In this paper we present a stable hybrid scheme for viscous problems. The hybrid method combines the unstructured finite volume method with high-order finite difference methods in complex geometries. The coupling procedure between the two numerical methods is based on energy estimates and stable interface conditions are constructed. Numerical calculations show that the hybrid method is efficien...

Convection-Diffusion Problems occur very frequently in applied sciences and engineering. In this paper, the crux of research articles published by numerous researchers during 2007-2011 in referred journals has been presented and this leads to conclusions and recommendations about what methods to use on Convection-Diffusion Problems. It is found that engineers and scientists are using finite ele...

We propose a numerical method for modeling highly deformable nonlinear incompressible solids that conserves the volume locally near each node in a finite element simulation. Our method works with arbitrary constitutive models, is applicable to both passive materials and active materials (e.g. muscles), and works with simple tetrahedra without the need for multiple quadrature points or stabiliza...

A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid describing the motion of the mixture. In cylindrical coordinates, and if an axially symmetric solution is assumed, the original problem reduces t...