Abstract. We propose and analyze a semi Lagrangian method for the convection-diffusion equation. Error estimates for both semi and fully discrete finite element approximations are obtained for convection dominated flows. The estimates are posed in terms of the projections constructed in [7, 8] and the dependence of various constants upon the diffusion parameter is characterized. Error estimates...

A localized axial Green’s function method for convection-diffusion equations is proposed, which is a unique and original one for general cases of partial differential equations including elliptic boundary value problems and the steady Stokes flows. The salient feature of the method is that only one-dimensional Green’s functions for the axially split differential operators are used to solve the ...

A variety of chaotic flows evolving in relatively high-dimensional spaces are considered. It is shown through the use of an optimal choice of basis functions, which are a consequence of the Karhunen-Loeve procedure, that an accurate description can be given in a relatively low-dimensional space. Particular examples of this procedure, which are presented, are the Ginzburg-Landau equation, turbul...

In this paper we consider the case of nonlinear convectiondiffusion problems with a dominating convection term and we propose exponential integrators based on the composition of exact pure convection flows. The main reason for developing this type of methods is that as it turns out they can be applied to the numerical integration of the considered PDEs in a semi-Lagrangian fashion. SemiLagrangi...

Recent investigations into convection in Europa’s ice shell have been based on nonNewtonian (stress-dependent) or Newtonian (stress-independent) viscosity for water ice. However, despite the wide use of Newtonian convection, experimentally observed water ice flow is non-Newtonian, and analysis of stability against convection of the ice shell using updated flow laws has been only performed for n...

Stability of fully developed mixed convection flows, with significant viscous dissipation, in a vertical channel bounded by isothermal plane walls having the same temperature and subject to pressure gradient is investigated. It is shown that one of the dual solutions is always unstable and that both are unstable when the total flow rate is big enough. The completely passive natural convection f...

As the consumer demand for smaller, more sophisticated computers grows, the need arises for new air cooling methods that will work in geometries that mechanical fans cannot. Ionic winds (also known as electrohydrodynamic flows) are flows that are produced by the generation of a gas discharge. These flows do not require moving parts to operate, making them attractive for small form-factor device...

In this paper, we simulate steady inviscid flows over a cylinder using potential and stream functions, including entropy and vorticity corrections for incompressible, subsonic, transonic and supersonic flows. The present hierarchical formulation is equivalent to Euler equations satisfying conservation of mass, momentum and energy. Standard numerical schemes and iterative algorithms are used for...