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The nonlinear weakly dispersive Serre equations contain higher-orderdispersive terms. This includes a mixed derivative flux term which is difficultto handle numerically. The mix spatial and temporal derivative dispersive termis replaced by a combination of temporal and spatial terms. The Serre equationsare re-written so that the system of equations contain homogeneous derivativeterms only. The reformulated Serre equations involve the water depth and a newquantity as the conserved variables which are evolved using the finite volumemethod. The remaining primitive variable, the velocity is obtained by solving asecond-order elliptic equation using the finite element method. To avoid theintroduction of numerical dispersion that may dominate the physical dispersion,the hybrid scheme has third-order accuracy. Using analytical solutions,laboratory flume data and by simulating the dam-break problem, the proposedscheme is shown to be accurate, simple to implement and stable for a range ofproblems, including discontinuous flows.

Third-order Finite Volume/Finite Element Solution of the Fully Nonlinear Weakly Dispersive Serre Equations