Fluid Mechanics
Traffic Flow
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  • Theory
  • Simulation
  • Simulation

    I am interested in numerical algorithms that are highly accurate and allow for easy quantitative comparison with theories of detonation instability and nonlinear dynamics. Some of my previous work on these problems is described below.

    A. R. Kasimov, Hyperbolic dynamics of weakly curved detonations, 2008 (Submitted for
    . This paper extends and simplifies our earlier work on the theory of weakly curved and slowly evolving detonations. The evolution equation of Kasimov & Stewart (JFM'05) is proved to be hyperbolic under all conditions and is solved numerically in two dimensions using a high-order WENO algorithm for spatial discretization and an RK3 time integration.

    A movie showing the development of shock-shocks. The normal speed D, the shock slope psi, and the shock shape phi, are shown.


    B. Taylor, A. R. Kasimov, D.S. Stewart, Mode selection in weakly unstable two-dimensional
    detonations, 2008 (Submitted for publication)
    . In this paper we report a new numerical algorithm for simulation of multi-dimensional detonation waves in a shock-attached frame.

    Watch these movies to see:

    1) How the initial very low-amplitude and high-frequency perturbation grows into a particular most unstable mode and later develops into a full-fledged cellular detonation. Shown are the shock shape f, the normal speed D, and the pressure field in the reaction zone.

    2) A 3D view of the same pressure field.


    A. R. Kasimov and D. S. Stewart, On the dynamics of self-sustained detonations: A numerical study in the shock-attached frame, Physics of Fluids, 16(10), 3566-3578, 2004 (PDF). In this paper we introduced a numerical algorithm for simulation of one-dimensional detonation waves in a frame attached to the lead shock. This allows for very accurate computation of the detonation speed as well as the reaction-zone dynamics.