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Hyperbolic Conservation Laws Having Source Terms And Donor Cell Differencing

Author

Listed:
  • FARHAD ALI

    (Dr Abdul Qadeer Khan Research Laboratories P.O. Box 502, Rawalpindi, Pakistan)

  • M.A. KASSAR

    (Dr Abdul Qadeer Khan Research Laboratories P.O. Box 502, Rawalpindi, Pakistan)

Abstract

Modifications in the integration of the source terms in hyperbolic conservation laws such as those governing combustion, detonation and radiative transport, with a first order upwind differencing technique are proposed and analysed. The von Neuman stability and phase error analysis for a linear scalar equation, together with a few test problems is presented in order to compare the performance of the resulting variants of the donor cell scheme. It is established that when the source term is integrated using higher order formulae, the resulting scheme gives better resolution and has better stability limit and phase accuracy, compared to the standard single nodal value replacement. It is shown that integration by the trapezoidal rule gives sufficient accuracy and further improvement may not necessarily be achieved using better methods, such as the Simpson’s rule.

Suggested Citation

  • Farhad Ali & M.A. Kassar, 1994. "Hyperbolic Conservation Laws Having Source Terms And Donor Cell Differencing," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 5(03), pages 519-536.
    • Handle: RePEc:wsi:ijmpcx:v:05:y:1994:i:03:n:s0129183194000702
    DOI: 10.1142/S0129183194000702
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