derivatives.The LBE solvers have clear physical background and intrinsically parallel nature.They can be implemented by codes without considering the high order derivatives in the N-S solvers.However,they also suffer from some drawbacks such as restricted to uniform mesh,tie-up of mesh spacing and time step,complicated implementation of boundary condtions.This thesis implements three different versions of lattice Boltzmann flux solvers(LBFS)respectively for isothermal,thermal incompressible flows and compressible flows based on open source codes OpenFOAM.LBFS for isothermal and thermal incompressible flows are implemented first.LBFS utilizes FVM to discretize the governing equations recovered by the LBE and the conservative flow variables can be updated by marching in time.The inviscid and viscous fluxes at the cell interface are evaluated simultaneously by local reconstruction of LBE solutions.We simulated both 2D and 3D cases using LBFS on the newly developed CFD platform.Numerical results show that LBFS overcomes the drawbacks of LBE solvers such as limitation to uniform mesh,tie-up of mesh spacing and time step,the complexity of boundary condition implementation.By absorbing the advantages of N-S solvers,LBFS has the ability of solving incompressible flows on arbitrary unstructured meshes.To further extend the application of LBFS to high Reynolds turbulent flows,we combine LBFS with turbulence model and study the aerodynamics of airfoils.Then we implement the compressible LBFS based on OpenFOAM.In the solver,the FVM is applied to discretize the N-S equations.The inviscid flux across the cell interface is evaluated by local reconstruction of solution using one-dimensional lattice Boltzmann model while the viscous flux is approximated by traditional method.The non-equilibrium part of the distribution function is treated as artificial viscosity and is controlled by a switch which varies from 0 to 1.Numerical experiments prove that the compressible LBFS can accurately capture strong shock waves and effectively simulate compressible flows with complex geometries.Overall,this thesis implements the LBFS based on OpenFOAM successfully and the newly developed CFD platform can simulate both incompressible and compressible flows accurately and efficiently.