A family of high-order numerical algorithms for the model of Wang

This study employs various WENO schemes to solve the Wang model, which is derived from hyperbolic conservation laws for chromatography. The proposed approach achieves high-order accuracy while maintaining essentially non-oscillatory results near discontinuities. The six high-order schemes demonstrate three key advantages: (1) The Lax-Friedrichs flux ensures numerical stability and computational efficiency, while the Harten-Lax-van Leer (HLL) flux reduces numerical dissipation, enhancing resolution and physical fidelity. (2) The WENO-JS and WENO-Z schemes employ nonlinear weights to effectively suppress high-frequency oscillations in discontinuous regions. (3) By exploiting polynomial sub-stencil characteristics, both the WENO6Z and TENO8 schemes achieve superior accuracy in smooth regions coupled with enhanced shock-capturing performance and numerical stability. Numerical experiments with various initial conditions confirm that these schemes can stably and efficiently simulate the Wang model with high resolution, demonstrating their effectiveness.