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We consider a special configuration of vorticity that consists of a pair of
externally tangent circular vortex sheets, each having a circularly symmetric core
of bounded vorticity concentric to the sheet, and each core precisely balancing the
vorticity mass of the sheet. This configuration is a stationary weak solution of the
2D incompressible Euler equations. We propose to perform numerical experiments to verify
that certain approximations of this flow configuration converge to a non-stationary...
We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
We study in this paper some numerical schemes for hyperbolic systems
with unilateral constraint. In particular, we deal with the scalar case, the isentropic
gas dynamics system and the full-gas dynamics system.
We prove the convergence of the scheme to an entropy solution
of the isentropic
gas dynamics with unilateral constraint on the density and mass loss.
We also study the non-trivial steady states of the system.
Motivated by well-driven flow transport in porous media, Chen
and Yue proposed a numerical homogenization method for Green
function [Multiscale Model. Simul.1 (2003) 260–303]. In that paper,
the authors focused on the well pore pressure, so the local error
analysis in maximum norm was presented. As a continuation, we will
consider a fully discrete scheme and its multiscale error analysis
on the velocity field.
In order to investigate effects of the dynamic capillary pressure-saturation relationship used in the modelling of a flow in porous media, a one-dimensional fully implicit numerical scheme is proposed. The numerical scheme is used to simulate an experimental procedure using a measured dataset for the sand and fluid properties. Results of simulations using different models for the dynamic effect term in capillary pressure-saturation relationship are presented and discussed.
Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinear surface tension terms. Finally, in the case of a thin film flow driven by a surface active agent (surfactant),...
We discuss the numerical modeling of heat exchange between the infiltrated water and porous media matrix. An unsaturated-saturated flow is considered with boundary conditions reflecting the external driven forces. The developed numerical method is efficient and can be used for solving the inverse problems concerning determination of transmission coefficients for heat energy exchange inside and also on the boundary of porous media. Numerical experiments support our method.
Modeling the movement of a rigid particle in viscous fluid is a problem physicists and mathematicians have tried to solve since the beginning of this century. A general model for an ellipsoidal particle was first published by Jeffery in the twenties. We exploit the fact that Jeffery was concerned with formulae which can be used to compute numerically the velocity field in the neighborhood of the particle during his derivation of equations of motion of the particle. This is our principal contribution...
We introduce in this paper some elements for the mathematical and numerical analysis of algebraic turbulence models for
oceanic surface mixing layers. In these models the turbulent diffusions are parameterized by means of the gradient Richardson number, that measures the balance between stabilizing buoyancy forces and destabilizing shearing forces. We analyze the existence and linear exponential asymptotic stability of continuous and discrete equilibria states. We also analyze the well-posedness...
We propose a new numerical scheme based on the finite volumes to simulate the
urethra flow based on hyperbolic balance law. Our approach is based on the Riemann
solver designed for the augmented quasilinear homogeneous formulation. The scheme has general semidiscrete wave–propagation form and can be extended to arbitrary high order accuracy. The first goal is to construct the scheme, which is well balanced, i.e. maintains not only some special steady states but all steady states which can occur....
This work presents the numerical solution of laminar incompressible viscous flow in a three dimensional branching channel with circular cross section for generalized Newtonian fluids. This model can be generalized by cross model in shear thinning meaning. The governing system of equations is based on the system of balance laws for mass and momentum. Numerical tests are performed on a three dimensional geometry, the branching channel with one entrance and two outlet parts. Numerical solution of the...
The aim of this paper is to describe the numerical results of numerical modelling of steady flows of laminar incompressible viscous and viscoelastic fluids. The mathematical models are Newtonian and Oldroyd-B models. Both models can be generalized by cross model in shear thinning meaning.
Numerical tests are performed on three dimensional geometry, a branched channel with one entrance and two output parts. Numerical solution of the described models is based on cell-centered finite volume method...
In this article, we investigate numerical schemes for solving a three component Cahn-Hilliard model. The space discretization is performed by using a Galerkin formulation and the finite element method. Concerning the time discretization, the main difficulty is to write a scheme ensuring, at the discrete level, the decrease of the free energy and thus the stability of the method. We study three different schemes and prove existence and convergence theorems. Theoretical results are illustrated by...
In this article, we investigate numerical schemes for solving
a three component Cahn-Hilliard model. The space discretization is
performed by using
a Galerkin formulation and the finite element method.
Concerning the time discretization,
the main difficulty is to write a scheme ensuring,
at the discrete level, the decrease of the free energy
and thus the stability of the method.
We study three different schemes and prove
existence and convergence theorems. Theoretical results are
illustrated by...
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