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

Abstract

AbstractA 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.