Related papers: Shifted polynomials in a convection problem
The equations governing the motion of a three-dimensional liquid drop moving freely in an unbounded liquid reservoir under the influence of a gravitational force are investigated. Provided the (constant) densities in the two liquids are…
Stationary equilibria of point vortices with arbitrary choice of circulations in a background flow are studied. Differential equations satisfied by generating polynomials of vortex configurations are derived. It is shown that these…
Mixed convection above a horizontal disk rotating in a semi-infinite fluid is examined when the disk is heated so that its temperature varies quadratically with distance away from its centre. Steady similarity solutions are presented for a…
Thermal convection is observed in molecular dynamic simulation of a fluidized granular system of nearly elastic hard disks moving under gravity, inside a rectangular box. Boundaries introduce no shearing or time dependence, but the energy…
We apply the convection stability criterion to a fluid in global thermodynamic equilibrium with a rigid rotation or with a constant acceleration along the streamlines. Different equations of state describing strongly interacting matter are…
The transition to turbulence in Rayleigh-Benard convection with phase changes and the resulting convective patterns are studied in a three-dimensional Galerkin model. Our study is focused to the conditionally unstable regime of moist…
In this paper, we propose a new hybridized discontinuous Galerkin (DG) method for the convection-diffusion problems with mixed boundary conditions. A feature of the proposed method, is that it can greatly reduce the number of…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
The basic stationary buoyant flow in a vertical annular porous passage induced by a boundary temperature difference is investigated. The vertical cylindrical boundaries are considered both isothermal and permeable to external fluid…
We study the flow of an incompressible liquid film down a wavy incline. Applying a Galerkin method with only one ansatz function to the Navier-Stokes equations we derive a second order weighted residual integral boundary layer equation,…
Exact solutions of a classical problem of a plane unsteady potential flow of an ideal incompressible fluid with a free boundary are presented. The fluid occupies a semi-infinite strip bounded by the free surface (from above) and (from the…
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant…
A hybridized discontinuous Galerkin method is proposed for solving 2D fractional convection-diffusion equations containing derivatives of fractional order in space on a finite domain. The Riemann-Liouville derivative is used for the spatial…
The present study examines the linear instability characteristics of double-diffusive mixed convective flow in a vertical channel with viscosity stratification. The viscosity of the fluid is modelled as an exponential function of…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
This work considers the gravitational instability of a saline boundary layer formed by an evaporation-induced flow through a fully-saturated porous slab. Evaporation of saline waters can eventually result in the formation of salt lakes as…
The Boussinesq system for buoyancy driven fluids couples the momentum equation forced by the buoyancy with the convection-diffusion equation for the temperature. One fundamental issue on the Boussinesq system is the stability problem on…
We devise and analyze a class of the primal discontinuous Galerkin methods for the magnetic advection-diffusion problems based on the weighted-residual approach. In addition to the upwind stabilization, we find a new mechanism under the…
Convection in horizontal layers of binary fluids heated from below and in particular the influence of the Soret effect on the bifurcation properties of extended stationary and traveling patterns that occur for negative Soret coupling is…
Wave propagation problems for heterogeneous media are known to have many applications in physics and engineering. Recently, there has been an increasing interest in stochastic effects due to the uncertainty, which may arise from impurities…