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http://dx.doi.org/10.12652/Ksce.2011.31.3B.293

Diagonalized Approximate Factorization Method for 3D Incompressible Viscous Flows  

Paik, Joongcheol (강릉원주대학교 공과대학 토목공학과)
Publication Information
KSCE Journal of Civil and Environmental Engineering Research / v.31, no.3B, 2011 , pp. 293-303 More about this Journal
Abstract
An efficient diagonalized approximate factorization algorithm (DAF) is developed for the solution of three-dimensional incompressible viscous flows. The pressure-based, artificial compressibility (AC) method is used for calculating steady incompressible Navier-Stokes equations. The AC form of the governing equations is discretized in space using a second-order-accurate finite volume method. The present DAF method is applied to derive a second-order accurate splitting of the discrete system of equations. The primary objective of this study is to investigate the computational efficiency of the present DAF method. The solutions of the DAF method are evaluated relative to those of well-known four-stage Runge-Kutta (RK4) method for fully developed and developing laminar flows in curved square ducts and a laminar flow in a cavity. While converged solutions obtained by DAF and RK4 methods on the same computational meshes are essentially identical because of employing the same discrete schemes in space, both algorithms shows significant discrepancy in the computing efficiency. The results reveal that the DAF method requires substantially at least two times less computational time than RK4 to solve all applied flow fields. The increase in computational efficiency of the DAF methods is achieved with no increase in computational resources and coding complexity.
Keywords
incompressible viscous flow; artificial compressibility; diagonalized approximate factorization; efficiency;
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