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Recently, Murthy et al. [2017] and Escande et al. [2020] adopted the LatticeBoltzmann Method (LBM) to model the linear elastodynamic behaviour of isotropicsolids. The LBM is attractive as an elastodynamic solver because it can beparallelised readily and lends itself to finely discretised dynamic continuumsimulations, allowing transient phenomena such as wave propagation to bemodelled efficiently.  This work proposes simple local boundary rules which approximate thebehaviour of Dirichlet and Neumann boundary conditions with an LBM for elasticsolids. Both lattice-conforming and non-lattice-conforming, curved boundarygeometries are considered.  For validation, we compare results produced by the LBM for the sudden loadingof a stationary crack with an analytical solution. Furthermore, we investigatethe performance of the LBM for the transient tension loading of a plate with acircular hole, using Finite Element (FEM) simulations as a reference.

Dirichlet and Neumann boundary conditions in a Lattice Boltzmann Method for Elastodynamics