A numerical study of heat island flows in an open domain: Stationary solutions

TL;DR

This paper uses two-dimensional numerical simulations to study heat island-induced natural convection in an unbounded domain, employing thermal sponge layers and finite volume methods to analyze stationary solutions at Rayleigh numbers up to 10^5.

Contribution

It introduces a numerical approach with thermal sponge layers and finite volume discretization to effectively simulate heat island flows in an unbounded domain.

Findings

Stationary solutions are obtained for Ra ≤ 10^5.

Thermal sponge layers effectively simulate unbounded domains.

Second-order finite volume scheme accurately captures flow dynamics.

Abstract

We present two dimensional numerical simulations of a natural convection problem in an unbounded domain. A thermal stratification is applied in the vertical direction and the flow circulation is induced by a heat island located on the ground. For this problem, thermal perturbations are convected in the horizontal direction far from the heated element so that very elongated computational domains have to be used in order to compute accurate numerical solutions. To avoid this difficulty thermal sponge layers are added at the vertical boundaries. With this approach, stationary solutions at $Ra\le 10^5$ are investigated. Boussinesq equations are discretized with a second-order finite volume scheme on a staggered grid combined with a second-order projection method for the time integration.