Abstract: We present a new class of numerical techniques to
solve shallow water flows over dry areas including run-up. Many
recent investigations on wave run-up in coastal areas are based on
the well-known shallow water equations. Numerical simulations have
also performed to understand the effects of several factors on tsunami
wave impact and run-up in the presence of coastal areas. In all these
simulations the shallow water equations are solved in entire domain
including dry areas and special treatments are used for numerical
solution of singularities at these dry regions. In the present study we
propose a new method to deal with these difficulties by reformulating
the shallow water equations into a new system to be solved only in the
wetted domain. The system is obtained by a change in the coordinates
leading to a set of equations in a moving domain for which the
wet/dry interface is the reconstructed using the wave speed. To solve
the new system we present a finite volume method of Lax-Friedrich
type along with a modified method of characteristics. The method is
well-balanced and accurately resolves dam-break problems over dry
areas.
Abstract: In this study, we investigated numerically heat
transfer by mixed convection coupled to radiation in a square cavity;
the upper horizontal wall is movable. The purpose of this study is to
see the influence of the emissivity ε and the varying of the
Richardson number Ri on the variation of average Nusselt number
Nu. The vertical walls of the cavity are differentially heated, the left
wall is maintained at a uniform temperature higher than the right
wall, and the two horizontal walls are adiabatic. The finite volume
method is used for solving the dimensionless Governing Equations.
Emissivity values used in this study are ranged between 0 and 1, the
Richardson number in the range 0.1 to 10. The Rayleigh number is
fixed to Ra=104 and the Prandtl number is maintained constant
Pr=0.71. Streamlines, isothermal lines and the average Nusselt
number are presented according to the surface emissivity. The results
of this study show that the Richardson number Ri and emissivity ε
affect the average Nusselt number.
Abstract: A numerical study is made in a parallel-plate porous
channel subjected to an oscillating flow and an exothermic chemical
reaction on its walls. The flow field in the porous region is modeled
by the Darcy–Brinkman–Forchheimer model and the finite volume
method is used to solve the governing equations. The effects of the
modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers,
the amplitude of oscillation (A), and the Strouhal number (St) are
examined. The main results show an increase of heat and mass
transfer rates with A and St, and their decrease with FKm and Dm.
Abstract: We numerically study the three-dimensional
magnetohydrodynamics (MHD) stability of oscillatory natural
convection flow in a rectangular cavity, with free top surface, filled
with a liquid metal, having an aspect ratio equal to A=L/H=5, and
subjected to a transversal temperature gradient and a uniform
magnetic field oriented in x and z directions. The finite volume
method was used in order to solve the equations of continuity,
momentum, energy, and potential. The stability diagram obtained in
this study highlights the dependence of the critical value of the
Grashof number Grcrit , with the increase of the Hartmann number
Ha for two orientations of the magnetic field. This study confirms
the possibility of stabilization of a liquid metal flow in natural
convection by application of a magnetic field and shows that the
flow stability is more important when the direction of magnetic field
is longitudinal than when the direction is transversal.