Related papers: Discontinuous Galerkin method for macroscopic traf…
The interior penalty discontinuous Galerkin method is applied to solve elliptic equations on either networks of segments or networks of planar surfaces, with arbitrary but fixed number of bifurcations. Stability is obtained by proving a…
We propose and analyse a new microscopic second order Follow-the-Leader type scheme to describe traffic flows. The main novelty of this model consists in multiplying the second order term by a nonlinear function of the global density, with…
Discontinuous Galerkin (DG) methods for the numerical solution of partial differential equations have enjoyed considerable success because they are both flexible and robust: They allow arbitrary unstructured geometries and easy control of…
Discrete fracture models with reduced-dimensional treatment of conductive and blocking fractures are widely used to simulate fluid flow in fractured porous media. Among these, numerical methods based on interface models are intensively…
In recent years, high-order discontinuous Galerkin (DG) methods have emerged as an attractive approach for numerical simulations of compressible flows. This paper presents an overview of the recent development of DG methods for compressible…
We present a compatible space-time hybridizable/embedded discontinuous Galerkin discretization for nonlinear free-surface waves. We pose this problem in a two-fluid (liquid and gas) domain and use a time-dependent level-set function to…
Fundamental to many transportation network studies, traffic flow models can be used to describe traffic dynamics determined by drivers' car-following, lane-changing, merging, and diverging behaviors. In this study, we develop a…
The study of uncertainty propagation poses a great challenge to design numerical solvers with high fidelity. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
This paper is concerned with highway traffic estimation using traffic sensing data, in a Lagrangian-based modeling framework. We consider the Lighthill-Whitham-Richards (LWR) model (Lighthill and Whitham, 1955; Richards, 1956) in…
In this work, we propose an algorithm performing short-term predictions of the flux of vehicles on a stretch of road, using past measurements of the flux. This algorithm is based on a physics-aware recurrent neural network. A discretization…
While macroscopic traffic flow models consider traffic as a fluid, microscopic traffic flow models describe the dynamics of individual vehicles. Capturing macroscopic traffic phenomena remains a challenge for microscopic models, especially…
We prove the well-posedness of a system of balance laws inspired by [8], describing macro-scopically the traffic flow on a multi-lane road network. Motivated by real applications, we allow for the the presence of space discontinuities both…
We review recent results and present new ones on a deterministic follow-the-leader particle approximation of first and second order models for traffic flow and pedestrian movements. We start by constructing the particle scheme for the first…
We develop a probabilistic framework for global modeling of the traffic over a computer network. This model integrates existing single-link (-flow) traffic models with the routing over the network to capture the global traffic behavior. It…
We present a new algorithm for the discretization of the Vlasov-Maxwell system of equations for the study of plasmas in the kinetic regime. Using the discontinuous Galerkin finite element method for the spatial discretization, we obtain a…
In this paper a spatial homogeneous vehicular traffic flow model based on a stochastic master equation of Boltzmann type in the acceleration variable is solved numerically for a special driver interaction model. The solution is done by a…
We examine a variational multiscale method in which the unresolved fine-scales are approximated element-wise using a discontinuous Galerkin method. We establish stability and convergence results for the methodology as applied to the scalar…
There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in…
We present a first numerical study of transport phenomena involving chemically reactive species, modeled by advection-diffusion-reaction systems with flow fields governed by Darcy's law. Among the various discretisation approaches, we…