A Cartesian grid method for viscous incompressible flows with complex immersed boundaries

A CARTESIAN GRID -METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS WITH COMPLEX IMMERSED BIOUNDAW’IES’ T. Ye’, R. Mittal* Department of Mechariictil Engineering University of Florida Gainesville, Florida, 32611 H. S. Udaykumafl and W. Shyy4 Department of Aerospace Engineering, Mechanics and Engineering Science University of Florida Gainesville, Florida. 32611 ABSTRACT A Cartesian-grid method has been developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite-volume method based on. a second-order accurate central-difference scheme is used in conjunction with a two-step fractional-step procedure. A new interpolation procedure for accurate discretization of the governing equation in cells that are’cut by immersed boundaries is presented which preserves the second-order spatial accuracy of the underlying solver. The convergence of the pressure Poisson equation 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 demonstrated.

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