Global classical solution of the Cauchy problem to 1D compressible Navier–Stokes equations with large initial data

In this paper, we prove that the 1D Cauchy problem of the compressible Navier–Stokes equations admits a unique global classical solution (ρ,u)$(\rho ,\mathrm{u})$ if the viscosity μ(ρ)=1+ρ^β$\mu (\rho )=1+{\rho }^{\beta }$ with β?0$\beta ?0$. The initial data can be arbitrarily large and may contain vacuum. Some new weighted estimates of the density and velocity are obtained when deriving higher order estimates of the solution.     

Inviscid limit for Navier–Stokes equations in domains with permeable boundaries

This work is concerned with 2D-Navier Stokes equations in a multiply-connected bounded domain with permeable walls. The permeability is described by a Navier type condition. Our aim is to show that the inviscid limit is a solution of the Euler equations, satisfying the Navier type condition on the inflow zone of the walls.     

Stokes flow past an assemblage of slip eccentric spherical particle‐in‐cell models

The quasisteady axisymmetrical flow of an incompressible viscous fluid past an assemblage of slip eccentric spherical particle‐in‐cell models with Happel and Kuwabara boundary conditions is investigated. A linear slip, Basset type, boundary condition on the surface of the spherical particle is used. Under the Stokesian approximation, a general solution is constructed from the superposition of the basic solutions in the two spherical coordinate systems based on the particle and fictitious spherical envelope. The boundary conditions on the particle's surface and fictitious spherical envelope are satisfied by a collocation technique. Numerical results for the normalized drag force acting on the particle are obtained with good convergence for various values of the volume fraction, the relative distance between the centers of the particle and fictitious envelope and the slip coefficient of the particle. In the limits of the motions of the spherical particle in the concentric position with cell surface and near the cell surface with a small curvature, the numerical values of the normalized drag force are in good agreement with the available values in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Unconventional Coding Technique Applied to Multi-Level Polarization Modulation

A new technique is proposed to improve information confidentiality in optical-fiber communications without bandwidth consumption. A pseudorandom vectorial sequence was generated by a dynamic system algorithm and used to codify a multi-level polarization modulation based on the Stokes vector. Optical-fiber birefringence, usually considered as a disturbance, was exploited to obfuscate the signal transmission. At the receiver end, the same pseudorandom sequence was generated and used to decode the multi-level polarization modulated signal. The proposed scheme, working at the physical layer, provides strong information security without introducing complex processing and thus latency.     

Euler–Goursat-like formula via Laplace–Borel duality

The Goursat formula for the hypergeometric function extends the Euler–Gauss relation to the case of logarithmic singularities.     

A multigrid approach for steady state laminar viscous flows

In this paper, we use the laminar viscous flow in a lid‐driven cavity as an example to describe and verify a numerical scheme for non‐linear partial differential equations. The proposed scheme combines a new analytical method for strongly non‐linear problems, namely the homotopy analysis method, with the multigrid techniques. A family of formulas at different orders is given. At the lowest order, the current approach is the same as the traditional multigrid methods. However, our high‐order scheme needs a fewer number of iterations and less CPU time than the classical ones. Copyright © 2001 John Wiley & Sons, Ltd.     

Coupled Models and Parallel Simulations for Three-Dimensional Full-Stokes Ice Sheet Modeling

A three-dimensional full-Stokes computational model is considered for determining the dynamics,temperature,and thickness of ice sheets.The goveming thermomechanical equations consist of the three-dimensional full-Stokes system with nonlinear rheology for the momentum,an advective-diffusion energy equation for temperature evolution,and a mass conservation equation for ice-thickness changes.Here,we discuss the variable resolution meshes,the finite element discretizations,and the parallel algorithms employed by the model components.The solvers are integrated through a well-designed coupler for the exchange of parametric data between components.The discretization utilizes high-quality,variable-resolution centroidal Voronoi Delaunay triangulation meshing and existing parallel solvers.We demonstrate the gridding technology,discretization schemes,and the efficiency and scalability of the parallel solvers through computational experiments using both simplified geometries arising from benchmark test problems and a realistic Greenland ice sheet geometry.     

Free surface Stokes flows obstructed by multiple obstacles

Gravity‐driven Stokes flow down an inclined plane over and around multiple obstacles is considered. The flow problem is formulated in terms of a boundary integral equation and solved using the boundary element method. A Hermitian radial basis function (RBF) is used for the interpolation of the free surface, generation of the unit normal and curvature, and to prescribe the far‐field conditions. For flow over an obstacle, hemispheres are taken. For flow around an obstacle, circular cylinders are modelled and the contact angle condition on the obstacle/free surface intersection specified using the RBF formulation. Explicit profiles are produced for flow over and around two obstacles placed in various locations relative to one another. Interaction due to two obstacles is given by comparisons made with the profiles for flow over and around individual obstacles. In general, when the obstacles are separated by a sufficiently large distance the flow profiles are identical to a single obstacle analysis. For flow over and around two obstacles in‐line with the incident flow, effects of the governing parameters are examined, with variations in plane inclination angle, Bond number, obstacle size, and in the case of obstacles intersecting the free surface, static contact angle is considered. Finally flows over and around three obstacles are modelled. Copyright © 2009 John Wiley & Sons, Ltd.