1. A high order positivity preserving DG method for coagulation-fragmentation equations
- Author
-
Hailiang Liu, Gerald Warnecke, and Robin Gröpler
- Subjects
Conservation law ,Discretization ,Applied Mathematics ,Population balance equation ,Fragmentation (computing) ,010103 numerical & computational mathematics ,Numerical Analysis (math.NA) ,01 natural sciences ,3. Good health ,Computational Mathematics ,Discontinuous Galerkin method ,65M60, 65M12, 65R20, 35L65, 82C22 ,FOS: Mathematics ,Applied mathematics ,Order (group theory) ,Mathematics - Numerical Analysis ,0101 mathematics ,Mathematics - 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., 16 pages, 2 figures, 6 tables
- Published
- 2017