A control-volume model of the compressible Euler equations with vertical Lagrangian Coordinate

esolving interactions between clouds and aerosol in the atmosphere, which have many direct and indirect effects in climate change, requires accurate and stable numerical discretization of the nonhydrostatic equations for the atmosphere. Here we are presenting a Lagrangian control-volume approach for solving the compressible Euler equations, which does not suppress propagation of the atmospheric sound waves on the small scale of the cloud resolving models. By reformulating the equations with Lagrangian vertical coordinate, the horizontal and vertical advection part can be isolated in two coupled 1D equations. This new approach is validated using 1D and 2D configurations.