Real-Time Solution of Velocity-Based First-Order Continuum Traffic Model with Finite Element Method

Abstract

Two approximate solution methods are investigated for the velocity-based version of a first-order continuum traffic flow model commonly known as the Lighthill–Whitham–Richards model. The finite difference and finite element methods are commonly used to numerically solve partial differential equations. The finite difference method adopted uses a standard Godunov scheme to solve the continuum model. The finite element method uses one-dimensional simplex elements with first-order interpolation function along with a Galerkin scheme to derive the element characteristic matrices and vectors. A high-resolution, real-world data set from the Next Generation Simulation program is used to evaluate the two solution methods. Results show that both methods provide accurate approximations to the observed speeds. The accuracy and quality of solutions and future directions of work in this area are discussed.