Related papers: A kinetic scheme with variable velocities and rela…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic for junctions with diverging lanes. We consider cases with and without directional preferences and present corresponding kinetic coupling…
We present a generalisation of surface photometry to the higher-order moments of the line-of-sight velocity distribution of galaxies observed with integral-field spectrographs. The generalisation follows the approach of surface photometry…
We study several examples of kinetically constrained lattice models using dynamically accessible volume as an order parameter. Thereby we identify two distinct regimes exhibiting dynamical slowing, with a sharp threshold between them. These…
We study compressible fluid flow in narrow two-dimensional channels using a novel molecular dynamics simulation method. In the simulation area, an upstream source is maintained at constant density and temperature while a downstream…
General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…
Many features of real granular fluids under rapid flow are exhibited as well by a system of smooth hard spheres with inelastic collisions. For such a system, it is tempting to apply standard methods of kinetic theory and hydrodynamics to…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
We consider several systems of nonlinear hyperbolic conservation laws describing the dynamics of nonlinear waves in presence of phase transition phenomena. These models admit under-compressive shock waves which are not uniquely determined…
This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transforming the original non-linear system into a linearized kinetic…
A finite volume scheme for the (Patlak-) Keller-Segel model in two space dimensions with an additional cross-diffusion term in the elliptic equation for the chemical signal is analyzed. The main feature of the model is that there exists a…
Physical systems with complex unsteady dynamics, such as fluid flows, are often poorly represented by a single mean solution. For many practical applications, it is crucial to access the full distribution of possible states, from which…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
A Lie-group based similarity theory is developed for both momentum and energy distributions in a turbulent pipe flow, leading to asymptotic logarithmic profiles of mean velocity and turbulent kinetic energy. Both channel and pipe data over…
Experimental studies on vehicular traffic provide data on quantities like density, flux, and mean speed of the vehicles. However, the diagrams relating these variables (the fundamental and speed diagrams) show some peculiarities not yet…
We propose finite-volume schemes for general continuity equations which preserve positivity and global bounds that arise from saturation effects in the mobility function. In the case of gradient flows, the schemes dissipate the free energy…
The present paper deals with some kind of quantum ``velocity'' which is introduced by the method of hydrodynamical analogy. It is found that this ``velocity'' is in general irrotational, namely, a vorticity vanishes, and then a velocity…
In this visualisation the instantaneous local velocity is expressed in terms of four components to capture the development of and interactions between coherent structures in turbulent flows. It is then possible to isolate the terms linked…
A novel model of intermittency is presented in which the dynamics of the rates of energy transfer between successive steps in the energy cascade is described by a hierarchy of stochastic differential equations. The probability distribution…
A comprehensive scheme for the spatial discretisation of continuity equation, momentum advection and normal and shear stresses at the fluid interfaces is presented for numerically simulating the incompressible two phase flows based on the…
The Gas-Kinetic Scheme (GKS), widely used in computational fluid dynamics for simulating hypersonic and other complicated flow phenomena, is extended in this work to electromagnetic problems by solving Maxwell's equations. In contrast to…