We study convection of an incompressible Newtonian fluid heated from below in a two-dimensional domain of height H: the Bénard problem. The lower wall is maintained at a temperature θbottom and the upper wall is maintained at a temperature θtop, where θbottom > θtop . The governing equations are the (2D) Navier–Stokes equations under the Boussinesq approximation, in which all variations in phys...

In this study, a steady, incompressible, and laminar-free convective flow of a two-dimensional electrically conducting viscoelastic fluid over a moving stretching surface through a porous medium is considered. The boundary-layer equations are derived by considering Boussinesq and boundary-layer approximations. The nonlinear ordinary differential equations for the momentum and energy equations a...

We study convection of an incompressible Newtonian fluid heated from below in a two-dimensional domain of height H: the Bénard problem. The lower wall is maintained at a temperature θbottom and the upper wall is maintained at a temperature θtop, where θbottom > θtop . The governing equations are the (2D) Navier–Stokes equations under the Boussinesq approximation, in which all variations in phys...

We consider an optimal control problem governed by a system of nonlinear partial differential equations modelling viscous incompressible flows submitted to variations of temperature. We use a generalized Boussinesq approximation. We obtain the existence of the optimal control as well as first order optimality conditions of Pontryagin type by using the Dubovitskii-Milyutin formalism.

This paper presents the Dual Scattering Channel (DSC) numerical solution of the Navier-Stokes equations for viscous quasi-incompressible flow in the Oberbeck-Boussinesq approximation. The implementation in hexahedral non-orthogonal mesh is outlined. A numerical example illustrates the approach. MSC-classes: 65C20, 65M06, 76D05 Westerham, March 31, 2006

We present a class of a high-resolution Godunov-type algorithms for solving flow problems governed by the incompressible Navier-Stokes equations. The algorithms use high-resolution finite volume methods developed in SIAM J. Numer. Anal., 33, (1996) 627-665 for the advective terms and finite difference methods for the diffusion and the Poisson pressure equation. The high-resolution algorithm adv...

This paper presents the Dual Scattering Channel (DSC) numerical solution of the Navier-Stokes equations for viscous quasi-incompressible flow in the Oberbeck-Boussinesq approximation. The implementation in hexahedral non-orthogonal mesh is outlined. A numerical example illustrates the approach. MSC-classes: 65C20, 65M06, 76D05 Westerham on October 05, 2005

In this paper we introduce the (I, J) similar method for incompressible two-dimensional Euler equations, and obtain a series of explicit (I, J) similar solutions to the incompressible two-dimensional Euler equations. These solutions include all of the twin wave solutions, some new singularity solutions, and some global smooth solutions with a finite energy. We also reveal that the twin wave sol...

We propose a modi…cation of the classical Navier-Stokes-Boussinesq system of equations, which governs buoyancy-driven ‡ows of viscous, incompressible ‡uids. This modi…cation is motivated by unresolved issues regarding the global solvability of the classical system in situations where viscous heating cannot be neglected. A simple model problem leads to a coupled system of two parabolic equations...

We describe in this work a discontinuous-Galerkin Finite-Element method to approximate the solutions of a new family of 1d Green-Naghdi models. These new models are shown to be more computationally efficient, while being asymptotically equivalent to the initial formulation with regard to the shallowness parameter. Using the free surface instead of the water height as a conservative variable, th...