COMPRESSIBLE COMPUTATIONAL FLUID DYNAMICS

    Hyperbolic partial differential equations describe a wide range of wave-propagation and transport phenomena arising in nearly every scientific and engineering discipline.  Here are a few animations of time-dependent solutions to 1D Euler Equations, which represent the behavior of a compressible gas.  These movies illustrate that third generation Essentially Non-Oscillatory (ENO) methods give much more accurate approximations than first generation schemes, such as Lax-Friedrichs, do. ENO schemes, originally developed by Harten, Engquist, Osher, and Chakravarthy, capture shocks, rarefactions, and contact discontinuities accurately.

Analyze results in .jpg format

   We consider the problem of an oblique shock, generated by a supersonic flow over a sharp wedge.  The problem involves the grid generation.  The Euler equations are solved in two spatial dimensions on nonrectangular grid by employing the finite volume formulations.  The animations below illustrate two different approaches.  The three shocks and four regions of homogeneous pressure are found.