A hybrid finite volume method for advection equations and its applications in population dynamics

TL;DR

This paper introduces a hybrid finite volume numerical scheme combining anti-dissipative and high-accuracy methods to precisely solve transport equations, especially useful in population dynamics modeling for accurate long-term behavior prediction.

Contribution

A novel hybrid finite volume scheme that effectively captures transport solutions without artifacts, suitable for long-term population dynamics analysis.

Findings

Accurately captures solutions without numerical diffusion or oscillations.

Preserves mass and asymptotic properties of the solution.

Applicable to both regular and discontinuous initial data.

Abstract

We present in this paper a very adapted finite volume numerical scheme for transport type-equation. The scheme is an hybrid one combining an anti-dissipative method with down-winding approach for the flux and an high accurate method as the WENO5 one. The main goal is to construct a scheme able to capture in exact way the numerical solution of transport type-equation without artifact like numerical diffusion 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 behavior of the solution are of central importance in the modeling what is often the case in context of population dynamics where the final distribution of the considered population and its mass preservation relation are required for prediction.