Date: Friday, March 13, 2015
Location: 1084 East Hall (3:00 PM to 4:00 PM)
Title: Uniform error estimates for fluid flow with moving boundaries using finite difference methods
Abstract: Recently there has been extensive development of numerical methods for fluid flow interacting with moving boundaries or interfaces, using regular finite difference grids which do not conform to the boundaries. Simulations at low Reynolds number have demonstrated that, with certain choices in the design of the method, the velocity can be accurate to about O(h^2) while discretizing near the interface with truncation error as large as O(h). We will describe error estimates which verify that such accuracy can be achieved in a simple prototype problem, even near the interface, using corrections to difference operators as in the immersed interface method. We neglect errors in the interface location and derive uniform estimates for the fluid velocity and pressure. We will first discuss maximum norm estimates for finite difference versions of the Poisson equation and diffusion equation with a gain of regularity. We will then describe the application to the NavierStokes equations.
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Speaker: J. Thomas Beale
Institution: Duke University
Event Organizer: Shravan Veerapaneni shravan@umich.edu
