A comparative study of the performance of high-resolution non-oscillating advection schemes in the context of the motion induced by mixed region in a stratified fluid

The problem of a two-dimensional fully mixed region collapsing in continuously density-stratified medium is considered. This article deals with the numerical treatment of the advective terms in the Navier-Stokes equations in the Oberbeck-Boussinesq approximation. Comparisons are performed between the upwind scheme, flux-limiter schemes, namely, Minmod, Superbee, Van Leer, and Monotonized Centred (MC), the monotone adaptive stencil schemes, namely, ENO3 and SMIF, and weighted stencil scheme WENO5. We used laboratory experimental data of Wu as a benchmark test to compare performance of different numerical approaches. It is found that the flux-limiter schemes have the smallest numerical diffusion. The WENO5 scheme describes more accurately the width of collapse region variation with time. All considered schemes give a realistic pattern of internal gravity waves generated by collapse region.