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    Numerical simulation of the wave (shock profile) propagation of the Kuramoto-Sivanshinky equation using an adaptive mesh method

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    Muzadziwa_NUMERICAL_SIMULATION-OF_THE_WAVE_SHOCK_PROFILE_PROPAGATION.pdf (1.096Mb)
    Date
    2016-04
    Author
    Muzadziwa, Denson
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    Abstract
    In this dissertation we solve the Kuramoto-Sivanshinsky equation numerically using an adaptive mesh method. Discretization in time is done using Crank- Nicolson with septic Hermite collocation method applied in space on an adaptive mesh. The adaptive mesh is a solution of moving mesh partial differential equations derived from the principle of equidistribution. A rezoning approach which works with a decoupled solution procedure is then used to develop a matlab code to produce the numerical results. The method is evaluated for effectiveness and computational efficiency with the most current best method available in the literature.
    URI
    http://hdl.handle.net/10646/2581
    Subject
    Kuramoto-Sivanshinsky
    adaptive mesh method
    Crank- Nicolson
    septic Hermite collocation method
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