The dispersionless Whitham modulation equations in 2+1 (two space dimensions and time) are reviewed and the instabilities identified. The modulation theory is then reformulated, near the Lighthill instability threshold, with a slow phase, moving frame and different scalings. The resulting nonlinear phase modulation equation near the Lighthill surfaces is a geometric form of the 2+1 two-way Bous...

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...

In this paper, a new nonlinear heat equation is studied that arises as model of the collective behavior automated vehicles. The properties solutions are by introducing appropriate notion weak solution requires certain entropy-like conditions. To obtain an approximation equation, conservative first-order finite difference scheme proposed respects corresponding entropy conditions, and links betwe...

We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill-Whitham-Richards (LWR) equation with the 2 × 2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. We describe the solutions of the Riemann problem, and we compare the result...

This paper gives rigorous numerical analysis of the error in prediction of aeroacoustic noise via Lighthill analogy. The first fundamental and intractable problem is to predict the sound power on surfaces. We give a full analysis of three methods of prediction. The second fundamental problem is the limited regularity of the underlying turbulent flow. This is handled herein by giving a negative ...

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 present simple discrete velocity models for traffic flows. The novel feature in the corresponding relaxation system is the presence of non negative velocities only. We show that in the small relaxation limit the discrete models reduce to the Lighthill-Whitham-Richards equation. In addition we propose second order schemes combined with IMEX time integrators as proper discretization of the rel...

In this study, the aerodynamic sound generated from the inclined circular cylinder was investigated experimentally and numerically. The generated sound and a coherent length of velocity fluctuation along the cylinder axis were measured by a low-noise wind tunnel with endplates. The sound and the flow in wake were also simulated by Large Eddy Simulation and Lighthill-Curle’s equation. We got the...