21 citations · 73 across the 16 of their papers we have counts for
20 papers
A spectral approach to interface layers on networks for the linearized BGK equation and its acoustic limit
Raul Borsche, Tobias Damm, Axel Klar +1
We consider in this paper a velocity discretized version of the full linear kinetic BGK model and the corresponding limit for small Knudsen number, the linearised Euler or acoustic…
Interface layers and coupling conditions for discrete kinetic models on networks: a spectral approac
Raul Borsche, Tobias Damm, Axel Klar +1
We consider kinetic and related macroscopic equations on networks. A class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given b…
A hierarchy of kinetic discrete-velocity models for traffic flow derived from a non-local Prigogine-Herman model
Raul Borsche, Axel Klar
Starting from a non-local version of the Prigogine-Herman traffic model, we derive a natural hierarchy of kinetic discrete velocity models for traffic flow consisting of systems of…
Implicit Active Flux methods for linear advection
Wasilij Barsukow, Raul Borsche
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to…
Relaxation models for scalar traffic networks and zero relaxation limit
Raul Borsche, Axel Klar
In this paper we propose coupling conditions for a relaxation model for vehicular traffic on networks. We present a matched asymptotic expansion procedure to derive a LWR- network…
Kinetic-controlled hydrodynamics for multilane traffic models
R. Borsche, A. Klar, M. Zanella
We study the application of a recently introduced hierarchical description of traffic flow control by driver-assist vehicles to include lane changing dynamics. Lane-dependent feedb…
A kinetic traffic network model and its macroscopic limit: diverging lanes
Raul Borsche, Axel Klar
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 direction…
A kinetic traffic network model and its macroscopic limit: merging lanes
Raul Borsche, Axel Klar
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 o…
Kinetic layers and coupling conditions for nonlinear scalar equations on networks
Raul Borsche, Axel Klar
We consider a kinetic relaxation model and an associated macroscopic scalar nonlinear hyperbolic equation on a network. Coupling conditions for the macroscopic equations are derive…
A nonlinear discrete-velocity relaxation model for traffic flow
Raul Borsche, Axel Klar
We derive a nonlinear 2-equation discrete-velocity model for traffic flow from a continuous kinetic model. The model converges to scalar Lighthill-Whitham type equations in the rel…
Kinetic layers and coupling conditions for macroscopic equations on networks I: the wave equation
Raul Borsche, Axel Klar
We consider kinetic and associated macroscopic equations on networks. The general approach will be explained in this paper for a linear kinetic BGK model and the corresponding limi…
Numerical Approximation of Hyperbolic Systems Containing an Interface
Nina Aguillon, Raul Borsche
In this paper we present an approach to approximate numerically the solution of coupled hyperbolic conservation laws. The coupling is achieved through a fixed interface, in which i…
Kinetic and related macroscopic models for chemotaxis on networks
Raul Borsche, Axel Klar, Ha T. N. Pham
In this paper we consider kinetic and associated macroscopic models for chemotaxis on a network. Coupling conditions at the nodes of the network for the kinetic problem are present…
Mean field models for interacting ellipsoidal particles
Raul Borsche, Axel Klar, Anne Meurer +1
We consider a mean field hierarchy of models for large systems of interacting ellipsoids suspended in an incompressible fluid. The models range from microscopic to macroscopic mean…
High order numerical methods for networks of hyperbolic conservation laws coupled with ODEs and lumped parameter models
Raul Borsche, Jochen Kall
In this paper we construct high order finite volume schemes on networks of hyperbolic conservation laws with coupling conditions involving ODEs. We consider two generalized Riemann…
A Retarded Mean-Field Approach for Interacting Fiber Structures
Raul Borsche, Axel Klar, Christian Nessler +2
We consider an interacting system of one-dimensional structures modelling fibers with fiber-fiber interaction in a fiber lay-down process. The resulting microscopic system is inves…
Differential Equations Modeling Crowd Interactions
Raul Borsche, Rinaldo M. Colombo, Mauro Garavello +1
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness…
Flooding in urban drainage systems: Coupling hyperbolic conservation laws for sewer systems and surface flow
Raul Borsche, Axel Klar
In this paper we propose a model for a sewer network coupled to surface flow and investigate it numerically. In particular, we present a new model for the manholes in storm sewer s…
A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models
Raul Borsche, Mark Kimathi, Axel Klar
In the present paper a review and numerical comparison of a special class of multi-phase traffic theories based on microscopic, kinetic and macroscopic traffic models is given. Mac…
Kinetic derivation of a Hamilton-Jacobi traffic flow model
Raul Borsche, Axel Klar, Mark Kimathi
Kinetic models for vehicular traffic are reviewed and considered from the point of view of deriving macroscopic equations. A derivation of the associated macroscopic traffic flow e…