A monotonic upstream-centred scheme for conservation law (MUSCL) for shallow water flows is formulated and applied. The scheme is explicit and first order in time and second order in space with stability governed by the Courant condition. The accuracy and efficiency of the MUSCL scheme in modeling complex flow features are compared to those of the Boltzmann Bhatnagar-Gross-Krook (BGK) scheme as well as a kinetic flux vector splitting (KFVS) scheme. In particular, all schemes are applied to (i) strong shock waves, (ii) extreme expansion waves, (iii) a combination of strong shock waves and extreme expansion waves, and (iv) a one-dimensional dam break problem. Additionally, the MUSCL, BGK and KFVS schemes are applied to a one-dimensional dam break problem for which laboratory data is avail...[ Read more ]

A monotonic upstream-centred scheme for conservation law (MUSCL) for shallow water flows is formulated and applied. The scheme is explicit and first order in time and second order in space with stability governed by the Courant condition. The accuracy and efficiency of the MUSCL scheme in modeling complex flow features are compared to those of the Boltzmann Bhatnagar-Gross-Krook (BGK) scheme as well as a kinetic flux vector splitting (KFVS) scheme. In particular, all schemes are applied to (i) strong shock waves, (ii) extreme expansion waves, (iii) a combination of strong shock waves and extreme expansion waves, and (iv) a one-dimensional dam break problem. Additionally, the MUSCL, BGK and KFVS schemes are applied to a one-dimensional dam break problem for which laboratory data is available. These test cases reveal that all three schemes provide solutions of comparable accuracy. The MUSCL scheme is improved to MUSCL-Hancock scheme, which is second order accuracy both in time and space, to study the stability of steady uniform and nonuniform flows. Small perturbation is imposed on the base flows with different types of water surface profiles. The evolutions of the perturbation are calculated through the direct numerical simulations by MUSCL-Hancock scheme. The numerical results are compared with both the linear stability analysis results and the nonlinear stability investigation results. In both cases good agreements are achieved.