NUMERICAL-SOLUTIONS OF A NONLINEAR DENSITY-CURRENT - A BENCHMARK SOLUTION AND COMPARISONS

A comparison between solutions from simulations of a non-linear densit y current test problem was made in order to study the behaviour of a v ariety of numerical methods. The test problem was diffusion-limited so that a grid-converged reference solution could be generated using hig h spatial resolution. Solutions of the test problem using several diff erent resolutions were computed by the participants of the 'Workshop o n Numerical Methods for Solving Nonlinear Flow Problems'. which was he ld on 11 - 13 September 1990 at the National Center for Supercomputing Applications (NCSA). In general, it was found that when the flow was adequately resolved, all of the numerical schemes produced solutions t hat contained the basic physics as well as most of the flow detail of the reference solution. However, when the flow was marginally resolved , there were significant differences between the solutions produced by the various models. Finally, when the flow was poorly resolved, none of the models performed very well. While higher-order and spectral-typ e schemes performed best for adequately and marginally resolved flow, solutions made with these schemes were virtually unusable for poorly r esolved flow. In contrast, the monotonic schemes provided the most coh erent and smooth solutions for poorly resolved flow, however with noti ceable amplitude and phase speed errors, even at finer resolutions.