Numerical modelling of flood flows over irregular topography

In solving the hyperbolic equations of environmental shallow water flows, computational difficulty arises when the topography is irregular. In particular, under a conventional operator-splitting framework, a very small time step is often necessary to ensure stability, and this limitation on the time step is dictated by the magnitude of the source terms in relation to the irregular topography and inevitably increases the computational cost. Here a practically efficient finite volume algorithm is presented for solving the hyperbolic equations of shallow water flows. The numerical solution is achieved under an operator-splitting framework, a second-order weighted average flux (WAF) total variation diminishing (TVD) method along with the Harten Lax van Leer (HLL) approximate Riemann solver for the homogeneous equations, and a Runge–Kutta scheme for the ordinary differential equations of source terms. For numerical stability, a self-adaptive time step method is proposed under the Runge–Kutta scheme. Numerical tests for a case of glacier-lake outburst flooding demonstrate that the present model is essentially free from the restriction on time step arising from irregular topography, and therefore computational efficiency is substantially enhanced. The model is benchmarked with an urban flooding event in Glasgow, UK, and the modelling results are in reasonable agreement with those attained by others from the Flood Risk Management Research Consortium, UK.