Assessment of a symmetry preserving JFNK method for atmospheric convection

TL;DR

This paper introduces a symmetry-preserving Jacobian-free Newton-Krylov (JFNK) method for atmospheric convection simulations, which maintains key physical symmetries and improves conservation properties, validated through benchmark and real-world data.

Contribution

The paper presents a novel symmetry-preserving JFNK method that better conserves physical quantities in atmospheric flow simulations compared to traditional approaches.

Findings

The method effectively conserves mass and energy.

It accurately models penetrative convection and urban heat island effects.

Results align well with laboratory and field measurements.

Abstract

Numerical simulations of nonhydrostatic atmospheric flow, based on linearly decoupled semi-implicit or fully-implicit techniques, usually solve linear systems by a pre-conditioned Krylov method without preserving the skew-symmetry of convective operators. We propose to perform atmospheric simulations in such a fully-implicit manner that the difference operators preserve both the skew-symmetry and the tightly nonlinear coupling of the differential operators. We demonstrate that a symmetry-preserving Jacobian-free Newton-Krylov~(JFNK) method mimics a balance between convective transport and turbulence dissipation. We present a wavelet method as an effective symmetry preserving discretization technique. The symmetry-preserving JFNK method for solving equations of nonhydrostatic atmospheric flows has been examined using two benchmark simulations of penetrative convection -- a) dry thermals rising in a neutrally stratified and stably stratified environment, and b) urban heat island circulations for effects of the surface heat flux $H_0$ varying in the range of $25 \le H_0 \le 930$Wm$^{-2}$.The results show that an eddy viscosity model provides the necessary dissipation of the subgrid-scale modes, while the symmetry-preserving JFNK method provides the conservation of mass and energy at a satisfactory level. Comparisons of the results from a laboratory experiment of heat island circulation and a field measurement of potential temperature also suggest the modelling accuracy of the present symmetry-preserving JFNK framework.