A Java-based numerical simulation model

Version history: Original version - January, 1999; Version 2.0 - March, 1999; Versions 3.0-3.2 - November, 2001.

Links on this page:

  • Quick Start
  • Running the model
  • What you see
  • About the model
  • Handling of sound waves
  • Platform/browser-dependent weirdness
  • Click here to start the model

    Clicking on the link opens a new window. Run this model at your own risk! So far, no one has complained that the applet has crashed their browsers, trashed their systems and/or ruined their lives, though :-)

    Quick Start

    The link above starts a two-dimensional (2D) quasi-compressible model written as a Java applet. This model runs within your web browser. The example problem is a simulation of a warm bubble of air; an animation of this phenomenon is also available. To start the model, simply press the "Step forward" button (more info below). This will integrate the model forward a chosen time interval, and then a contour plot of the selected model field will be displayed (more information below). Click the button again to run the model forward another set of time steps.

    This model may run slowly on older machines. I have gotten acceptable performance from:

    For me, Netscape 4.0x runs the model very slowly on Sun Solaris workstations, up to and including the Ultra 10 model. Netscape 4.0x with Red Hat Linux 5.1 on the aforementioned Pentium II is also quite sluggish. Feel free to e-mail me with your experiences and comments.

    Running the model

    Four selectable menus are arrayed across the top. These values must be set before hitting the "Step forward" button for the first time. To change these values after running the model, you will need to reload the applet. The menus control:

    Below the plot area are two additional selectable menus:

    You can change the plot interval or field viewed at any time. These plots are made using Leigh Brookshaw's contour graphing classes. Unfortunately, negative contours are not specially marked.

    Some rudimentary information regarding model integration statistics are printed to the Java Console as the model runs. To access the Java Console in Netscape Communicator, see the "Communicator" or "Communicator > Tools" menus, depending on the program version. Each time step, the model reports the domain maximum values of each of the four prognostic variables.

    Click here to start the model

    Clicking on the link opens a new window.

    What you see

    Temperature field at 810 sec

    When you start the applet, the initial perturbation temperature field is displayed. This shows a bubble of warm air (a "thermal") that subsequently rises relative to its surroundings. The thermal's positive buoyancy creates rising motion within it and sinking motion on its flanks. The bubble initially induces high (low) perturbation pressure above (below) the bubble's center, which itself provokes divergence above (convergence below) the thermal. As the integration proceeds, the temperature field starts evincing a "mushroom" shape (see picture above). If run long enough, the thermal slams into the model's rigid upper top.

    About the model

    This is a brutally simple numerical model, being used as a demonstration device. The numerical method is a very simple one: the second-order leapfrog time/center space scheme. The lateral boundaries are periodic; the upper and lower boundaries are rigid plates. Computational diffusion is handled via a second-order term with constant coefficients that are selected by the user.

    Handling of sound waves

    In this "quasi-compressible" model, the speed of sound (normally about 350 meters per second) is treated as a free parameter. The sound wave is typically the fastest moving signal in the model, and its speed limits the time step that may be stably employed. In this model, the default sound speed is specified as 50 meters per second, which is far to small to produce a truly physically valid solution. However, it allows the model to use larger time steps, and thus runs more quickly.

    Platform/browser-dependent weirdness

    This applet exhibits different strange characteristics in different browsers and platforms. In Netscape 4.0x on the Mac, for example, the plot's background color may not be repainted after the initial plot. Also, contour labels may not appear. In the Solaris version of Netscape, the grid labelings may not show up. Also with Netscape Solaris, you may have to pass the cursor over the grey window to get the first plot to show. Etc., etc..

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    Page created January 1999, by Robert Fovell
    Updated March 1999 and November 2001