Hybrid Galerkin numerical modelling of elastodynamics and compressible Navier–Stokes couplings: applications to seismo-gravito acoustic waves

We introduce a hybrid Galerkin modelling tool for the nonlinear acoustic and gravity wave propagation in planetary atmospheres coupled through topography to a solid medium. We rely on a 2-D spectral-element technique to model linear visco-elastic solid media and couple it to a discontinuous Galerkin method for the atmosphere modelled by the fully nonlinear Navier–Stokes equations. Significant benefits of such a method are, first, its versatility because it handles both acoustic and gravity waves in the same simulation, second, it enables one to observe nonlinear effects as convection or wave-breaking and, finally, it allows one to study the impact of ground-atmosphere coupling for waves propagating from seismic sources. Simulations are performed for 2-D isothermal atmosphere models with complex wind and viscosity profiles. We validate the computations by comparing them to finite-difference solutions, already validated in a previous paper. Specific benchmark validation cases are considered for both acoustic and gravity waves subject to viscosity variations, wind duct and nonlinear wave breaking. We apply this tool to study acoustic and gravity waves generated by a strong seismic source and its nonlinear breaking in the upper atmosphere.