High order positivity-preserving finite volume WENO schemes for a hierarchical size-structured population model

In this paper we develop high order positivity-preserving finite volume weighted essentially non-oscillatory (WENO) schemes for solving a hierarchical size-structured population model with nonlinear growth, mortality and reproduction rates. We carefully treat the technical complications in boundary conditions and global integration terms to ensure high order accuracy and positivity-preserving property. Comparing with the previous high order difference WENO scheme for this model, the positivity-preserving finite volume WENO scheme has a comparable computational cost and accuracy, with the added advantage in positivity-preserving and L1 stability. Numerical examples including the one for the evolution of the population of Gambusia affinis, are presented to illustrate the good performance of the scheme.