Related papers: A kinetic scheme with variable velocities and rela…
Numerical schemes derived from gas-kinetic theory can be applied to simulations in the hydrodynamics limit, in laminar and also turbulent regimes. In the latter case, the underlying Boltzmann equation describes a distribution of eddies, in…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
We study the propagation of regularity of solutions to a three dimensional system of linear parabolic PDE known as the kinematic dynamo equations. The divergence free drift velocity is assumed to be at the critical regularity level with…
In this work, we consider an advection-diffusion equation, coupled to a Poisson equation for the velocity field. This type of coupling is typically encountered in models arising from plasma physics or porous media flow. The aim of this work…
This paper synthesizes anytime algorithms, in the form of continuous-time dynamical systems, to solve monotone variational inequalities. We introduce three algorithms that solve this problem: the projected monotone flow, the safe monotone…
We study a finite volume scheme for the approximation of the solution to convection diffusion equations with nonlinear convection and Robin boundary conditions. The scheme builds on the interpretation of such a continuous equation as the…
We aim to study a finite volume scheme to solve the two dimensional inviscid primitive equations of the atmosphere with humidity and saturation, in presence of topography and subject to physically plausible boundary conditions to the system…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
A finite-volume method for the one-dimensional shallow-water equations including topographic source terms is presented. Exploiting an original idea by Leroux, the system of partial-differential equations is completed by a trivial equation…
Starting from the Liouville equation, and using a BBGKY-like hierarchy, we derive a kinetic equation for the point vortex gas in two-dimensional (2D) hydrodynamics, taking two-body correlations and collective effects into account. This…
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…
Thin fluid or elastic films and membranes are found in nature and technology, for instance, as confinements of living cells or in loudspeakers. When applying a net force, resulting flows in an unbounded two-dimensional incompressible…
We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The…
We propose a positivity preserving entropy decreasing finite volume scheme for nonlinear nonlocal equations with a gradient flow structure. These properties allow for accurate computations of stationary states and long-time asymptotics…
Kinetic theory provides an elegant framework for studying dispersed particles in turbulent flows. Here the application of such probability density function (PDF)-based descriptions is considered in the context of particle clustering. The…
An implicit multiscale method with multiple macroscopic prediction for steady state solutions of gas flow in all flow regimes is presented. The method is based on the finite volume discrete velocity method (DVM) framework. At the cell…
Simulation of plasmas in electromagnetic fields requires numerical solution of a kinetic equation that describes the time evolution of the particle distribution function. In this paper we propose a finite volume scheme based on integral…
We present Finite Volume methods for diffusion equations on generic meshes, that received important coverage in the last decade or so. After introducing the main ideas and construction principles of the methods, we review some literature…
In this paper we propose coupling conditions for a kinetic two velocity model for vehicular traffic on networks. These conditions are based on the consideration of the free space on the respective roads. The macroscopic limit of the kinetic…
We develop new variational principles to study stability and equilibrium of axisymmetric flows. We show that there is an infinite number of steady state solutions. We show that these steady states maximize a (non-universal) $H$-function. We…