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Fluid Dynamics Seminar

Monday, Apr. 16, 2012, 4:00 PM
Cullimore, Room 611
New Jersey Institute of Technology

Convergence analysis of the immersed boundary method

Yang Liu

Department of Mathmatics, Drexel University

Abstract

Many problems involving internal interfaces can be formulated as partial differential equations with singular source terms. Numerical approximation to such problems on a regular grid necessitates suitable regularizations of delta functions. We study the convergence properties of such discretizations for constant coefficient elliptic problems using the immersed boundary method as an example. We show how the order of the differential operator,or der of the finite difference discretization, and properties of the discrete delta function all influence the local convergence behavior. In particular,w e show how a recently introduced property of discrete delta functions - the smoothing order - is important in the determination of local convergence rates.