Abstract
Abstract In this article we discuss a fictitious domain method for the numerical solutions of three-dimensional elliptic problems with Dirichlet boundary conditions and also of the Navier-Stokes equations modeling incompressible viscous flow. The methodology for the Navier-Stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection, imbedding and incompressibility. Due to the decoupling, fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry. The resulting methodology is applied to two-dimensional unsteady external incompressible viscous flow problems and three-dimensional Stokes problems.
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