Simplified Lattice Boltzmann Method For Incompressible Flows And Its Applications

Numerical simulation of isothermal and non-isothermal incompressible flows is crucial for engineering applications of naval architecture and ocean engineering.As one of the most recent advances in the mesoscopic numerical methods,the simplified lattice Boltzmann method(SLBM)is gaining popularity due to its capacity to save computational memory,enhance numerical stability,and simplify boundary conditions.It is now used to simulate a brode range of isothermal and non-isothermal incompressible flows.However,SLBM still has certain drawbacks,such as:(1)When recovering to macroscopic scale,the present SLBM corresponds to the Navier-Stokes equations in the compressible form,implying that SLBM is an artificial compressible method,and the compressibility effect causes computation inaccuracy.(2)The existing model for introducing forces in SLBM is inconsistent in several aspects,and the modeling capability for flows with irregular external forces is insufficient.(3)The accuracy is poor or the calculation consumption is large when using SLBM to model non-isothermal flows.(4)The evolution of the STLBM and HSTLBM models includes non-equilibrium distribution functions that demand extrapolation when the boundary treatment is applied,which introduces additional errors and lacks generality.As a result,the following works are carried out in this thesis:To begin with,the theoretical analysis of SLBM is performed,and the results show that the equilibrium distribution function used in SLBM is a low Mach number expansion form of the Maxwell distribution function,omitting the high order term of velocity,namely,SLBM is an artificial compressibility method for solving incompressible N-S equations.As a result of the compressibility effects,numerical inaccuracy is unavoidable.This thesis proposes incompressible simplified lattice Boltzmann techniques(IC-SLBMs)to overcome this weakness of SLBM.After correcting for the errors of compressible effects,IC-SLBMs can recover the N-S equations in incompressible form,and the model is validated using benchmarks.Second,the existing external force models for SLBM are shown to be inconsistent in three aspects,namely,the governing equation of SLBM is inconsistent with LBM,the continuous external force is inconsistent with the discrete equation,and the macroscopic external force is inconsistent with the mesoscopic modeling scale.In this thesis,the consistent force model for SLBM is developed by considering the influence of external force at the distribution function level,and the inaccuracy caused by inconsistency is effectively minimized and lays the groundwork for the multi-field coupling method.Finally,the coupled simplified lattice Boltzmann method(CSLBM)is presented.The temperature field and the hydrodynamic field are coupled using the consistent external force model.The boundary condition of the temperature field is optimized,and the error introduced by the extrapolation approach in the original SLBM is eliminated.The CSLBM is also used to simulate heat transfer and natural convection,and the results are in accord well with the analytical solution or reference values in the literature.In addition,the CSLBM is utilized to numerically investigate the mixed convection in a two-dimensional square cavity,and for the first time,the combined effects of multiple temperature gradient orientations,different heat source heating durations and different Richardson numbers are given.