Solving Lid Driven Flow Problem in Fluid Mechanics Using LBM Method

The Lattice Boltzmann Method (LBM) can be employed to solve lid driven flow problems in fluid mechanics. This problem involves simulating fluid motion within a confined container where the top wall (lid) moves with a specified velocity. By inputting the number of iterations, the method generates velocity vector distribution plots of the flow field. LBM is a computational fluid dynamics technique that discretizes the fluid domain into small volumetric units called lattice cells. Each cell undergoes collision and streaming operations based on the Boltzmann equation to simulate fluid motion at discrete locations. The algorithm typically involves: - Initialization of distribution functions - Implementation of boundary conditions (bounce-back for walls, moving lid velocity) - Collision step using BGK approximation with relaxation parameter - Streaming step where distribution functions propagate to neighboring nodes The method calculates macroscopic variables (density, velocity) through moment summation of distribution functions. Key functions in implementation include: - computeMacroscopic(): calculates density and velocity from distribution functions - collide(): handles collision process with relaxation time - stream(): propagates distribution functions to adjacent lattices - applyBoundaryConditions(): implements lid velocity and wall boundaries LBM has gained widespread application in fluid mechanics research, particularly in micro-scale fluid dynamics and porous media flow simulations due to its inherent parallelizability and handling of complex geometries. The simulation outputs comprehensive flow field data including velocity magnitude and direction vectors, enabling detailed analysis of recirculation zones and vortex formation patterns.