Study On Lattice Boltzmann Method For Two Types Of Flow Problems

Lattice Boltzmann method(LBM)is a numerical simulation method based on the movement of mesoscopic particles.Currently,LBM has been successfully applied in simulating complex fluid flow and other fields.However,LBM struggles to directly simulate high Reynolds number flow,while large eddy simulation(LES)can simulate flow phenomena under high Reynolds numbers by controlling energy transfer.Therefore,combining LES with LBM can overcome the limitations of LBM in simulating high Reynolds number flow fields.Additionally,the computational process of LBM requires a significant amount of memory,and the generated data volume can be very large.To reduce the dimensionality and storage requirements of the data,proper orthogonal decomposition(POD)can be used to transform high-dimensional data into low-dimensional data.This method retains the most representative information from the original data and is commonly used for analyzing flow field data.In LBM,when the boundary conditions involve complex geometric shapes,grid generation can become extremely complex and time-consuming.In contrast,immersed boundary method(IBM)is more suitable for handling boundary problems with complex geometric shapes.Therefore,effectively combining LBM and IBM can handle complex boundary problems well.The main contributions of this study are as follows:(ⅰ)The introduction of the inertial-range model into the multiple relaxation time lattice Boltzmann method(MRT-LBM)and establishes the corresponding multiple relaxation time inertial-range(MRT-IR)method.This method has better stability and accuracy in simulating high Reynolds number flow,and can effectively solve non-physical oscillation problems.(ⅱ)The MRT-IR method was applied to numerically simulate the two-dimensional lid-driven cavity flow.The computed results were compared with classical methods to validate the effectiveness of the approach.The study analyzed the changes in flow characteristics and vortex center position under different Reynolds number conditions,obtaining the critical Reynolds number.Additionally,the periodic changes in flow inside the lower cavity under high Reynolds number were investigated.In three-dimensional cavity flows,a single-sided driven three-dimensional cavity was numerically simulated,analyzing the flow characteristics,vortex center position,and pressure distribution under different parameter conditions such as Reynolds number and aspect ratio.(ⅲ)The flow field was then analyzed using POD method,which revealed that the energy of the flow field was mainly concentrated in a few low-order modes.The first 7 modes accounted for 93%of the total energy,allowing for accurate reconstruction of the flow field.As the Reynolds number increased,the energy proportion of the first-order mode gradually decreased,indicating an increase in the disorderliness of the flow field.Energy gradually transferred from large-scale structures to small-scale structures.(ⅳ)The combination of IBM and the previously established MRT-IR method has led to the development of a method called IB-MRT-IR method,which can satisfy the no-slip boundary condition.Numerical investigations of two-dimensional and three-dimensional flow around single and double cylinders at different Reynolds numbers were conducted using IB-MRT-IR method,and an analysis of the force coefficients and the shedding vortex structure in the wake was carried out.Through this work,the aim is to enhance the capability of LBM in simulating complex fluid flow and to address issues related to boundary conditions.The combination of these methods will provide a more accurate and efficient numerical simulation approach for studying high Reynolds number flow problems.