Lattice Boltzmann model in curvilinear coordinates for the study of the vibrational modes of a trumpet

摘要

Since its origins, lattice-Boltzmann methods have been restricted torectangular coordinates, a fact which jeopardizes the applications to problemswith cylindrical or spherical symmetries and complicates the implementationswith complex geometries. However, M. Mendoza [2] recently proposed in hisdoctoral thesis a general procedure (based on Christoffel symbols) to constructlattice-Boltzmann models on curvilinear coordinates, which has shown very goodresults for hydrodynamics on cylindrical and spherical coordinates. In thiswork, we construct a lattice-Boltzmann model for the propagation of scalarwaves in curvilinear coordinates, and we use it to determine the vibrationalmodes inside cylinders and trumpets (both problems with axial symmetry). Themodel correctly reproduces the theoretical expectations for the vibrationalmodes, and exemplifies the wide range of future applications oflattice-Boltzmann models on general curvilinear coordinates.