Second order scheme for scalar conservation law with discontinuous flux

TL;DR

This paper extends second order flux TVD schemes to scalar conservation laws with discontinuous flux, ensuring entropy conditions and demonstrating improved accuracy over first order schemes through numerical experiments.

Contribution

It adapts the flux TVD second order scheme for discontinuous flux problems, satisfying (A,B)-entropy conditions with proper interface modifications.

Findings

Second order schemes outperform first order schemes in accuracy.

Numerical solutions are comparable to those from minimod limiter schemes.

The proposed schemes satisfy (A,B)-entropy conditions.

Abstract

Burger et al.in \cite{karlsen-1} proposed a flux TVD (FTVD) second order scheme by using a new non local limiter algorithm for conservation laws with discontinuous flux modeling clarifier thickener units. In this work we show that their idea of constructing FTVD second order schemes also can be used to construct second order schemes satisfying (A,B)-entropy condition for the scalar conservation law with discontinuous flux with proper modification at the interface. We present numerical experiments to show the superiority of the second order schemes over the monotone first order schemes. We show further from numerical experiments that solutions from these schemes are comparable with the second order schemes obtained from minimod limiter.