Lattice Boltzmann Simulation of Plane Strain Problems

Abstract

AbstractThe Lattice Boltzmann Method (LBM), e.g. in [3] and [4], can be interpreted as an alternative method for the numerical solution of partial differential equations. The LBM is usually applied to solve fluid flows. However, the interpretation of the LBM as a general numerical tool, allows to extend the LBM to solid mechanics as well. In this spirit, the LBM has been studied in recent years. First publications [5], [6] present a LBM scheme for the numerical solution of the dynamic behavior of a linear elastic solid under simplified deformation assumptions. For so‐called anti‐plane shear deformation, the only non‐zero displacement component is governed by the two‐dimensional wave equation. In this work, the existing LBM for the two‐dimensional wave equation is extended to more general plane strain problems. The algorithm reduces the plane strain problem to the solution of two separate wave equations for the volume dilatation and the non‐zero component of the rotation vector, respectively.