Absorbing boundary and free-surface conditions in lattice solid approaches

Absorbing boundary conditions are necessary for any numerical approach to wave propagation in an unbounded model due to the computer memory size limit. The phononic lattice solid by interpolation (PLSI) and the phononic lattice solid with fluids (PLSF) are microscopic approaches for modelling wave phenomena in strongly heterogeneous media based on the Boltzmann lattice gas methods. An absorbing boundary condition for these microscopic approaches has been designed by setting the microscopic reflect ion coefficients at the borders of a model to zero and adding viscous layers to the borders. The viscosities of the viscous absorbing boundary layers are adjusted by choosing different values of the mean number densities of quasi-particles. Numerical examples using the PLSI demonstrate that the artificial boundary reflections can be eliminated almost completely when the incidence angle is less than approximately 70”. Beyond this angle, the artificial boundary reflect ions are not easy to attenuate. Many models for the study of wave propagation involve one or more free surfaces such as the sea and Earth's surfaces. Four approaches are suggested for modelling free surface reflections in lattice solid simulations. In the first three approaches, special interaction rules at the free surface are specified to take into account the effect of the free surface on quasi-particle movements (cf. wave propagation). These are termed the specular bouncing, backward bouncing-I and combined bouncing models and involve quasi-particle reflections with a coefficient of negative one. They require the free surface to be exactly located along lattice nodes. Numerical examples demonstrate that the results for these three approaches are almost identical. The backward bouncing approach-I is modified for the case when the free surface is located at any position along lattice links and is thus termed backward bouncing approach-II. It uses the reflection coefficient at the free surface to calculate the reflected number densities during the PLSI or PLSF simulation. Hence, the free surface is handled in the same way as an interface within a model. Numerical examples demonstrate the ability of four to simulate free surface reflections.