A generalization of the Hille--Yosida theorem to the case of degenerate semigroups in locally convex spaces.
A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations
We deal with a suitable weak solution to the Navier-Stokes equations in a domain . We refine the criterion for the local regularity of this solution at the point , which uses the -norm of and the -norm of in a shrinking backward parabolic neighbourhood of . The refinement consists in the fact that only the values of , respectively , in the exterior of a space-time paraboloid with vertex at , respectively in a ”small” subset of this exterior, are considered. The consequence is that...
A geometric lower bound on Grad’s number
In this note we provide a new geometric lower bound on the so-called Grad’s number of a domain in terms of how far is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
A geometric lower bound on Grad's number
In this note we provide a new geometric lower bound on the so-called Grad's number of a domain Ω in terms of how far Ω is from being axisymmetric. Such an estimate is important in the study of the trend to equilibrium for the Boltzmann equation for dilute gases.
A Global a posteriori Error Estimate for Quasilinear Elliptic Problems.
A global branch of steady vortex rings.
A gradient weighted moving finite-element method with polynomial approximation of any degree.
A heterogeneous alternating-direction method for a micro-macro dilute polymeric fluid model
We examine a heterogeneous alternating-direction method for the approximate solution of the FENE Fokker–Planck equation from polymer fluid dynamics and we use this method to solve a coupled (macro-micro) Navier–Stokes–Fokker–Planck system for dilute polymeric fluids. In this context the Fokker–Planck equation is posed on a high-dimensional domain and is therefore challenging from a computational point of view. The heterogeneous alternating-direction scheme combines a spectral Galerkin method for...
A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids
The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form....
A high-precision algorithm for axisymmetric flow.
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different HLLC solvers. Some results concerning the non-negativity...
A HLLC scheme for nonconservative hyperbolic problems. Application to turbidity currents with sediment transport
The goal of this paper is to obtain a well-balanced, stable, fast, and robust HLLC-type approximate Riemann solver for a hyperbolic nonconservative PDE system arising in a turbidity current model. The main difficulties come from the nonconservative nature of the system. A general strategy to derive simple approximate Riemann solvers for nonconservative systems is introduced, which is applied to the turbidity current model to obtain two different...
A hybrid multigrid method for the steady-state incompressible Navier-Stokes equations.
A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems
The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density and additional...
A hybrid scheme to compute contact discontinuities in one-dimensional Euler systems
The present paper is devoted to the computation of single phase or two phase flows using the single-fluid approach. Governing equations rely on Euler equations which may be supplemented by conservation laws for mass species. Emphasis is given on numerical modelling with help of Godunov scheme or an approximate form of Godunov scheme called VFRoe-ncv based on velocity and pressure variables. Three distinct classes of closure laws to express the internal energy in terms of pressure, density...
A Kinetic equation for granular media
A kinetic equation for granular media
In this short note we correct a conceptual error in the heuristic derivation of a kinetic equation used for the description of a one-dimensional granular medium in the so called quasi-elastic limit, presented by the same authors in reference[1]. The equation we derived is however correct so that, the rigorous analysis on this equation, which constituted the main purpose of that paper, remains unchanged.
A Lagrangian approach for the compressible Navier-Stokes equations
Here we investigate the Cauchy problem for the barotropic Navier-Stokes equations in , in the critical Besov spaces setting. We improve recent results as regards the uniqueness condition: initial velocities in critical Besov spaces with (not too) negative indices generate a unique local solution. Apart from (critical) regularity, the initial density just has to be bounded away from and to tend to some positive constant at infinity. Density-dependent viscosity coefficients may be considered. Using...
A Langevin Description for Driven Granular Gases
The study of the fluctuations in the steady state of a heated granular system is reviewed. A Boltzmann-Langevin description can be built requiring consistency with the equations for the one- and two-particle correlation functions. From the Boltzmann-Langevin equation, Langevin equations for the total energy and the transverse velocity field are derived. The existence of a fluctuation-dissipation relation for the transverse velocity field is also...
A logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain
This paper proves a logarithmic regularity criterion for 3D Navier-Stokes system in a bounded domain with the Navier-type boundary condition.