##  [Lighthill–Whitham–Richards Model](/lighthill-whitham-richards-model) 

  ##  [Lighthill–Whitham–Richards Model](https://mathlogic.quantumdictionary.io/lighthill-whitham-richards-model-0) 

  

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**Mathematics & Logic Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A macroscopic traffic-flow model that treats vehicle density ρ(x,t) as a conserved scalar satisfying a hyperbolic conservation law ρ_t + q(ρ)_x = 0, where the flux q(ρ) = ρ v(ρ) is given by a fundamental diagram relating density to mean speed; it describes kinematic waves, shocks, and rarefactions in traffic.