A Monotone, Higher-Order Accurate, Fixed-Grid Finite-Volume Method for Advection Problems with Moving Boundaries

In this paper, 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 an intelligent way such that they accurately accommodate the boundary conditions valid on the moving body. The first results obtained are very accurate, without requiring much computational overhead. It is anticipated that the method can be easily and successfully extended to real fluid-flow equations.