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

[摘要] In this paper we develop high order positivity-preserving finite volume weighted essentially non-oscillatory (WEND) 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 the positivity-preserving property. Comparing with the previous high order difference WEND scheme for this model, the positivity-preserving finite volume WEND scheme has a comparable computational cost and accuracy, with the added advantages of being positivity-preserving and having L(1) stability. Numerical examples, including that of the evolution of the population of Gambusia affinis, are presented to illustrate the good performance of the scheme. (C) 2011 Elsevier B.V. All rights reserved.

[发布日期] 2011-10-01

[效力级别]  Proceedings Paper

[关键词] Weighted essentially non-oscillatory (WENO) schemes;Finite volume schemes;Accuracy;Positivity-preserving