The subject of this work is the analysis and implementation of stabilized finite element methods on anisotropic meshes. We develop the anisotropic a priori error analysis of the residual-free-bubble (RFB) method applied to elliptic convection-dominated convection-diffusion problems in two dimensions, with finite element spaces of type Qk, k ≥ 1. In the case of P1 finite elements, relying on the...

The effect of uniform distribution of internal heat generation on the linear stability analysis of the Benard-Marangoni convection in an Eringen’s micropolar fluids with feedback control is investigated theoretically. The upper free surface is assumed to be non-deformable and the lower boundary is taken to be rigid and isothermal with fixed temperature and spanvanishing boundaries. The eigenval...

Control strategy on Rayleigh-Benard convection in rotating nanofluids saturated anisotropic porous layer heated from below is studied the presence of uniformly internal heat source for rigid-rigid, free-free, and lower-rigid upper-free boundaries. Feedback control with an array sensors situated at top plate actuators located bottom are considered this study. Linear stability analysis based norm...

Rayleigh-Bénard convection in rotating spherical shells can be considered as a simplified analogue of many astrophysical and geophysical fluid flows. Here, we use threedimensional direct numerical simulations to study this physical process. We construct a dataset of more than 200 numerical models that cover a broad parameter range with Ekman numbers spanning 3 × 10−7 ≤ E ≤ 10−1, Rayleigh number...