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A numerical study on a nonlinear conservation law model pertaining to manufacturing system

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  • Tanmay Sarkar

    (Indian Institute of Technology Madras)

Abstract

This paper deals with a numerical scheme applied to a conservation law model of manufacturing system incorporating yield loss. Yield loss involving a singular term has been considered. Even though an explicit form of the material density in a production system can be obtained under certain assumptions, in general, it is difficult to get an explicit form of the material density. On the other hand, the singular term in a conservation law model imposes severe challenges for the numerical approximations on regular grids. Moreover, an approximate solution often converges to a wrong weak solution. A finite volume type numerical scheme has been studied. The convergence of the numerical solution towards entropy solution (in the Kruzkov sense) is proved. Numerical experiments are presented to get the overview of density distribution and outflux of the system.

Suggested Citation

  • Tanmay Sarkar, 2016. "A numerical study on a nonlinear conservation law model pertaining to manufacturing system," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 655-671, December.
    • Handle: RePEc:spr:indpam:v:47:y:2016:i:4:d:10.1007_s13226-016-0199-y
    DOI: 10.1007/s13226-016-0199-y
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    References listed on IDEAS

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    1. Dieter Armbruster & Daniel E. Marthaler & Christian Ringhofer & Karl Kempf & Tae-Chang Jo, 2006. "A Continuum Model for a Re-entrant Factory," Operations Research, INFORMS, vol. 54(5), pages 933-950, October.
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