The Godunov scheme is a conservative finite volume numerical method used to solve hyperbolic partial differential equations, such as those governing traffic flow or pedestrian dynamics, by computing fluxes at cell interfaces using solutions to local Riemann problems. It matters because it provides a stable, entropy-satisfying discretization of conservation laws like the Lighthill-Whitham-Richards (LWR) model, making it well-suited for capturing shock waves and discontinuities in density that arise in crowd and traffic simulations. Key variants include the first-order classical Godunov method and higher-order extensions, as well as its integration into Physics-Informed Deep Learning frameworks where it serves as the physics-based component within hybrid computational graphs to enforce physical consistency during traffic state estimation.
Source Papers
- A high-resolution meshfree particle method for numerical investigation of second-order macroscopic pedestrian flow models ↗ — A high-resolution meshfree particle method for numerical inv
- Continuum theory for pedestrian traffic flow: Local route choice modelling and its implications ↗ — Continuum theory for pedestrian traffic flow: Local route ch
- Physics-Informed Deep Learning for Traffic State Estimation: A Survey and the Outlook ↗ — Physics-Informed Deep Learning for Traffic State Estimation:
- Revisiting Hughes’ dynamic continuum model for pedestrian flow and the development of an efficient solution algorithm ↗ — Revisiting Hughes’ dynamic continuum model for pedestrian fl