Performance Analyses of IDEAL Algorithm on Highly Skewed Grid System

Dongliang Sun,Peng Ding,Jinliang Xu

doi:10.1155/2014/813510

Abstract

IDEAL is an efficient segregated algorithm for the fluid flow and heat transfer problems. This algorithm has now been extended to the 3D nonorthogonal curvilinear coordinates. Highly skewed grids in the nonorthogonal curvilinear coordinates can decrease the convergence rate and deteriorate the calculating stability. In this study, the feasibility of the IDEAL algorithm on highly skewed grid system is analyzed by investigating the lid-driven flow in the inclined cavity. It can be concluded that the IDEAL algorithm is more robust and more efficient than the traditional SIMPLER algorithm, especially for the highly skewed and fine grid system. For example, at θ = 5° and grid number = 70 × 70 × 70, the convergence rate of the IDEAL algorithm is 6.3 times faster than that of the SIMPLER algorithm, and the IDEAL algorithm can converge almost at any time step multiple.

Highlights

SIMPLE [1] is the first pressure-correction algorithm, which was proposed by Patankar and Spalding in 1972
Based on the body-fitted collocated grid system in the 3D nonorthogonal curvilinear coordinates, the major points of the IDEAL algorithm are reviewed in the following
For the SIMPLER algorithm, the robustness is weakened with the decrease of the inclination angle, due to the increase of the grid skewness

Summary

Introduction

SIMPLE [1] is the first pressure-correction algorithm, which was proposed by Patankar and Spalding in 1972. The second is that the velocity corrections of the neighboring grids are neglected in order to make the final pressure-correction equation manageable. These two approximations do not affect the final converged solutions but influence the convergence rate and robustness of the algorithm greatly [2]. The first inner iteration process for pressure equation can almost completely overcome the first approximation of the SIMPLE algorithm. Skewed grids in the nonorthogonal curvilinear coordinates can decrease the convergence rate and deteriorate the calculating stability. Due to the flow complexity and convergence difficulty, the lid-driven flow in the inclined cavity is adopted to analyze the solving performance of the IDEAL algorithm on highly skewed grid system.

Governing Equations

Brief Review of IDEAL in 3D Nonorthogonal Curvilinear Coordinates

Numerical Analyses of IDEAL on Highly Skewed Grid System

Conclusions

E: Time step multiple