Advection-reaction type partial differential equations model a wide variety of phenomena in several disciplines in physics, chemistry, environmental sciences, geometry, financial mathematics and many others. Generally, these non-linear inhomo-geneous equations must be solved in complicated multi-dimensional domains and thus analytical solutions are only available under very special circumstance...

ADER schemes are numerical methods, which can reach an arbitrary order of accuracy in both space and time. They are based on a reconstruction procedure and the solution of generalized Riemann problems. However, for general boundary conditions, in particular of Dirichlet type, a lack of accuracy might occur if a suitable treatment of boundaries conditions is not properly carried out. In this wor...

A space-time Finite Volume method is devised to simulate incompressible viscous flows in an evolving domain. Inspired by the ADER (based on a Finite-Element-prediction/Finite-Volume-correction approach), Navier-Stokes equations are discretized onto overset grid which able take into account both shape of possibly moving object and evolution compact transmission condition employed order mutually ...