Finite element solution for advection and natural convection flows

Finite Element Methods for Convection Diffusion Equation

This paper deals with the finite element solution of the convection diffusion equation in one and two dimensions. Two main techniques are adopted and compared. The first one includes Petrov-Galerkin based on Lagrangian tensor product elements in conjunction with streamlined upwinding. The second approach represents Bubnov/Petrov-Galerkin schemes based on a new group of exponential elements. It ...

A Simplified Solution for Advection Dominated Accretion Flows with Outflow

The existence of outflow in the advection dominated accretion flows has been confirmed by both numerical simulations and observations. The outow models for ADAF have been investigated by several groups with a simple self similar solution. But this solution is inaccurate at the inner regions and can not explain the emitted spectrum of the flow; so, it is necessary to obtain a global solution for...

Parallel Adaptive Finite Element Methods for Problems in Natural Convection

Global dynamics of radiatively inefficient accretion flows: advection versus convection

We obtain global solutions of radiatively inefficiently accretion flows around black holes. Whether and where convection develops in a flow are self-consistently determined with the mixing-length theory. The solutions can be divided into three types according to the strength of normal viscosity. Type I solution corresponds to large viscosity parameter α>∼ 0.1, which is purely advectiondominated...

Pure Lagrangian and Semi-lagrangian Finite Element Methods for the Numerical Solution of Convection-diffusion Problems

In this paper we propose a unified formulation to introduce and analyze (pure) Lagrangian and semi-Lagrangian methods for solving convection-diffusion partial differential equations. This formulation allows us to state classical and new numerical methods. Several examples are given. We combine them with finite element methods for spatial discretization. One of the pure Lagrangian methods we int...