A periodic representation of the interface for the volume of fluid method

We extend the volume of fluid method for the computation of two-phase flow to a higher order accurate method in two dimensions. The interface reconstruction by the PLIC method is thereby replaced by a periodic interface reconstruction. The advection step is reformulated and extended to higher order in order to account for the present interface representation. This periodic interface reconstruction describes the interface in terms of higher order periodic B-splines. Numerical tests verify that the theoretical order of convergence is indeed exhibited by the present method.