Towards perfectly matching layers for lattice Boltzmann equation

Following the efficient technique of Bérenger in classical computational fluid dynamics methods to avoid reflection of sound waves on the boundaries of the computational domain, we propose a new LBE scheme that behaves like a Bérenger medium for absorbing waves without reflection. This model is presented and its’ properties are discussed using the method of “equivalent equations”. We also proposed a general method to introduce zero-order damping terms in Boltzmann schemes that are used to absorb the waves propagating in the Bérenger medium. Results of the simulation are discussed with theoretical interpretation in the case of waves incoming normal to the interface. We shall also show that the reflection of sound waves can be reduced simply by changing the “advection step” of the lattice Boltzmann algorithm on the nodes close to the interface.