On the regularized modeling of density currents

Abstract

 In this work we studied four regularization models with deconvolution for density currents, namely, Boussinesq-α, Boussinesq-ω, Boussinesq-Leray and Modified-BoussinesqLeray. A Crank-Nicolson in time and Finite Element in space algorithm is proposed and proved to be unconditionally stable and optimally convergent, which is also verified through convergence rates in computational simulations. Finally, the models are compared through the Marsigli’s flow problem. We found that all regularization models produced accurate solutions for low Reynolds number. Moreover, as expected, we observe that increasing deconvolution order improves solution. On the other hand, for high Reynolds number BoussinesqLeray and Boussinesq-α with deconvolution produced the most accurate solutions. However, from the computational viewpoint, the Boussinesq-Leray model presented advantage due to its decoupling between momentum and filter equations which permits to increase the deconvolution order with no significant increase in the computational cost.