Numerical solutions of a non‐linear density current: A benchmark solution and comparisons

Abstract A comparison between solutions from simulations of a non‐linear density current test problem was made in order to study the behaviour of a variety of numerical methods. The test problem was diffusion‐limited so that a grid‐converged reference solution could be generated using high spatial resolution. Solutions of the test problem using several different resolutions were computed by the participants of the ‘Workshop on Numerical Methods for Solving Nonlinear Flow Problems’, which was held 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 that 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‐type schemes performed best for adequately and marginally resolved flow, solutions made with these schemes were virtually unusable for poorly resolved flow. In contrast, the monotonic schemes provided the most coherent and smooth solutions for poorly resolved flow, however with noticeable amplitude and phase speed errors, even at finer resolutions.