Currently, the Electronic CD Forum provides participants with the definitions of the 1-D problems from the original CD forums. It also provides them with animations of solutions to some of these problems. These solutions are obtained using a range of finite difference (FD) or finite element (FE) techniques. An interface is provided which allows the participants to experiment with the input parameters (e.g. velocity and diffusion) and the solution method.
An important but only partially implementd feature of the Electronic CD forum is be the ability of participants to submit and retrieve solutions. This involves maintaining a database of solutions submitted to the CD forum, and providing the ability to search this database for several parameters including author, problem type, and solution method. This feature will allow developers of new solution techniques to compare their results with those contained in the CD forum solution database.
Problems ranged in complexity from the transport of Gauss and triangle-hills or advancing fronts in one-dimensional uniform flow to the transport of cone-hills in a two-dimensional multi-cell deformational flow. Error measures differed somewhat for each problem, but included integral and discrete norms (measures of overall square error), peak concentration error (point measure of artificial damping), maximum negative concentration (point measure of artificial dispersion or spurious oscillation), 0th spatial moment (integral measure of mass conservation), 1st spatial moment (integral measure of phase error), and 2nd spatial moment (integral measure of artificial diffusion).
Approximately twenty sets of solutions were submitted, with some contributors choosing to solve as few as one problem and others solving all five. Techniques varied widely and included centered and upwind Eulerian methods using both finite difference and finite element formulations, several types of Eulerian-Lagrangian methods, spectral methods and particle tracking methods. The disciplines of the contributors also varied widely, representing civil engineering, oceanography, atmospheric modeling, and groundwater hydrology.
We now picture the ECDF behaving more like a live forum while also functioning as an archive for information pertaining to CD problems. We want the ECDF to be interactive, allowing the body of knowledge contained in it to evolve dynamically through contributions by the participants themselves.
Several components will be required to support our vision of the ECDF. These include general information about CD problems, a database of solutions to CD Forum problems, and a bibliographic database of literature related to CD problems. General information will include anything that helps participants to become more familiar with CD problems (e.g. problem definitions, example solutions, and an interactive model). The solution database will allow participants to submit their own solutions and compare solutions contained within the database. Much like the solution database, the bibliographic database will allow participants to add relevant references.
Our current implementation of the CD Forum allows a participant to choose a particular 1-D problem for which they would like to see a solution. This choice is made from an HyperText Markup Language (HTML) form (Figure 1). Once the selection is made, the HTTPD server returns the appropriate animation in FLC (Autodesk Animator Pro(TM)) format and tags it with a unique MIME type (video/x-flc) (Figure 2). In order to actually view the animation, the participants browser must be configured to recognize the video/x-flc and then send the animation to an appropriate viewer. (XAnim [2] is an example of one such tool for X11)
Mosaic can be configured to recognize files with MIME type video/x-flc by adding the line "video/x-flc; xanim %s" to a file called .mailcap in the participants home directory. This assumes that you have the XAnim software already installed. (For further information on multimedia configuration, see http://www.ncsa.uiuc.edu/SDG/Software/Mosaic/Docs/d2-multimedia.html)
BB1D is a CD model which solves 1-D problems using either a FD or FE method. The FD method can use either centered or upwind differencing, and the FE method can use either 2 or 3 node elements with Lagrangian shape functions and a Galerkin formulation. BB1D also provides participants with the option of specifying their own differencing scheme. The initial condition is a Gauss hill which has configurable location, standard deviation, and amplitude. Other model parameters include the number of nodes in the grid, the length of the domain, time step, velocity, diffusion coefficient, and a fractional step parameter.
Participants control BB1D through an HTML form (Figure 3) which collects the data entered and sends it off to a CGI (Common Gateway Interface) script. This CGI script then generates the input file for BB1D, runs the simulation, and then returns the results. The results are returned to the participant in a form that is understood by the plotting package ACE/gr [3] and has a unique MIME type (application/x-xmgr-pipe). If you have ACE/gr installed and your browser is configured correctly, the solution should appear as an animation.
Since the model actually runs on the server itself, only one participant is allowed to be running the model at any given moment. The interface form provides instructions on how to configure a browser to correctly handle MIME type application/x-xmgr-pipe, and how to obtain a copy of ACE/gr, if you don't already have one.
For security reasons, the solution database is currently not available to the entire Web. As currently implemented the solution database will eventually require a large commitment of disk space. This will become even more of a problem when we start accepting 2-D solutions. A better long term solution would be to have participants submit URLs (Universal Resource Locators) to their solutions. One potential drawback is that this requires the participants to have a mechanism for making their solutions available to the Web (e.g. HTTPD, anonymous FTP, or Gopher). However, the benefits of this approach, in our opinion, far outweigh the potential drawbacks.
The ECDF also provides the participant with a listing of solutions contained in the database. Each solution in this list is distinguished by its meta-data. The participant can select a set of solutions from the list, by clicking on the checkboxes next to the appropriate items, and receive a comparison of the solutions selected.
[2] XAnim Rev 2.68.3 by Mark Podlipec (c) 1991-1994. (ftp://ftp.x.org/contib/applications)
[3] Turner P. J., "ACE/gr User's Manual: Graphics for exploratory data analsys", Software Documentation Series, SD93, 91-3, Center for Coastal and Land-Margin Research, Oregon Graduate Institute of Science & Technology, P.O. Box 91000, Portland, OR 97291-1000, USA. (ftp://ftp.ccalmr.ogi.edu/CCALMR/pub/acegr/)
