A Godunov-type finite-volume solver for nonhydrostatic Euler equations with a time-splitting approach

A two-dimensional conservative nonhydrostatic (NH) model based on the compressible Euler system has been developed in the Cartesian (x, z) domain. The spatial discretization is based on a Godunov-type finite-volume (FV) method employing dimensionally split fifth-order reconstructions. The model uses the explicit strong stability-preserving Runge-Kutta scheme and a split-explicit method. The time-split approach is generally based on the split-explicit method, where the acoustic modes in the Euler system are solved using small time steps, and the advective modes are treated with larger time steps. However, for the Godunov-type FV method this traditional approach is not trivial for the Euler system of equations. In the present study, a new strategy is proposed by which the Euler system is split into three modes, and a multirate time integration is performed. The computational efficiency of the split scheme is compared with the explicit one using the FV model with various NH benchmark test cases.