A family of well-balanced WENO and TENO schemes for atmospheric flows

We herein present a novel methodology to construct very high order well-balanced schemes for the computation of the Euler equations with gravitational source term, with application to numerical weather prediction (NWP). The proposed method is based on augmented Riemann solvers, which allow preserving the exact equilibrium between fluxes and source terms at cell interfaces. In particular, the augmented HLL solver (HLLS) is considered. Different spatial reconstruction methods can be used to ensure a high order of accuracy in space (e.g. WENO, TENO, linear reconstruction), being the TENO reconstruction the preferred method in this work. To the knowledge of the authors, the TENO method has not been applied to NWP before, although it has been extensively used by the computational fluid dynamics community in recent years. Therefore, we offer a thorough assessment of the TENO method to evidence its suitability for NWP considering some benchmark cases which involve inertia and gravity waves as well as convective processes. The TENO method offers an enhanced behavior when dealing with turbulent flows and underresolved solutions, where the traditional WENO scheme proves to be more diffusive. The proposed methodology, based on the HLLS solver in combination with a very high-order discretization, allows carrying out the simulation of meso-and micro-scale atmospheric flows in an implicit Large Eddy Simulation manner. Due to the HLLS solver, the isothermal, adiabatic and constant Brunt-Vaisala frequency hydrostatic equilibrium states are preserved with machine accuracy. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Automated summary

We present a novel methodology for constructing high order schemes for computational simulations of the Euler equations with gravitational source term, specifically for numerical weather prediction (NWP). The proposed method employs augmented Riemann solvers and the augmented HLL solver (HLLS) is considered. The TENO reconstruction method, which has not been applied to NWP before, is thoroughly assessed and found to have enhanced behavior for turbulent flows and underresolved solutions compared to the traditional WENO scheme. The proposed methodology allows for the simulation of atmospheric flows at meso- and micro-scales in an implicit Large Eddy Simulation manner.