Meshfree Methods: Moving Beyond the Cumulan! Lattice Boltzmann Method

Identifier:  TDX:4088

Handle: https://hdl.handle.net/20.500.11797/TDX4088

Authors:  Gorakifard, Mohsen

Abstract:
In this dissertation, the fundamental acoustical properties of the cumulan! lattice Boltzmann method (CLBM) are first considered. Then, the coupled CLBM- finite element method is applied to predict the effect of adding hairy flaps to a cylinder on the noise emission at high Reynolds numbers. The CLBM provides a good agreement with theoretical results, while suffering from issues of accuracy related to the use of uniform meshes. Therefore, two MFree local weak-form CLB methods, the local radial point interpolation CLBM (LRPIC-LBM) and the meshless local Petrov-Galerkin CLBM (MLPGC-LBM) are suggested. The LB equation is divided into collision and streaming steps. The collision step is modeled by the cumulan! method. The streaming step is discretized in time using the Lax-Wendroff scheme. lt is discretized in space, using the local radial point interpolation method and the meshless local Petrov-Galerkin method, for LRPIC-LBM and MLPGC-LBM, respectively. The study of the results illustrates the LRPIC-LBM replicates the analytical results. The MLPGC-LBM predicts better results than the CLBM, reproducing LRPIC-LBM results with relatively shorter runtimes. Therefore, these new methods can offer an alternative to the CLBM, without parametric dependency on Nppw and a.