| Title |
Diagonalized Approximate Factorization Method for 3D Incompressible Viscous Flows |
| Keywords |
incompressible viscous flow;artificial compressibility;diagonalized approximate factorization;efficiency;비압축성 점성 흐름;인공압축성;대각행렬화된 근사 인수분해;효율성 |
| Abstract |
An efficient diagonalized approximate factorization algorithm (OAF) 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. |