Discontinuous Galerkin finite element scheme for a conserved higher-order traffic flow model by exploring Riemann solvers

Abstract

The discontinuous Galerkin (DG) scheme is used to solve a conserved higherorder (CHO) traffic flow model by exploring several Riemann solvers. The second-order accurate DG scheme is found to be adequate in that the accuracy is comparable to the weighted essentially non-oscillatory (WENO) scheme with fifth-order accuracy and much better than the scheme with first-order accuracy in resolving a wide moving jam with a shock profile. Moreover, it considerably reduces the differences between the proposed solvers in generating numerical viscosities or errors. Thus, this scheme can maintain high efficiency when a simple solver is adopted. The scheme could be extended to solve more complex problems, such as those related to traffic flow in a network.

A Runge–Kutta discontinuous Galerkin scheme for hyperbolic conservation laws with discontinuous fluxes

“…To ensure the same order of accuracy, all integrals are computed by the Gauss formula with sufficiently high accuracy (e.g., the two-point formula for k = 1). We refer the reader to [2,10,15,20,29] for general account of the formulation.…”

High-order finite volume shallow water model on the cubed-sphere: 1D reconstruction scheme

“…They are broadly classified into upwind and central schemes depending on the final projection step. Upwind schemes employ Riemann solvers to resolve discontinuity at cell interfaces, this requires characteristic information of the wave propagation at the discontinuity (Riemann fans), often resulting in a complex and expensive upwind algorithm (see for example [15,17,22]). Where as the central schemes do not require characteristic decomposition or expensive Riemann solvers, and the projection is done by averaging over the Riemann fans [23], nevertheless, the central schemes are dissipative but computationally inexpensive.…”