A High Order Positivity Preserving DG Method for Coagulation-Fragmentation Equations

Abstract

We design, analyze, and numerically validate a novel discontinuous Galerkin (DG) method for solving the coagulation-fragmentation equations. The DG discretization is applied to the conservative form of the model, with flux terms evaluated by Gaussian quadrature with $Q=k+1$ quadrature points for polynomials of degree $k$. The first moment (total mass) is naturally conserved by the scheme construction, and the positivity of the mass density is enforced by the use of a scaling limiter based on positive cell averages. The positivity of cell averages is shown to propagate by the time discretization, provided a proper time step restriction is imposed.