An entropy admissible time splitting scheme for a conservation law model of manufacturing system

TL;DR

This paper introduces a new splitting scheme for a conservation law model of manufacturing systems with yield loss, ensuring stability and convergence to entropy solutions, validated through numerical experiments.

Contribution

It proposes a novel entropy admissible splitting scheme that handles yield loss implicitly and guarantees stability and convergence for manufacturing system models.

Findings

The scheme is total variation bounded despite yield loss.

Convergence to entropy solutions is rigorously proved.

Numerical experiments confirm the scheme's effectiveness.

Abstract

This paper deals with a splitting method applied to a conservation law model of manufacturing system incorporating yield loss. A splitting scheme has been proposed. The yield loss term is treated by solving implicitly an ordinary differential equation and the hyperbolic part is approximated by a finite volume scheme. Bounded variation stability has been studied. Due to yield loss, proposed scheme is total variation bounded. The convergence of the numerical solution towards entropy solution (in the Kruzkov sense) is proved. Numerical experiments are presented to demonstrate the performance of the scheme.