A study of a WENO-TVD finite volume scheme for the numerical simulation of atmospheric advective and convective phenomena

TL;DR

This paper introduces a WENO-TVD finite volume scheme designed for simulating atmospheric advective and convective phenomena, combining high-order spatial reconstruction with robust time integration for improved accuracy.

Contribution

The paper develops a novel WENO-TVD scheme with flux-centered limiters and third-order RK-TVD time discretization tailored for atmospheric simulations involving complex flow dynamics.

Findings

Demonstrates convergence and robustness in linear advection tests

Effectively captures atmospheric convection in 2D Euler simulations

Provides comprehensive performance evaluation for atmospheric applications

Abstract

We present a WENO-TVD scheme for the simulation of atmospheric phenomena. The scheme considers a spatial discretization via a second-order TVD flux based upon a flux-centered limiter approach, which makes use of high-order accurate extrapolated values arising from a WENO reconstruction procedure. Time discretization is performed with a third order RK-TVD scheme, and splitting is used for the inclusion of source terms. We present a comprehensive performance study of the method in atmospheric applications involving advective and convective motion. We present a set of tests for space-dependent linear advection, where we assess convergence and robustness with respect to the parameters of the scheme. We apply the method to approximate the 2D Euler equations in a series of tests for atmospheric convection.