36 research outputs found
Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux
A fully adaptive finite volume multiresolution scheme for one-dimensional
strongly degenerate parabolic equations with discontinuous flux is presented.
The numerical scheme is based on a finite volume discretization using the
Engquist--Osher approximation for the flux and explicit time--stepping. An
adaptivemultiresolution scheme with cell averages is then used to speed up CPU
time and meet memory requirements. A particular feature of our scheme is the
storage of the multiresolution representation of the solution in a dynamic
graded tree, for the sake of data compression and to facilitate navigation.
Applications to traffic flow with driver reaction and a clarifier--thickener
model illustrate the efficiency of this method
Komplexe Verletzungen des Ellenbogens durch eine Schussverletzung aus kurzer Entfernung - Rekonstruktion durch Mikrovaskulären Osteomuskulokutanen Lappen
Traumatische proximale Sehnenruptur des Musculus Biceps Femoris und des Musculus Semitendiosus - Fallbericht einer seltenen Verletzung
Nachweis von Orthotrikresylphosphat und Isonicotinsäurehydrazid in verschiedenen Organen, insbesondere in der Nervensubstanz, in Abhängigkeit vom Lebensalter
Microscopic selection of solutions to scalar conservation laws with discontinuous flux in the context of vehicular traffic
In the context of road traffic modeling we consider a scalar hyperbolic conservation law with the flux (fundamental diagram) which is discontinuous at x = 0, featuring variable velocity limitation. The flow maximization criterion for selection of a unique admissible weak solution is generally admitted in the literature, however justification for its use can be traced back to the irrelevant vanishing viscosity approximation. We seek to assess the use of this criterion on the basis of modeling proper to the traffic context. We start from a first order microscopic follow-the-leader (FTL) model deduced from basic interaction rules between cars. We run numerical simulations of FTL model with large number of agents on truncated Riemann data, and observe convergence to the flow-maximizing Riemann solver. As an obstacle towards rigorous convergence analysis, we point out the lack of order-preservation of the FTL semigroup