Taylor series expansion and least square-based lattice Boltzmann method and its applications in incompressible viscous flows

Abstract

In this thesis, a differential lattice Boltzmann equation and a Taylor series expansion and least square-based lattice boltzmann method were derived and developed for modeling incompressible viscous flows with complex geometries on irregular grid systems. An axisymmetric lattice boltzmann equation was also derived for modeling the three-dimensional axisymmetric flows. all new equations and method have been successfully applied to model different incompressible viscous flows with good accuracy and efficiency.