Finite-volume discretizations and immersed boundaries
Yunus Hassen, Barry Koren · Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands · 2010
In this chapter, an accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems.As is standard in immersed-boundary methods, moving bodies are embedded in a fixed 'Cartesian' grid.The essence of the present method is that specific fluxes in the vicinity of a moving body are computed in such a way that they accurately accommodate the boundary conditions valid on the moving body.To suppress wiggles, tailor-made limiters are introduced for these special fluxes.The first results obtained are very accurate, without requiring much computational overhead.It is anticipated that the method can readily be extended to real fluid-flow equations.