CONTROL VOLUME FINITE-ELEMENT METHOD FOR HEAT TRANSFER AND FLUID FLOW USING COLOCATED VARIABLES— 1. COMPUTATIONAL PROCEDURE

Abstract

A novel computational procedure for the prediction of incompressible fluid flow using primitive variables is presented. The formulation retains the geometric flexibility of the finite-element method and derives the governing discrete algebraic equations by using a conservation balance applied to discrete control volumes distributed throughout the domain. A novel method of closure, to relate the control volume surface values to the nodal point values, is introduced whereby a local discrete analog to the governing differential equation is formed at the control volume Surfaces. From this discrete equation analog the control surface values are determined in terms of the nodal values that represent the discrete problem unknowns. The manner in which this discrete equation is formed, solved, and used permits resolution of two longstanding problems in computational fluid dynamics, namely accurate convection modeling and preclusion of pressure field decoupling. A new and general boundary condition specification in terms of normal and tangential entities is also introduced.