We study the limiting behavior of systems of hyperbolic conservation laws with stiff relaxation terms. Reduced systems, inviscid and viscous local conservation laws, and weakly nonlinear limits are derived through asymptotic expansions. An entropy condition is introduced for N × N systems that ensures the hyperbolicity of the reduced inviscid system. The resulting characteristic speeds are shown to be interlaced with those of the original system. Moreover, the first correction to the reduced system is shown to be dissipative. A partial converse is proved for 2 × 2 systems. This structure is then applied to study the convergence to the reduced dynamics for the 2 × 2 case. © 1994 John Wiley & Sons, Inc.

Hyperbolic conservation laws with stiff relaxation terms and entropy

http://abadshapoor.persiangig.com/document/LBM/Inamuro%20et%20al%202004.pdf

A lattice Boltzmann method for incompressible two-phase flows with large density differences

Asymptotic analysis of the lattice Boltzmann equation

In this letter, we derive entropy functions whose local equilibria are suitable to recover the Navier-Stokes equations in the framework of the Lattice Boltzmann method. For the two-dimensional nine-velocity lattice we demonstrate that such an entropy function is unique, and that the expansion of the corresponding local equilibrium is the well-known local equilibrium of Y. H. Qian et al. (Europhys. Lett., 17 (1992) 479). Based on the knowledge of entropy functions, we introduce a new version of the Lattice Boltzmann method with an H-theorem built in.

https://iopscience.iop.org/article/10.1209/epl/i1999-00370-1/pdf

Perfect entropy functions of the Lattice Boltzmann method

Multiple-relaxation-time lattice Boltzmann model for the convection and anisotropic diffusion equation

Advances in Kinetic Theory and Continuum Mechanics

I Classical Kinetic Theory and Fluid Dynamics.- Trend to Equilibrium in a Gas According to the Boltzmann Equation.- The Dirichlet Boundary Value Problem for B.G.K. Equation.- Asymptotic Theory of a Steady Flow of a Rarefied Gas Past Bodies for Small Knudsen Numbers.- Computation of Transitional Rarefied Flow.- Gas Flows Around the Condensed Phase with Strong Evaporation or Condensation - Fluid Dynamic Equation and Its Boundary Condition on the Interface and Their Application.- II Discrete Kinetic Theory.- Fluid Dynamic Limits of Discrete Velocity Kinetic Equations.- On the Euler Equation in Discrete Kinetic Theory.- Existence globale et diffusion en theorie cinetique discrete.- On the Cauchy Problem for the Semidiscrete Enskog Equation.- On Uniform Boundedness of Solutions to Discrete Velocity Models in Several Dimensions.- Temperature and Local Entropy Overshoots for the Second Fourteen-Velocity Cabannes Model.- A One Dimensional Lattice Boltzmann Equation with Galilean Invariance.- The Euler Description for a Class of Discrete Models of Gases with Multiple Collisions.- On the Semidiscrete Boltzmann Equation with Multiple Collisions.- A Discrete Velocity Model for Gases with Chemical Reactions of Dissociation and Recombination.- III Applied Fluid Mechanics.- Frozen and Equilibrium Speeds of Sound in Non-equilibrium Flows.- Nonlinear Propagation of Acoustic and Internal Waves in a Stratified Fluid.- A Higher Order Panel Method for Nonlinear Gravity Wave Simulation.- Numerical Reliability of MHD Flow Calculations at High Hartmann Numbers.- Interaction Between an Oblique Shock and a Detached Shock Upstream of a Cylinder in Supersonic Flow.- The Design of Super-Concorde and Space Vehicles Using Global Optimization Techniques.- IV Continuum Mechanics.- Vibrating Strings with Obstacles: The Analytic Study.- Vibrations of Euler-Bernoulli Beams with Pointwise Obstacles.- Contribution to the Fracture Analysis of Composite Materials.- Homogenization Method Applied to Porous Media.- Modal Analysis of Flexible Multibody Systems.- Index of Contributors.

Advances in kinetic theory and continuum mechanics : proceedings of a symposium held in honor of professor Henri Cabannes at the University Pierre et Marie Curie, Paris, France, on 6 July 1990

Soubbaramayer

Papers

Advances in Kinetic Theory and Continuum Mechanics

Advances in kinetic theory and continuum mechanics : proceedings of a symposium held in honor of professor Henri Cabannes at the University Pierre et Marie Curie, Paris, France, on 6 July 1990