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An accurate Cartesian grid method for viscous incompressible flows with complex boundaries (1999)
| Venue: | J. Comput. Phys |
| Citations: | 91 - 12 self |
BibTeX
@ARTICLE{Ye99anaccurate,
author = {T. Ye and R. Mittal and H. S. Udaykumar and W. Shyy},
title = {An accurate Cartesian grid method for viscous incompressible flows with complex boundaries},
journal = {J. Comput. Phys},
year = {1999},
pages = {209}
}
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Abstract
A Cartesian grid method has been developed for simulating two-dimensional unsteady, viscous, incompressible flows with complex immersed boundaries. A finitevolume method based on a second-order accurate central-difference scheme is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second-order spatial accuracy of the underlying solver. The presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations. The convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh. The accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is
Keyphrases
viscous incompressible flow complex boundary immersed boundary accurate cartesian grid method key aspect spatial discretization scheme finitevolume method incompressible flow second-order accurate central-difference scheme linear operator second-order spatial accuracy iterative solution systematic development new interpolation procedure complex immersed boundary underlying solver accurate discretization boundary condition underlying mesh preconditioned conjugate gradient method structured nature two-step fractional-step procedure canonical flow cartesian grid method
