The Lattice Boltzmann Method can be interpreted as an alternative numerical approach for solving partial differential equations. The main idea behind the Lattice Boltzmann Method is to bridge the gap between the microscale and the macroscale. To achieve this, the Lattice Boltzmann Equation is separated into two steps: collision and streaming. In this work, the existing Lattice Boltzmann Method for the two-dimensional wave equation is extended to more general plane strain problems.


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Fig. 1: The collision and streaming step of the lattice Boltzmann method is demonstrated with five lattice points: a) The center lattice point has initially five distribution functions, whose summation is the macroscopic dependent variable (such as temperature, species, momentum, etc.); b) The equilibrium function of this lattice point is calculated; c) The collision process is applied for every distribution function; d) The post-collision distribution function is used to transfer to its neighbors.
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