Enrico Bertolazzi

A Second-Order Maximum Principle Preserving Finite Volume Method for Steady Convection-Diffusion Problems

A cell-centered finite volume method is proposed to approximate numerically the solution to the steady convection-diffusion equation on unstructured meshes of

Supporting Drivers in Keeping Safe Speed and Safe Distance: The SASPENCE Subproject Within the European Framework Programme 6 Integrating Project PReVENT

d

ON VERTEX RECONSTRUCTIONS FOR CELL-CENTERED FINITE VOLUME APPROXIMATIONS OF 2D ANISOTROPIC DIFFUSION PROBLEMS

-simplexes, where

A Holistic Approach to the Integration of Safety Applications: The INSAFES Subproject Within the European Framework Programme 6 Integrating Project PReVENT

d\geq 2

A CELL-CENTERED SECOND-ORDER ACCURATE FINITE VOLUME METHOD FOR CONVECTION–DIFFUSION PROBLEMS ON UNSTRUCTURED MESHES

is the spatial dimension. The method is formally second-order accurate by means of a piecewise linear reconstruction within each cell and at mesh vertices. An algorithm is provided to calculate nonnegative and bounded weights. Face gradients, required to discretize the diffusive fluxes, are defined by a nonlinear strategy that allows us to demonstrate the existence of a maximum principle. Finally, a set of numerical results documents the performance of the method in treating problems with internal layers and solutions with strong gradients.

Combining safety margins and user preferences into a driving criterion for optimal control-based computation of reference maneuvers for an ADAS of the next generation

This paper describes a novel driver-support system that helps to maintain the correct speed and headway (distance) with respect to lane curvature and other vehicles ahead. The system has been developed as part of the Integrating Project PReVENT under the European Framework Programme 6, which is named SAfe SPEed and safe distaNCE (SASPENCE). The application uses a detailed description of the situation ahead of the vehicle. Many sensors [radar, video camera, Global Positioning System (GPS) and accelerometers, digital maps, and vehicle-to-vehicle wireless local area network (WLAN) connections] are used, and state-of-the-art data fusion provides a model of the environment. The system then computes a feasible maneuver and compares it with the drivers behavior to detect possible mistakes. The warning strategies are based on this comparison. The system “talks” to the driver mainly via a haptic pedal or seat belt and “listens” to the driver mainly via the vehicle acceleration. This kind of operation, i.e., the comparison between what the system thinks is possible and what the driver appears to be doing, and the consequent dialog can be regarded as simple implementations of the rider-horse metaphor (H-metaphor). The system has been tested in several situations (driving simulator, hardware in the loop, and real road tests). Objective and subjective data have been collected, revealing good acceptance and effectiveness, particularly in awakening distracted drivers. The system intervenes only when a problem is actually detected in the headway and/or speed (approaching curves or objects) and has been shown to cause prompt reactions and significant speed correction before getting into really dangerous situations.

Algorithm 817: P2MESH: generic object-oriented interface between 2-D unstructured meshes and FEM/FVM-based PDE solvers

The accuracy of the diamond scheme is experimentally investigated for anisotropic diffusion problems in two space dimensions. This finite volume formulation is cell-centered on unstructured triangulations and the numerical method approximates the cell averages of the solution by a suitable discretization of the flux balance at cell boundaries. The key ingredient that allows the method to achieve second-order accuracy is the reconstruction of vertex values from cell averages. For this purpose, we review several techniques from the literature and propose a new variant of the reconstruction algorithm that is based on linear Least Squares. Our formulation unifies the treatment of internal and boundary vertices and includes information from boundaries as linear constraints of the Least Squares minimization process. It turns out that this formulation is well-posed on those unstructured triangulations that satisfy a general regularity condition. The performance of the finite volume method with different algorithms for vertex reconstructions is examined on three benchmark problems having full Dirichlet, Dirichlet-Robin and Dirichlet–Neumann boundary conditions. Comparison of experimental results shows that an important improvement of the accuracy of the numerical solution is attained by using our Least Squares-based formulation. In particular, in the case of Dirichlet–Neumann boundary conditions and strongly anisotropic diffusions the good behavior of the method relies on the absence of locking phenomena that appear when other reconstruction techniques are used.

Artificial Co-Drivers as a Universal Enabling Technology for Future Intelligent Vehicles and Transportation Systems

This paper deals with the integration of multiple advanced driver-assistance systems (ADAS) and in-vehicle information systems (IVIS) in a holistic driver-support system. The paper presents the results of a project named Integrated Safety Systems (INSAFES), which was part of PReVENT: an integrating project carried out under the European Framework Programme 6. Integration in INSAFES is tackled at three different levels in the framework of a “cognitive car” perspective: 1) at the perception level, to represent the world around the vehicle, including object-tracking between sensor fields and the detection of driver intentions; 2) at the decision level, to reproduce humanlike holistic motion plans, which serve as “reference maneuvers” to evaluate the motion alternatives that a driver faces; and 3) at the level of interaction with the driver and vehicle control ( action level), to arbitrate between the requests of functions competing for driver attention. A function that provides simultaneous longitudinal and lateral support has been developed. It gives support for safe speed, safe distance, lane change, and all-around collision avoidance all at the same time. At its core, there is a tool (evasive/reference maneuver) that constantly evaluates two possible alternatives (in lane and evasive/lane change) and compares them with the driver input to detect which one applies, which dictates warnings and driver interactions, and whether there is a better alternative. In addition, a “warning manager” has been developed, acting like a referee who lets the ADAS applications work standalone and then combines the requests of each application, prioritizes them, and manages the interaction with the user. The warning manager can be particularly useful in the case of integration of pre-existing standalone functions, which can be quickly reused. If a holistic ADAS is developed, the warning manager can still be used to combine it with IVIS functions. In fact, depending on the kind of ADAS and IVIS considered, the most suitable approach can be either to combine functions in a unified multifunctional driver-support application or to arbitrate between them through the warning manager.

DISCRETE CONSERVATION AND DISCRETE MAXIMUM PRINCIPLE FOR ELLIPTIC PDEs

A MUSCL-like cell-centered finite volume method is proposed to approximate the solution of multi-dimensional steady advection–diffusion equations. The second-order accuracy is provided by an appropriate definition of the diffusive and advective numerical fluxes. The method is based on a least squares reconstruction of the vertex values from cell averages. The slope limiter, which is required to prevent the formation and growth of spurious numerical oscillations, is designed to guarantee that the discrete solution of the nonlinear scheme exists. Several theoretical issues regarding the solvability of the resulting discrete problems are thoroughly discussed. Finally, numerical experiments that validate the effectiveness of the approach are presented.

Construction of a Finite Element Basis of the First de Rham Cohomology Group and Numerical Solution of 3D Magnetostatic Problems

This paper outlines a methodology for combining users preferred driving style and safety margins into an ADASs module for optimal reference maneuver computation. The module for optimal reference maneuver computation is part of the system decision planning chain, which links scenario interpretation to warning intervention strategies. The module objective is the computation of a reference maneuver and produce a measure of the related risk by solving an optimal control problem. In this case, the optimal control problem consists in finding the control functions that minimize the integral of a given penalty function over a planning distance subject to a set of constraints. The penalty function is the mean to implement the safe maneuver concept, which has to comply with three top-level requirements: safety-margins, user acceptance and mobility. In the present work only the safe-speed functionality is addressed and a new penalty function formulation is proposed in order to include both safety criteria and preferred driving style. In this paper it is shown that each users personal driving style can be characterized through a small set of parameters from the analysis of car longitudinal and lateral accelerations that can be easily used in optimal control formulation.