Lattice Boltzmann model for the simulation of the wave equation in curvilinear coordinates

•A lattice-Boltzmann method for the simulation of acoustics in general curvilinear coordinates was developed.•The information of the systems geometry is content in additional forcing terms and interpolation steps are not required.•The model was tested by finding the normal modes inside a cylindrical pipe and a Bessel horn trumpet.•Symmetries of the system can reduce the dimension of the simulation space.•The proposal widely opens the applicability of the model to acoustic systems with very complicated geometries. Since its origins, lattice-Boltzmann methods have been restricted to rectangular coordinates, a fact which jeopardizes the applications to problems with cylindrical or spherical symmetries and complicates the implementations with complex geometries. However, M. Mendoza [1] recently proposed in his doctoral thesis a general procedure (based on Christoffel symbols) to construct lattice-Boltzmann models on curvilinear coordinates, which has shown very good results for hydrodynamics on cylindrical and spherical coordinates. In this work, we construct a lattice-Boltzmann model for the propagation of scalar waves in curvilinear coordinates, and we use it to determine the vibrational modes inside cylinders, trumpets and tori. The model correctly reproduces the theoretical expectations for the vibrational modes, and exemplifies the wide range of future applications of lattice-Boltzmann models on general curvilinear coordinates.