Euler solutions using flux‐based wave decomposition

Abstract

The Euler equations are solved for non-hydrostatic atmospheric flow problems in two dimensions using a high-resolution Godunov-type scheme. The Riemann problem is solved using a flux-based wave decomposition suggested by LeVeque. This paper describes in detail, the design and implementation of the Riemann solver used for computing the Godunov fluxes. The methodology is then validated against benchmark cases for non-hydrostatic atmospheric flows. Comparisons are made with solutions obtained from the National Center for Atmospheric Research's state-of-the-art numerical model. The method shows promise in simulating non-hydrostatic flows, which are characterized by steep gradients on the meso-, micro-and urban-scales.

Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects

“…This shows that the thermal energy of the theta perturbation leads to the acceleration of the vertical velocity. This result agrees well with the study of Ahmad and Lindeman (2007).…”

A study of spectral element and discontinuous Galerkin methods for the Navier–Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases

“…Note, however, that if the discretization method is not formally conservative, then this set should have little or no advantage over set 1. Existing mesoscale models based on this equation set includes WRF [48] and the model by Ahmad and Lindeman [1].…”

“…Included in this list are models such as ARPS (University of Oklahoma), COAMPS (US Navy), LM (German Weather Service), MC2 (Environment Canada), MM5 (Penn State/NCAR), NMM (National Center for Environmental Prediction), and WRF (NCAR). The only models in the literature not based on the FD method are the FV models found in [7] and [1], and the SE and DG models presented in our paper. One of the biggest advantages that SE and DG methods have over the FD method is that no terrain following coordinates of the type presented in [16] need to be included in the governing equations.…”

Physics-Based Stabilization of Spectral Elements for the 3D Euler Equations of Moist Atmospheric Convection

“…The inviscid version of [1] is used for our analysis. This is because we are interested in assessing the current LES-like approach as a stabilizing tool that does not require further viscosity.…”