A finite-volume method for convection problems with embedded moving boundaries

An accurate method, using a novel immersed-boundary approach, is presented for numerically solving linear, scalar convection problems. Moving interior boundary conditions are embedded in the fixed-grid fluxes in the direct neighborhood of the moving boundaries. Tailor-made limiters are derived such that the resulting scheme is monotone. The 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.