Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 200, Issue 23-24, Pages 2083-2093Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2011.02.007
Keywords
ADI; Direction splitting; Incompressible flows; Navier-Stokes; Pressure Poisson equation; Time splitting
Funding
- King Abdullah University of Science and Technology (KAUST) [KUS-C1-016-04]
- Institute of Applied Mathematics and Computational Science
- Institute of Scientific Computing at Texas AM University
- NSERC
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We introduce in this paper a new direction splitting algorithm for solving the incompressible Navier-Stokes equations. The main originality of the method consists of using the operator (1 - partial derivative(xx))(1 - partial derivative(yy))(1 -partial derivative(zz)) for approximating the pressure correction instead of the Poisson operator as done in all the contemporary projection methods. The complexity of the proposed algorithm is significantly lower than that of projection methods, and it is shown the have the same stability properties as the Poisson-based pressure-correction techniques, either in standard or rotational form. The first-order (in time) version of the method is proved to have the same convergence properties as the classical first-order projection techniques. Numerical tests reveal that the second-order version of the method has the same convergence rate as its second-order projection counterpart as well. The method is suitable for parallel implementation and preliminary tests show excellent parallel performance on a distributed memory cluster of up to 1024 processors. The method has been validated on the three-dimensional lid-driven cavity flow using grids composed of up to 2 x 10(9) points. (c) 2011 Elsevier B.V. All rights reserved.
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