A Hybrid Finite Volume Method for Advection Equations and Its Applications in Population Dynamics

Chang Yang (1) , Léon Matar Tine (2, 3, 4)

1 HIT Harbin Institute of Technology - Department of Mathematics
2 ICJ - Institut Camille Jordan
3 DRACULA - Multi-scale modelling of cell dynamics : application to hematopoiesis
4 MMCS - Modélisation mathématique, calcul scientifique

We present in this article a very adapted finite volume numerical scheme for transport type-equation. Thescheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux(Després and Lagoutière, C R Acad Sci Paris Sér I Math 328(10) (1999), 939–944; Goudon, Lagoutière,and Tine, Math Method Appl Sci 23(7) (2013), 1177–1215) and an high accurate method as the WENO5one (Jiang and Shu, J Comput Phys 126 (1996), 202–228). The main goal is to construct a scheme ableto capture in exact way the numerical solution of transport type-equation without artifact like numericaldiffusion or without “stairs” like oscillations and this for any regular or discontinuous initial distribution.This kind of numerical hybrid scheme is very suitable when properties on the long term asymptotic behaviorof the solution are of central importance in the modeling what is often the case in context of populationdynamics where the final distribution of the considered population and its mass preservation relation arerequired for prediction.

Mots clés: Discontinuity detector; WENO scheme; anti-diffusive method; population dynamics

Domaines: Mathématiques [math]

Chang Yang, Léon Matar Tine. A Hybrid Finite Volume Method for Advection Equations and Its Applications in Population Dynamics. Numerical Methods for Partial Differential Equations, 2017, 33 (4), pp.1114 - 1142. ⟨10.1002/num.22134⟩. ⟨hal-01646859⟩