Traffic waves are phenomena that emerge when the vehicular density exceeds a critical threshold. Considering the presence of increasingly automated vehicles in the traffic stream, a number of research activities have focused on the influence of automated vehicles on the bulk traffic flow. In the present article, we demonstrate experimentally that intelligent control of an autonomous vehicle is able to dampen stop-and-go waves that can arise even in the absence of geometric or lane changing triggers. Precisely, our experiments on a circular track with more than 20 vehicles show that traffic waves emerge consistently, and that they can be dampened by controlling the velocity of a single vehicle in the flow. We compare metrics for velocity, braking events, and fuel economy across experiments. These experimental findings suggest a paradigm shift in traffic management: flow control will be possible via a few mobile actuators (less than 5%) long before a majority of vehicles have autonomous capabilities.

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Shallow water models are widely used to describe and study free-surface water flow. Even though, in many practical applications the bottom friction does not have much influence on the solutions, the friction terms will play a significant role when the depth of the water is very small. In this paper, we study the Saint-Venant system of shallow water equations with friction terms and develop a well-balanced central-upwind scheme that is capable of exactly preserving its steady states. The scheme also preserves the positivity of the water depth. We test the designed scheme on a number of one-and two-dimensional examples that demonstrate robustness and high resolution of the proposed numerical approach. The data in the last numerical example correspond to the laboratory experiments reported in [L. Cea, M. Garrido, and J. Puertas, J. Hydrol, 382 (2010), pp. 88-102], designed to mimic the rain water drainage in urban areas containing houses. Since the rain water depth is typically several orders of magnitude smaller than the height of the houses, we develop a special technique, which helps to achieve a remarkable agreement between the numerical and experimental results.

In this paper, we develop a family of second-order semi-implicit time integration methods for systems of ordinary differential equations (ODEs) with stiff damping term. The important feature of the new methods resides in the fact that they are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only. The new semi-implicit methods are based on the modification of explicit strong stability preserving Runge-Kutta (SSP-RK) methods and are proven to have a formal second order of accuracy, A(α)-stability, and stiff decay. We illustrate the performance of the proposed SSP-RK based semi-implicit methods on both a scalar ODE example and a system of ODEs arising from the semi-discretization of the shallow water equations with stiff friction term. The obtained numerical results clearly demonstrate that the ability of the introduced ODE solver to exactly preserve equilibria plays an important role in achieving high resolution when a coarse grid is used.Key words. ordinary differential equations with stiff damping terms, semi-implicit methods, strong stability preserving Runge-Kutta methods, implicit-explicit methods, shallow water equations with friction terms

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purely conservative reformulation of the equations using global fluxes. The proposed scheme is capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. A crucial step in the construction of the second-order scheme is a well-balanced piecewise linear reconstruction of equilibrium variables combined with a well-balanced central-upwind evolution in time, which is adapted to reduce the amount of numerical viscosity when the flow is at (near) steady-state regime. We show the performance of our newly developed central-upwind scheme and demonstrate importance of perfect balance between the fluxes and gravitational forces in a series of one-and twodimensional examples.