Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 197, Issue 25-28, Pages 2119-2130Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2007.08.008
Keywords
immersed boundary method; Navier-Stokes equations; Cartesian grid method; finite difference; fast Poisson solvers; irregular domains
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We present a method for solving the incompressible Navier-Stokes equations in irregular domains. These equations are discretized using finite difference method in a uniform Cartesian grid. Stationary rigid boundaries are embedded in the Cartesian grid and singular forces are applied at the rigid boundaries to impose the no-slip conditions. The singular forces are then distributed to the nearby Cartesian grid points using the immersed boundary method. In the present work, the singular forces are computed implicitly by solving a small system of equations at each time step. This system of equations is derived from a second order projection method. The main advantage of this method is that it imposes the no-slip boundary condition exactly and avoids the need for small time step to maintain stability. The ability of the method to simulate viscous flows in irregular domains is demonstrated by applying to 2-dimensional flows past a circular cylinder, multiple rigid obstacles and 3-dimensional flow past a sphere. (C) 2007 Elsevier B.V. All rights reserved.
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