10.1111/sapm.12740">
 

Steady Boussinesq Convection: Parametric Analyticity and Computation

Document Type

Article

Publication Date

7-2024

Abstract

Steady solutions to the Navier-Stokes equations with internal temperature forcing are considered. The equations are solved in two dimensions using the Boussinesq approximation to couple temperature density fluctuations. A perturbative Stokes expansion is used to prove that that steady flow variables are parametrically analytic in size of the forcing. The Stokes expansion is complemented with analytic continuations, via functional Padé approximation. The zeros of the denominator polynomials in the Padé approximants are observed to agree with a numerical prediction for the location of singularities of the steady flow solutions. The Padé representations not only prove to be good approximations to the true flow solutions for moderate intensity forcing, but are also used to initialize a Newton solver to compute large amplitude solutions. The composite procedure is used to compute steady flow solutions with forcing several orders of magnitude larger than the fixed-point method developed in previous work.

Comments

This is a subscription-access article, available to readers with a subscription to Studies in Applied Mathematics, using the DOI link below.

Current AFIT students, faculty, and staff may access the full article by clicking here.

Source Publication

Studies in Applied Mathematics

This document is currently not available here.

Share

COinS