Numerical modeling of laminar and chaotic natural convection flows using a non-residual dynamic VMS formulation

Abstract

In this article, the performance of a stabilized VMS-type finite element formulation of a non-residual structure is numerically verified for highly convective natural flows. The novelty of the method is the time-dependent nature of the sub-scales and the introduction of two components for the sub-scale velocities, which allows the resolution of chaotic and highly convective problems without the need to include an additional turbulence model and its using equal order interpolation between velocity and pressure. The natural heat convection problems of the square and cubic cavities are solved up to a Rayleigh number of 1010 and 3.3×107, respectively. Additionally, the stability of the problem is investigated by conducting an analysis of its Hopf bifurcation. As a distinctive feature, the work includes the assessment of the influence of incorporating dynamic sub-scales, with an emphasis on the accuracy of the numerical solutions obtained, that includes a comparison with the results predicted by the quasi-static formulation of the same method. The comparisons between both formulations were made using direct and iterative solvers. The results reported in this article allow verifying the performance, precision, and robustness of the dynamic formulation used to solve highly nonlinear problems with strong thermal coupling.