We consider the Lighthill-Witham-Richards traffic flow model on a junction composed by one mainline, an onramp and an offramp, which are connected by a node. The onramp dynamics is modeled using an ordinary differential equation describing the evolution of the queue length. The definition of the solution of the Riemann problem at the junction is based on an optimization problem and the use of a...

We address a problem of boundary control for nonlinear scalar conservation law. Namely, this article is devoted to the Lighthill-Whitham-Richards (LWR) partial differential equation (PDE) with triangular flux function evolving along single road. The target state time- and space-dependent trajectory. law constructed using analytical solution Hamilton–Jacobi (H–J) equation, which an integral form...

When shock speed s times ∆t/∆x is rational, the existence of solutions of shock profile equations on bounded intervals for monotonicity preserving schemes with continuous numerical flux is proved. A sufficient condition under which the above solutions can be extended to −∞ < j < ∞, implying the existence of discrete shock profiles of numerical schemes, is provided. A class of monotonicity prese...

A validation study is presented for a numerical code which calculates a two-dimensional steady-state solution for inviscid hypersonic flows in the presence of strong surface blowing. A higher-orde: Godunov-type finite-volume approach is used to discretize the inviscid Euler equations. Interface values of the state quantities are reconstructed nsing a monotone interpolation technique suggested b...

We consider a scalar conservation law with a discontinuous flux function. The fluxes are non-convex, have multiple points of extrema and can have arbitrary intersections. We propose an entropy formulation based on interface connections and associated jump conditions at the interface. We show that the entropy solutions with respect to each choice of interface connection exist and form a contract...

We present a theoretical solution for the Riemann problem for the five-equation two-phase non-conservative model of Saurel and Abgrall. This solution is then utilized in the construction of upwind non-conservative methods to solve the general initial-boundary value problem for the two-phase flow model in non-conservative form. The basic upwind scheme constructed is the non-conservative analogue...

Conservative discretizations of two uid ow problems generally exhibit pressure oscillations In this work we show that these pressure oscillations are induced by the loss of a pressure invariance property under discretiza tion and we introduce a non oscillatory conservative method for barotropic two uid ows The conservative formulation renders the two uid ow problem suitable to treatment by a Go...

ties. In this paper we investigate the behavior of shock-capturing shocks. Here slowly moving means that the ratio of the methods for slowly moving shocks. It is known that for slowly movshock speed to the maximum wave speed in the domain ing shocks even a first-order scheme, such as the Godunov or Roe is much smaller than one. Several references have reported type methods, will generate downst...