The discontinuous Galerkin (DG) scheme is used to solve a conserved higherorder (CHO) traffic flow model by exploring several Riemann solvers. The second-order accurate DG scheme is found to be adequate in that the accuracy is comparable to the weighted essentially non-oscillatory (WENO) scheme with fifth-order accuracy and much better than the scheme with first-order accuracy in resolving a wide moving jam with a shock profile. Moreover, it considerably reduces the differences between the proposed solvers in generating numerical viscosities or errors. Thus, this scheme can maintain high efficiency when a simple solver is adopted. The scheme could be extended to solve more complex problems, such as those related to traffic flow in a network.

The paper proposes a scheme by combining the Runge-Kutta discontinuous Galerkin method with a δ-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to nonlinear elasticity in heterogeneous media and multi-class traffic flow with inhomogeneous road conditions. Numerical examples indicate the scheme's efficiency in resolving complex waves of the two systems. Moreover, the discussion implies that the so-called δ-mapping algorithm can also be combined with any other classical methods for solving similar problems in general.

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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.