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Abstract: A high-resolution relaxed scheme which requires little information of the eigenstructure is presented for the multi-class Lighthill-Whitham-Richards (LWR) model on an inhomogeneous highway. The scheme needs only an estimate of the upper boundary of the maximum of absolute eigenvalues. It is based on incorporating an improved fifth-order weighted essentially non-oscillatory (WENO) reconstruction with relaxation approximation. The scheme benefits from the simplicity of relaxed schemes in that it requires no exact or approximate Riemann solvers and no projection along characteristic directions. The effectiveness of our method is demonstrated in several numerical examples.

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