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Partial regularity of solution to generalized Navier-Stokes problem

Václav Mácha (2014)

Open Mathematics

In the presented work, we study the regularity of solutions to the generalized Navier-Stokes problem up to a C 2 boundary in dimensions two and three. The point of our generalization is an assumption that a deviatoric part of a stress tensor depends on a shear rate and on a pressure. We focus on estimates of the Hausdorff measure of a singular set which is defined as a complement of a set where a solution is Hölder continuous. We use so-called indirect approach to show partial regularity, for dimension...

Particle Dynamics Methods of Blood Flow Simulations

A. Tosenberger, V. Salnikov, N. Bessonov, E. Babushkina, V. Volpert (2011)

Mathematical Modelling of Natural Phenomena

Various particle methods are widely used to model dynamics of complex media. In this work molecular dynamics and dissipative particles dynamics are applied to model blood flows composed of plasma and erythrocytes. The properties of the homogeneous particle fluid are studied. Capillary flows with erythrocytes are investigated.

Particle-in-wavelets scheme for the 1D Vlasov-Poisson equations ⋆⋆⋆

Romain Nguyen van yen, Éric Sonnendrücker, Kai Schneider, Marie Farge (2011)

ESAIM: Proceedings

A new numerical scheme called particle-in-wavelets is proposed for the Vlasov-Poisson equations, and tested in the simplest case of one spatial dimension. The plasma distribution function is discretized using tracer particles, and the charge distribution is reconstructed using wavelet-based density estimation. The latter consists in projecting the Delta distributions corresponding to the particles onto a finite dimensional linear space spanned by...

Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes, Sergio González (2009)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...

Path following methods for steady laminar Bingham flow in cylindrical pipes

Juan Carlos De Los Reyes, Sergio González (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

This paper is devoted to the numerical solution of stationary laminar Bingham fluids by path-following methods. By using duality theory, a system that characterizes the solution of the original problem is derived. Since this system is ill-posed, a family of regularized problems is obtained and the convergence of the regularized solutions to the original one is proved. For the update of the regularization parameter, a path-following method is investigated. Based on the differentiability properties...

Peristaltic Pumping of Solid Particles Immersed in a Viscoelastic Fluid

J. Chrispell, L. Fauci (2011)

Mathematical Modelling of Natural Phenomena

Peristaltic pumping of fluid is a fundamental method of transport in many biological processes. In some instances, particles of appreciable size are transported along with the fluid, such as ovum transport in the oviduct or kidney stones in the ureter. In some of these biological settings, the fluid may be viscoelastic. In such a case, a nonlinear constitutive equation to describe the evolution of the viscoelastic contribution to the stress tensor...

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