A high order positivity preserving DG method for coagulation-fragmentation equations
This provides a provably positivity-preserving high-order numerical method for a class of integro-differential equations relevant to aerosol science and population dynamics.
The authors developed a new discontinuous Galerkin method for coagulation-fragmentation equations that preserves positivity, and validated it numerically with high-order accuracy.
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.