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

Abstract

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.

A novel Large Eddy Simulation model for the Quasi-Geostrophic equations in a Finite Volume setting

“…This section focuses on the details of space discretization for the hydrostatic balances ( 13) and ( 17), the buoyancy and pressure terms appearing in eq. ( 35) and (38), the state equations ( 37) and ( 40), the density splitting (34), pressure splitting (39), and the conservation equation for the potential temperature (36). Details on the space discretization for all the other equations and terms can be found in [26].…”

“…We conclude with the fully discretized form of eq. (36). After applying the Gauss-divergence theorem, the integral form of eq.…”

“…For a quantitative comparison, we consider the potential temperature perturbation θ ′ along the horizontal direction at height z = 1200 m. Fig. 6 compares the results given by CE1, CE2 and CE3 models with the results from [23,36] denoted with Reference 1 and Reference 2. Reference 1 [23] was obtained with model CE3, mesh resolution of 25 m, and a spectral element method that provided very similar results to a discontinuous Galerkin method.…”

An Optimally Stable and Accurate Second‐Order SSP Runge‐Kutta IMEX Scheme for Atmospheric Applications

“…The presence of different waves in the atmospheric field has been discussed in the literature (e.g., Ghosh & Constantinescu, ; Nazari & Nair, ). Due to these various fast and slow waves in nonhydrostatic models, extensive attention has been paid to time‐split schemes (e.g., Nazari & Nair, ; Ullrich & Jablonowski, ) and more specifically to IMEX Runge‐Kutta schemes (Durran & Blossey, ; Giraldo et al, ; Weller et al, ). It has been proposed to resolve fast waves implicitly, as they have less significant physical effects (except for the inertial gravity waves) (Durran & Blossey, ; Giraldo et al, ; Weller et al, ).…”

High-Resolution Wave Propagation Method for Stratified Flows

“…[3][4][5][6][7] In recent years, there has been a growing interest in using schemes other than finite-differences for atmospheric modeling. [8][9][10][11][12][13][14] Substantial efforts have been made in evaluating finite-volume schemes for dynamical cores of atmospheric flow models. The FV3 (Finite-Volume3) 13 developed by the Geophysical Fluid Dynamics Laboratory has recently been selected as the dynamical core of the National Oceanic and Atmospheric Administration's next generation models.…”