Grid adaptation with WENO schemes for non-uniform grids to solve convection-dominated partial differential equations

J. Smit, M. van Sint Annaland, J.A.M. Kuipers

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    Abstract

    The numerical solution of non-stationary convection-dominated partial differential equations (PDEs), as for example encountered in the simulation of reverse flow reactors, can be a computationally quite demanding task because of the prevailing steep concentration and temperature gradients. The computational effort can be greatly reduced with higher-order discretisation schemes for the convection terms and with an automatic, local grid adaptation. In this paper, WENO schemes (e.g. Advanced Numerical Approximations of Nonlinear Hyperbolic Equations, Lecture Notes in Mathematics, vol. 1697, Springer, Berlin, 1998, pp. 325¿432) are used for the convection terms and a local grid adaptation technique is presented that uses the smoothness indicators and interpolation polynomials of the WENO schemes. It is shown that the number of grid cells required to accurately capture steep gradients can be greatly reduced with this grid adaptation technique. Finally, the capabilities of the numerical algorithm is demonstrated for the simulation of a reverse flow reactor.
    Original languageUndefined
    Pages (from-to)2609-2619
    Number of pages10
    JournalChemical engineering science
    Volume60
    Issue number10
    DOIs
    Publication statusPublished - 2005

    Keywords

    • METIS-228856
    • IR-54576

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