A 2D parallel diffusive wave model for floodplain inundation with variable time step (P-DWave)

Abstract

Please cite this article as: Leandro, J., Chen, A.S., Schumann, A., A 2D Parallel Diffusive Wave Model for floodplain inundation with variable time step (P-DWave), Journal of Hydrology (2014), doi: http://dx.doi.org/10. 1016/ j.jhydrol.2014.05.020 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Growing advances in remote sensing technologies together with the widespread availability of 11 Digital terrain models (DTM) have intensified the research into two-dimensional (2D) models. 12Supported by detailed DTM, 2D models can become very accurate tools yet not without an added 13 cost on the computational effort. Floodplain inundation is characterized by a slow varying 14 phenomenon which can last hours, days or even weeks. In this paper we aim to develop a specific 15 parallel diffusive wave model with variable time step suitable for flood inundation. Taking advantage 16 of up to 12 processors, speed-up times ranging from 1.7 to 5.2 and 1.2 to 1.7 are achieved with the 17 Matlab parallel computing toolbox and Fortran OpenMP Application Programming, respectively. The 18 variable time method and the process devised to represent Wet-Dry fronts kept the solution stable 19 and preserved absolute mass conservation. P-DWave performed well against known analytical 20 solutions and dynamic and diffusive models in a total of seven tests. 21

A comparison of three dual drainage models: shallow water vs local inertial vs diffusive wave

“…Bed friction source term is calculated outside the fluxes with a semi implicit, Runge-Kutta based, point-wise scheme (Liang and Marche, 2009;Song et al, 2011). The Wet-Dry front is treated using Leandro et al (2014a) approach that avoids localised "negative depths", formulated for each set of equations. Details about these models can be found in Martins et al (2015).…”

“…A finite volume explicit scheme with cell centred control volumes is used. The time step increment is controlled by CFL condition, which is proportional to (Leandro et al, 2014a). PDWAVE uses a prediction correction Wet-Dry front treatment that restricts the movement of water in case of negative depths, obtaining absolute mass conservation (Leandro et al, 2014a).…”

“…The time step increment is controlled by CFL condition, which is proportional to (Leandro et al, 2014a). PDWAVE uses a prediction correction Wet-Dry front treatment that restricts the movement of water in case of negative depths, obtaining absolute mass conservation (Leandro et al, 2014a). SIPSON (D et al, 2005) is a well established model that solves the full dynamic SaintVenant equations in the pipes in the form (8) (9) where the values are related to a cross-section located at the coordinate at time with as the water level, the surface width, the discharge, the friction slope and the area.…”

Validation of 2D shock capturing flood models around a surcharging manhole

“…It is often modelled using the depth-integrated Navier-Stokes Equations, termed shallow water equations (SWE), or one of the SWE simplifications in 1D or 2D, which can be numerically solved using a variety of approaches common in computational hydraulics (Kesserwani and Wang 2014, Neal et al 2012, Martins et al 2015, Leandro et al 2014. Due to its inherent ability to incorporate flow transition, including shocks, the finite volume (FV) approach of Godunov has gained popularity in solving the fully dynamic SWE when modelling 2D floodplain flow.…”

Developing an effective 2-D urban flood inundation model for city emergency management based on cellular automata

“…The calculation of the differential equations in these physics-based models is complex and requires an immense computation time. In contrast, floodplain inundation is most often characterized by a much slower phenomenon (Leandro et al, 2014); thus, the physics-based hydrologic model via calculation of the differential equations is tolerable in a floodplain inundation simulation but impractical in the urban flooding inundation modeling and emergency management at present (Versini et al, 2010).…”