Donor acceptor scheme

The donor-acceptor scheme is a numerical scheme for treating the volume of fluid method in the field of computational fluid dynamics. Originally introduced by Ramshaw and Trapp in 1976 and extend by Hirt and Nichols in their VOF article from 1981, the donor-acceptor scheme revolves around the idea of including data from the downwind cell (acceptor cell) of a cell face to predict the volume fraction transported through it during a time step. In addition to this information from the acceptor scheme, information of the availability of the fluids from the upwind cell (donor cell) is required. This approach, known as controlled downwinding, is necessary in order to avoid non-physical volume fraction values smaller than zero or larger than unity. The donor-acceptor scheme has since its introduction served as a basis for compressive differencing schemes and higher order schemes used to treat the advection of the fraction function in the volume of fluid method.