Six finite-difference equations often used to approximate the continuity equation of traffic flow are compared in terms of their ability to solve the Lighthill-Whitham-Richards model. Ten representative initial traffic flow conditions were selected, and numerical solutions were obtained for the selected cases using the six finite-difference equations. Results are compared with analytical solutions, and the numerical properties of these approximations are examined. It was found that the upwind finite-difference schemes with volume corrections (Godunov-type schemes) produce the best results for all 10 cases and are reasonable finite-difference schemes for simulating traffic flow.
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