ANTIDIFFUSIVE AND RANDOM-SAMPLING LAGRANGIAN-REMAP SCHEMES FOR THE MULTICLASS LIGHTHILL-WHITHAM-RICHARDS TRAFFIC MODEL

The multiclass Lighthill-Whitham-Richards (MCLWR) traffic model, which distinguishes N classes of drivers differing in preferential velocity, gives rise to a system of N strongly coupled, nonlinear first-order conservation laws for the car densities as a function of distance and time. The corresponding velocities involve a hindrance function that depends on the local total density of cars. Since the eigenvalues and eigenvectors of the flux Jacobian have no closed algebraic form, characteristic-wise numerical schemes for the MCLWR model become involved. Alternative simple schemes for this model directly utilize that the velocity functions are nonnegative and strictly decreasing, which allows one to construct a new class of schemes by splitting the system of conservation laws into two different first-order quasi-linear systems, which are solved successively for each time iteration, namely, the Lagrangian and remap steps. The new schemes are called Lagrangian-remap (LR) schemes. One version of LR schemes incorporates recent antidiffusive techniques for transport equations. The corresponding subclass of LR schemes are called Lagrangian-antidiffusive-remap (L-AR) schemes. Alternatively, the remap step can be handled by Glimm-like random sampling, which gives rise to a statistically conservative Lagrangian-random-sampling (L-RS) scheme that is less diffusive than other remap techniques. The LR schemes for the MCLWR model are supported by a partial analysis of the L-AR schemes for N = 1, which are total variation diminishing under a suitable CFL condition and therefore converge to a weak solution, and by numerical examples for both L-AR and L-RS subclasses of schemes.