We consider a linearized kinetic BGK equation and the associated acoustic system on a network.
Coupling conditions for the macroscopic equations are derived from the kinetic conditions via an asymptotic analysis near the nodes of the network.
This analysis leads to the consideration of a fixpoint problem involving the solutions of kinetic half-space problems.
This work extends the procedure developed in [13], where coupling conditions for a simplified BGK model have been derived.
Numerical comparisons between different coupling conditions
confirm the accuracy of the proposed approximation.
Simulating the flow of water in district heating networks requires numerical methods which are independent of the CFL condition. We develop a high order scheme for networks of advection equations allowing large time steps. With the MOOD technique unphysical oscillations of non smooth solutions are avoided. In numerical tests the applicability to real networks is shown.
A distributional solution framework is developed for systems consisting of linear hyperbolic partial differential equations (PDEs) and switched differential algebraic equations (DAEs) which are coupled via boundary conditions. The unique solvability is then characterize in terms of a switched delay DAE. The theory is illustrated with an example of electric power lines modeled by the telegraph equations which are coupled via a switching transformer where simulations confirm the predicted impulsive solutions.
In this article a new numerical solver for simulations of district heating networks is presented. The numerical method applies the local time stepping introduced in [11] to networks of linear advection equations. In combination with the high order approach of [4] an accurate and very efficient scheme is developed. In several numerical test cases the advantages for simulations of district heating networks are shown.
In this paper we construct a numerical solver for the Saint Venant equations. Special attention
is given to the balancing of the source terms, including the bottom slope and variable cross-
sectional profiles. Therefore a special discretization of the pressure law is used, in order to
transfer analytical properties to the numerical method. Based on this approximation a well-
balanced solver is developed, assuring the C-property and depth positivity. The performance
of this method is studied in several test cases focusing on accurate capturing of steady states.
In this article we present a method to extend high order finite volume schemes
to networks of hyperbolic conservation laws with algebraic coupling conditions. This method is based on an ADER approach in time to solve the
generalized Riemann problem at the junction. Additionally to the high order accuracy, this approach maintains an exact conservation of quantities if
stated by the coupling conditions. Several numerical examples confirm the
benefits of a high order coupling procedure for high order accuracy and stable
shock capturing.
In the present paper scalar macroscopic models for traffic and pedestrian flows are coupled and the resulting system is investigated numerically. For the traffic flow the classical
Lighthill-Whitham model on a network of roads and for the pedestrian flow the Hughes
model are used. These models are coupled via terms in the fundamental diagrams mod-
eling an influence of the traffic and pedestrian flow on the maximal velocities of the
corresponding models. Several physical situations, where pedestrians and cars interact,
are investigated.