Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh--B\'enard convection

TL;DR

This paper adapts a Fourier pseudospectral method to handle Dirichlet boundary conditions for simulating Rayleigh--Bénard convection, enabling high-Rayleigh-number 2D simulations relevant to dry air and wet convection studies.

Contribution

It introduces a novel adaptation of a Fourier pseudospectral method for non-free boundary conditions in Rayleigh--Bénard convection simulations.

Findings

First 2D high-Rayleigh-number convection simulation with no-slip and Dirichlet conditions.

Demonstrates the method's effectiveness for dry air convection at R~10^9.

Provides a foundation for future wet convection studies in solar stills.

Abstract

We present the adaptation to non--free boundary conditions of a pseudospectral method based on the (complex) Fourier transform. The method is applied to the numerical integration of the Oberbeck--Boussinesq equations in a Rayleigh--B\'enard cell with no-slip boundary conditions for velocity and Dirichlet boundary conditions for temperature. We show the first results of a 2D numerical simulation of dry air convection at high Rayleigh number ($R\sim10^9$). These results are the basis for the later study, by the same method, of wet convection in a solar still.