Development of an accurate method for advection problems with embedded moving-boundaries

An accurate method, using a novel immersed-boundary approach, is presented for numerically solving advection problems. As is standard in immersed-boundary methods, moving bodies are embedded in a fixed, ‘Cartesian,’ finite-volume 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 and monotonously accommodate the boundary conditions valid on the moving body. Higher-order accurate discretizations in both space and time are presented. To suppress wiggles, tailor-made limiters are introduced for the special fluxes. The results obtained for linear scalar advection problems are very accurate, without requiring much computational overhead. It is anticipated that the method can be easily extended to real fluid-flow equation