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Indexed by:Journal Papers

Date of Publication:2021-05-19

Journal:INTERNATIONAL JOURNAL OF NUMERICAL METHODS FOR HEAT & FLUID FLOW

Volume:30

Issue:12

Page Number:5037-5062

ISSN No.:0961-5539

Key Words:Natural convection; Lid-driven cavity flow; Exact solutions; Artificial compressibility method; Incompressible flow and heat transfer; Spectral collocation method

Abstract:Purpose
   The purpose of this paper is to develop a combined method for three-dimensional incompressible flow and heat transfer by the spectral collocation method (SCM) and the artificial compressibility method (ACM), and further to study the performance of the combined method SCM-ACM for three-dimensional incompressible flow and heat transfer.
   Design/methodology/approach
   The partial differentials in space are discretized by the SCM with Chebyshev polynomial and Chebyshev-Gauss-Lobbatto collocation points. The unsteady artificial compressibility equations are solved to obtain the steady results by the ACM. Three-dimensional exact solutions with trigonometric function form and exponential function form are constructed to test the accuracy of the combined method.
   Findings
   The SCM-ACM is developed successfully for three-dimensional incompressible flow and heat transfer with high accuracy that the minimum value of variance can reach. The accuracy increases exponentially along with time marching steps. The accuracy is also improved exponentially with the increasing of nodes before stable accuracy is achieved, while it keeps stably with the increasing of the time step. The central processing unit time increases exponentially with the increasing of nodes and decreasing of the time step.
   Research limitations/implications - It is difficult for the implementation of the implicit scheme by the developed SCM-ACM. The SCM-ACM can be used for solving unsteady impressible fluid flow and heat transfer.
   Practical implications - The SCM-ACM is applied for two classic cases of lid-driven cavity flow and natural convection in cubic cavities. The present results show good agreement with the published results with much fewer nodes.
   Originality/value
   The combined method SCM-ACM is developed, firstly, for solving three-dimensional incompressible fluid flow and heat transfer by the SCM and ACM. The performance of SCM-ACM is investigated. This combined method provides a new choice for solving three-dimensional fluid flow and heat transfer with high accuracy.