Fictitious domain method with penalty for an incompressible fluid

Abstract

Fictitious domain method shows great advantages when handling problems with complex and constantly varying domains. In this article, we propose an algorithm which extends the fictitious domain method by introducing penalties. Test results with the numerical examples of backward facing step problem and the flow around steady and dynamic cylinder problem show that the algorithm we propose is highly efficient for solving incompressible fluid problems.

Topology design of three-dimensional continuum structures using isosurfaces

“…FDM is capable of simplifying the domain of the problem by using a regular fixed domain. This method has been in existence since the early 1950s and has been extensively used to solve problems such as: particle flow, heat transfer, fluid flow, shape and topology optimization, to name but a few [25][26][27][28][29][30][31][32][33]. In 1999 Garcia and Steven [34], were amongst the first to applied FDM for structural shape optimization, calling the method Fixed-Grid Finite Elements Analysis (FG-FEA).…”