A class of central unstaggered schemes for nonlocal conservation laws: Applications to traffic flow models

Abstract

This study introduces a new class of central unstaggered finite volume methods that are used to approximate solutions to nonlocal conservation laws. The proposed method is based on Nessyahu and Tadmor's (NT). Instead of solving Riemann's problems at the level of cell interfaces, as in the NT scheme, the approach we develop implicitly uses ghost cells while still generating the numerical solution on a single grid. We use our method with the aim of solving one-dimensional nonlocal traffic flow problems. The numerical results we present demonstrate the accuracy, high resolution, and non-oscillatory nature of the proposed method and compare very favorably with those obtained using the original NT method, demonstrating the expected simplicity of a family of unstaggered central schemes and confirming that nonlocal traffic flow models can be treated very efficiently by the suggested method.