Asymptotic traveling wave solutions to anisotropic higher-order traffic flow models with viscosities

The boundary layer correction method is applied to study asymptotic traveling wave solutions to anisotropic higher-order traffic flow model with viscous coefficient, which clearly indicates that the truncation error between the original and approximate equations is an equivalent infinitesimal of the coefficient. Therefore, the solution is exact in the case when the coefficient vanishes, which corresponds to a certain nonviscous model following the standard hyperbolic and viscous conservation laws. Numerical simulation is implemented to reproduce a typical traveling wave or wide moving jam consisting of a transitional layer (the downstream front) and a shock (the upstream front) profiles, of which the parameters converge not only for refined meshes but for refined viscous coefficient as well. These are highly in agreement with the analytical results.