A Pseudospectral Multidomain Method for Conjugate Conduction-Convection in Enclosures

Abstract

A pseudospectral multidomain method is proposed for the solution of the two-dimensional incompressible Navier-Stokes equations and energy equation. The governing equations are spatially discretized by the Chebyshev pseudospectral method. Within each subdomain, the algebraic system is solved by a semi-implicit pseudotime method, in which the convective and source terms are explicitly marched by the Runge-Kutta method, and the diffusive terms are implicitly marched by the matrix diagonalization method. An interface/boundary-value updating algorithm is proposed to obtain the interfaces and boundaries values to satisfy both the boundary conditions and interface transmission conditions. Since the solution of the interior collocation point values and the updating of interface/boundary values are carried out independently, the multidomain method is easy to implement with an existing single-domain solver. The pseudospectral multidomain method is validated by three benchmark heat transfer problems: natural convection in a cavity, conjugate conduction-convection in a cavity with one finite-thickness wall, and conjugate conduction-convection in a cavity with both an internal heat source and finite-thickness walls. The numerical results are in excellent agreement with the benchmark solutions; high accuracy and the ability to treat complex problems with the present pseudospectral multidomain method are confirmed. The effects of wall thermal conductivity and Rayleigh number are accurately predicted.