Abstract : Gas flow in pipes, open channel flows, water distribution, traffic flow and blood flow are some modelling applications very often represented as hyperbolic one-dimensional systems in networks. Key modelling ingredients for these systems are the correct definition of boundary conditions at terminal network points, proper coupling conditions among one-dimensional domains and the coupling of one-dimensional domains to zero-dimensional models. Further complexity may be added: parameters varying in space and time, flow regimes varying from sub- to supercritical, diffusive and dispersive terms, etc. All these aspects result in challenging situations for numerical methods designed to discretise this type of models.
Organizer(s) : Ernesto Pimentel-García, Lucas O. Müller
[02382] Control of advection-diffusion equations on networks and singular limits
Format : Talk at Waseda University
Author(s) :
Nicola De Nitti (FAU Erlangen-Nürnberg )
Abstract : We consider advection-diffusion equations posed on a tree-shaped network with suitable transmission conditions at the junctions. We study the asymptotic behavior of the cost of the null-controllability as the diffusivity parameter vanishes: we show that it decays for a sufficiently large time and explodes for short times with an exponential rate.
[02297] A second order model of traffic with organization marker
Format : Talk at Waseda University
Author(s) :
Abraham Sylla (University of Milano-Bicocca)
Abstract : We present a toy model for self-organized road traffic taking into account the state of orderliness in drivers’ behavior. The model is reminiscent of the wide family of
generalized second-order models of road traffic. The orderliness marker is evolved along vehicles’ trajectories and it influuences the fundamental diagram of the traffic flow. The coupling we have in mind is nonlocal, leading to a kind of "weak decoupling" of the resulting $2 \times 2$ system.
[02293] Limiting flow in atrial-ventricular function
Format : Talk at Waseda University
Author(s) :
Javier Murillo (I3A, University of Zaragoza,)
Juan Mairal (I3A, University of Zaragoza,)
Pilar García-Navarro (I3A, University of Zaragoza,)
Abstract : To date, no methodology is available for coupling 1D blood flow to models of the peripheral vasculature, valves, or heart when the flow regime is other than subsonic. When modeling complex fluid networks using 1D approaches, boundary conditions can be imposed using 0D models. An application case is the modeling of the human circulation using closed-loop models. These can be considered a tool to investigate short-term transient hemodynamic responses to postural changes in atrial-ventricular function.
01195 (2/2) : 2E @G601 [Chair: Ernesto Pimentel-García]
[02299] The Junction Riemann Problems under transonic scenarios: application to veins.
Format : Talk at Waseda University
Author(s) :
Juan Mairal (I3A - Universidad de Zaragoza)
Javier Murillo (I3A, University of Zaragoza,)
Pilar García-Navarro (I3A - Universidad de Zaragoza)
Abstract : Current 1D numerical methods for flow in junctions provide good results in most cases. In the 1D framework, the junction is a singular point. One of the shortcomings of existing methods is their inability to deal with transonic and supersonic flow at junctions in physiological flows. Existing methods that rely on coupling approaches for conservation of mass, energy or momentum and the characteristic equations for subsonic flow conditions are revisited here.
[02244] Numerical and physical impact of coupling conditions for one dimensional blood flow models
Format : Talk at Waseda University
Author(s) :
Lucas Omar Müller (University of Trento)
Abstract : One dimensional blood flow models consist of hyperbolic or hyperbolic-dominant systems of balance laws. This specific mathematical property plays a key role in the derivation of coupling and boundary conditions necessary to model blood flow in networks of vessels. In this talk we will derive coupling and boundary conditions for a general velocity profile and study their physical and numerical impact in simulations of the arterial and venous system across several spatial scales.
[02355] High-order fully well-balanced numerical methods for one-dimensional blood flow in networks
Format : Talk at Waseda University
Author(s) :
Ernesto Pimentel-García (University of Málaga)
Abstract : We are interested in the numerical study of one-dimensional blood flow model in networks with discontinuous mechanical and geometrical properties. We do an exhaustive investigation of all its stationary solutions and we propose high-order fully well-balanced numerical methods that are able to preserve all of them. These methods are able to deal with more than one discontinuous parameter and friction. Some numerical tests are shown to prove its well-balanced and high-order properties.
