A CONSERVATIVE ISOPARAMETRIC SPECTRAL ELEMENT METHOD FOR FORCED CONVECTION; APPLICATION TO FULLY DEVELOPED FLOW IN PERIODIC GEOMETRIES

Abstract

This paper addresses the problem of unsteady, flux-driven, fully developed forced convection in general periodic configurations, in which globed conservation properties are used to uniquely determine the proper form for developed thermal profiles. A numerical implementation of the problem is formulated using the isoparametric spectral element method, a high-order (exponentially convergent) finite-element technique for solution of the unsteady incompressible Navier-Stokes and energy equations. As the problem statement requires global energy balance, special emphasis is placed on proper treatment of the convective terms so as to ensure conservation of thermal energy in the appropriate discrete sense. The technique is applied to several test problems, including steady-periodic flow in grooved channels and steady flow past cylindrical obstructions, to indicate the stability, accuracy, and generality of the formulation.