A regularity result for a solid-fluid system associated to the compressible Navier-Stokes equations
A Relaxation Procedure for Domain Decomposition Methods Using Finite Elements.
A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition
We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain under the general outflow condition. Let be a 2-dimensional straight channel . We suppose that is bounded and that . Let be a Poiseuille flow in and the flux of . We look for a solution which tends to as . Assuming that the domain and the boundary data are symmetric with respect to the -axis, and that the axis intersects every component of the boundary, we have shown the existence...
A remark on the regularity for the 3D Navier-Stokes equations in terms of the two components of the velocity.
A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid
For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.
A review on the improved regularity for the primitive equations
In this work we will study some types of regularity properties of solutions for the geophysical model of hydrostatic Navier-Stokes equations, the so-called Primitive Equations (PE). Also, we will present some results about uniqueness and asymptotic behavior in time.
A Riemann–Hilbert problem and the Bernoulli boundary condition in the variational theory of Stokes waves
A Right-Inverse for the Divergence Operator in Spaces of Piecewise Polynomials. Application to the p-Version of the Finite Element Method
A robust entropy−satisfying finite volume scheme for the isentropic Baer−Nunziato model
We construct an approximate Riemann solver for the isentropic Baer−Nunziato two-phase flow model, that is able to cope with arbitrarily small values of the statistical phase fractions. The solver relies on a relaxation approximation of the model for which the Riemann problem is exactly solved for subsonic relative speeds. In an original manner, the Riemann solutions to the linearly degenerate relaxation system are allowed to dissipate the total energy in the vanishing phase regimes, thereby enforcing...
A Roe-type scheme for two-phase shallow granular flows over variable topography
We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid components, coupled together by both conservative and non-conservative terms involving the derivatives of the...
A second order anti-diffusive Lagrange-remap scheme for two-component flows
We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...
A Second Order Splitting Method for the Cahn-Hilliard Equation.
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame 60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model. 5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order multi-fluid model for evaporating sprays
The aim of this paper is to present a method using both the ideas of sectional approach and moment methods in order to accurately simulate evaporation phenomena in gas-droplets flows. Using the underlying kinetic interpretation of the sectional method [Y. Tambour, Combust. Flame60 (1985) 15–28] exposed in [F. Laurent and M. Massot, Combust. Theory Model.5 (2001) 537–572], we propose an extension of this approach based on a more accurate representation of the droplet size number density in each...
A second-order upwinding finite difference scheme for the steady Navier-Stokes equations in primitive variables in a driven cavity with a multigrid solver
A shock indicator for adaptive transonic flow computations.
A shock-capturing discontinuous Galerkin method for the numerical solution of inviscid compressible flow
A short note on theory for Stokes problem with a pressure-dependent viscosity
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on and on the symmetric part of a gradient of , namely, it is represented by a stress tensor which satisfies -growth condition with . In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in...
A short note on regularity criteria for the Navier-Stokes equations containing the velocity gradient
We review several regularity criteria for the Navier-Stokes equations and prove some new ones, containing different components of the velocity gradient.
A simple bioclogging model that accounts for spatial spreading of bacteria.