Well-Balanced Finite Volume Scheme for Shallow Water Flooding and Drying Over Arbitrary Topography

Abstract

ABSTRACT:The depth-averaged shallow water equations based on Godunov-type finite volume method are developed for unsteady flow over arbitrary topography with moving lateral boundaries caused by flooding or recession. An HLLC approximate Riemann solver is invoked to evaluate fluxes. A linear reconstruction procedure with WBAP-L1 limiter and modified 4 stages Runge-Kutta time stepping are employed to provide a second order accuracy that is free from spurious oscillations. Also, a robust technique is presented to efficiently and accurately simulate the movement of wet/dry fronts. The model predictions are compared with analytical solutions, experimental data and a two-dimensional dam-break event. Numerical results show that the model performs satisfactorily with respect to its effectiveness and robustness and thus has good application prospects.

Agent‐based simulator of dynamic flood‐people interactions

“…The non‐sequential hydrodynamic ABM implementation on FLAMEGPU was verified in reproducing two 2D dam‐break flow tests (Huang, Zhang, & Pei, 2013; Wang et al, 2011). In both tests, the hydrodynamic ABM on FLAMEGPU reproduced the same predictions as the sequential counterpart and shows close agreement alternative predictions (see Appendix for more details).…”

“…The imaginary dam was located along x = 16 m locking an initial body of water with a height of 1.875 m. The roughness is represented by Manning coefficient n M = 0.018 s m −1/3 . Figure A2 (left) shows the simulated water surface elevation produced at the same output times as the results in Huang et al (2013), also shown in Figure A2 (right). As shown in Figure A2, the outputs delivered by the non-sequential hydrodynamic model on FLAMEGPU were similar to those of Huang et al (2013), both demonstrating capability to capture wave reflections, wetting-and-drying fronts, and to conserve mass as the dam-break flood ultimately settles decelerated by friction effects.…”

The MOOD method for the non-conservative shallow-water system

“…We consider a modified version of the classic HLLC solver [52], initially presented in [53], which derives from the simple HLL flux adding one more contact wave to take into account of the tangential velocity. For such, an additional simple intermediate wave, with velocity a * ∈ [a L , a R ] in the approximated Riemann problem solution, is considered and the numerical flux vector takes the following expression:…”

2D numerical modelling of dam break- applying for Namchien dam in Vietnam

“…This procedure makes sure the conservation of mass and momentum, is extremely flexible and conceptually simple. Numerous researchers have applied FVM to real case studies simulated water propagation over arbitrary topographies, [7][8][9][10][11][12]. Besides, the numerical simulation of natural case study is characterized by several problems, such as: complex geometry, high roughness coefficient or wet/dry front.…”