A high order positivity preserving DG method for coagulation-fragmentation equations

TL;DR

This paper introduces a high-order discontinuous Galerkin method for coagulation-fragmentation equations that preserves positivity of the solution through a novel limiter and proper time step restrictions.

Contribution

The paper presents a new high-order DG method with a positivity-preserving limiter specifically designed for coagulation-fragmentation equations.

Findings

Numerical validation confirms the positivity preservation.

The method achieves high-order accuracy.

Positivity is maintained under suitable time step restrictions.

Abstract

We design, analyze and numerically validate a novel discontinuous Galerkin 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 positivity of the numerical solution is enforced through a simple scaling limiter based on positive cell averages. The positivity of cell averages is propagated by the time discretization provided a proper time step restriction is imposed.