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Simplification. Conservation and Adaptivity in the Front Tracking Method

In: Hyperbolic Problems: Theory, Numerics, Applications

Author

Listed:
  • E. George

    (SUNY at Stony Brook)

  • J. Glimm

    (SUNY at Stony Brook
    Brookhaven National Laboratory)

  • J. W. Grove

    (Los Alamos National Laboratory)

  • X. L. Li

    (SUNY at Stony Brook)

  • Y. J. Liu

    (SUNY at Stony Brook)

  • Z. L. Xu

    (SUNY at Stony Brook)

  • N. Zhao

    (SUNY at Stony Brook)

Abstract

The front tracking method was first introduced by Richtmyer for the numerical solution of hyperbolic equations. The solution of hyperbolic equations contains discontinuities such as contact discontinuities and shocks. The former exist even in linear equations when the initial condition is discontinuous. The latter are associated with the nonlinearity of the hyperbolic system. Finite difference and finite volume methods give a satisfactory numerical approximation and convergence rate in the region where the solution is smooth. However they fail to deliver physically correct solutions at discontinuities, especially when the equation of state across the discontinuity is sharply different. By separating the smooth regions at the discontinuity through an interface, the front tracking method overcomes this numerical difficulty by applying finite difference solvers to each smooth subdomain while treating the discontinuity with special care and propagating the front using the exact solution of the Riemann problem.

Suggested Citation

  • E. George & J. Glimm & J. W. Grove & X. L. Li & Y. J. Liu & Z. L. Xu & N. Zhao, 2003. "Simplification. Conservation and Adaptivity in the Front Tracking Method," Springer Books, in: Thomas Y. Hou & Eitan Tadmor (ed.), Hyperbolic Problems: Theory, Numerics, Applications, pages 175-184, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-55711-8_15
    DOI: 10.1007/978-3-642-55711-8_15
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