17,380 research outputs found
A hyperbolic model of chemotaxis on a network: a numerical study
In this paper we deal with a semilinear hyperbolic chemotaxis model in one
space dimension evolving on a network, with suitable transmission conditions at
nodes. This framework is motivated by tissue-engineering scaffolds used for
improving wound healing. We introduce a numerical scheme, which guarantees
global mass densities conservation. Moreover our scheme is able to yield a
correct approximation of the effects of the source term at equilibrium. Several
numerical tests are presented to show the behavior of solutions and to discuss
the stability and the accuracy of our approximation
Air entrainment in transient flows in closed water pipes: a two-layer approach
In this paper, we first construct a model for free surface flows that takes
into account the air entrainment by a system of four partial differential
equations. We derive it by taking averaged values of gas and fluid velocities
on the cross surface flow in the Euler equations (incompressible for the fluid
and compressible for the gas). The obtained system is conditionally hyperbolic.
Then, we propose a mathematical kinetic interpretation of this system to
finally construct a two-layer kinetic scheme in which a special treatment for
the "missing" boundary condition is performed. Several numerical tests on
closed water pipes are performed and the impact of the loss of hyperbolicity is
discussed and illustrated. Finally, we make a numerical study of the order of
the kinetic method in the case where the system is mainly non hyperbolic. This
provides a useful stability result when the spatial mesh size goes to zero
Parametric uncertainty analysis of pulse wave propagation in a model of a human arterial network
Accepted versio
Coupling techniques for nonlinear hyperbolic equations. IV. Multi-component coupling and multidimensional well-balanced schemes
This series of papers is devoted to the formulation and the approximation of
coupling problems for nonlinear hyperbolic equations. The coupling across an
interface in the physical space is formulated in term of an augmented system of
partial differential equations. In an earlier work, this strategy allowed us to
develop a regularization method based on a thick interface model in one space
variable. In the present paper, we significantly extend this framework and, in
addition, encompass equations in several space variables. This new formulation
includes the coupling of several distinct conservation laws and allows for a
possible covering in space. Our main contributions are, on one hand, the design
and analysis of a well-balanced finite volume method on general triangulations
and, on the other hand, a proof of convergence of this method toward entropy
solutions, extending Coquel, Cockburn, and LeFloch's theory (restricted to a
single conservation law without coupling). The core of our analysis is, first,
the derivation of entropy inequalities as well as a discrete entropy
dissipation estimate and, second, a proof of convergence toward the entropy
solution of the coupling problem.Comment: 37 page
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