An Efficient Segregated Algorithm for Incompressible Fluid Flow and Heat Transfer Problems—IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations) Part I: Mathematical Formulation and Solution Procedure

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Abstract
An efficient segregated solution procedure for incompressible fluid flow and heat transfer problems is proposed. The new algorithm is called IDEAL (Inner Doubly Iterative Efficient Algorithm for Linked Equations). In the new algorithm there exist inner doubly iterative processes for the pressure equation, which almost completely overcome two approximations in the SIMPLE algorithm. Thus the coupling between velocity and pressure is fully guaranteed, greatly enhancing the convergence rate and stability of the iteration process. The mathematical formulation and solution procedure of the IDEAL algorithm are described in this article. In Part II, application examples are provided to show the features and feasibility of the new algorithm.