An explicitly uncoupled VMS stabilization finite element method for the time-dependent Darcy-Brinkman equations in double-diffusive convection (Q1646674)

The Darcy-Brinkman equations in double-diffusive convection, arising e.g. in problems of combined heat and mass transfer in porous media, are solved numerically using a finite element method. A full explicitly decoupled variational multiscale (VMS) method is applied for stabilization. In each time step, the quantities velocity, temperature and concentration are postprocessed to perform the VMS filtering. The unconditional stability of the method is proven and a rigorous error analysis is carried out. Numerical two-dimensional examples in a square domain using the software package FreeFem++ on uniform triangles illustrate the predicted convergence rates and comparisons of the presented method with some benchmark data illustrate its efficiency.