Solution of the system of differential equations related to Marangoni convections in one fluid layer.
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem
We consider the Stokes problem provided with non standard boundary conditions which involve the normal component of the velocity and the tangential components of the vorticity. We write a variational formulation of this problem with three independent unknowns: the vorticity, the velocity and the pressure. Next we propose a discretization by spectral element methods which relies on this formulation. A detailed numerical analysis leads to optimal error estimates for the three unknowns and numerical...
Spectral element simulations of flow past an ellipsoid at different Reynolds numbers.
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [25, 26] and show that the kernel modes that define the spectral method have the correct...
Spectral methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit
In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [CITE] and show that the kernel modes that define the spectral method have the correct...
Spectral Numerical Study of a Problem Governed by Navier-Stokes Equations, Influence of Rayleigh and Prandtl Numbers
We present in this work a numerical study of a problem governed by Navier-Stokes equations and heat equation. The mathematical problem under consideration is obtained by modelling the natural convection of an incompressible fluid, in laminar flow between two horizontal concentric coaxial cylinders, the temperature of the inner cylinder is supposed to be greater than the outer one. The numerical simulation of the flow is carried out by collocation-Legendre...
Stability analysis of shallow wake flows with free surface.