A conservative MURD scheme on moving domains: Application to three-dimensional free surface flows

Abstract

We introduce a monotonic and conservative numerical scheme for the resolution of the linear advection problem set on a moving domain. The scheme is based on an extension to moving domains of the Multidimensional Upwind Residual Distributive (MURD) approach. The properties ensured by the residual distribution schemes set on fixed domains are not altered by the domain movement, except for the conservation of the advected quantity. We introduce in this paper an additional condition which ensures the conservation properties of the MURD scheme on amoving domain. Several numerical tests have been performed, providing satisfying results in terms of conservation of the advected quantity