A Computationally Wise Nonhydrostatic Finite-Volume Solver with the Split-Explicit Time Stepping

A two-dimensional nonhydrostatic 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) employing fourth-order piecewise quartic reconstructions. The model uses the explicit strong stability-preserving (SSP) Runge-Kutta (RK) scheme and various novel time-splitting methods. The time-split approach is generally based on the so-called split-explicit method, where the acoustic (fast) waves in the Euler system solved using small time-steps and advective (slow) modes are treated with larger time-step.