Integral Porosity Research Articles

Self-similar solutions of shallow water equations with porosity

Simulated free surface transients in periodic urban layouts have been reported to be self-similar in the space-time domain when averaged on the scale of the building period. Such self-similarity is incompatible with the head loss model formulae used in most porosity-based shallow water models. Verifying it experimentally is thus of salient importance. New dam-break flow laboratory experiments are reported, where two different configurations of idealized periodic buildings layouts are explored. A space-time analysis of the experimental water level fields validates the self-similar character of the flow. Simulating the experiment using the two-dimensional shallow water model also yields self-similar period-averaged flow solutions. Then, the Single Porosity (SP), Integral Porosity (IP) and Dual Integral Porosity (DIP) models are applied. Although all three models behave in a similar fashion when the storage and connectivity porosities are close to each other, the DIP model is the one that upscales best the refined 2D solution.

Flux closures and source term models for shallow water models with depth-dependent integral porosity

Abstract A two-dimensional shallow water model with depth-dependent porosity is presented. The purpose is the coarse grid simulation of shallow flows over complex topographies and geometries. Two flux closures are examined: the Integral Porosity (IP) and Dual Integral Porosity (DIP) closures. Energy losses are described using a subgrid scale model that accounts for bottom and wall friction, transient momentum dissipation and energy losses induced by obstacle submersion. A complete wave propagation property analysis is provided for the IP and DIP closures, yielding more accurate numerical stability constraints than published previously. Five computational examples are presented, including transients in compound and meandering channels, urban dambreak problems with building submersion and runoff over variable microtopography. The ability of the model to deal with subgrid-scale features is confirmed. The DIP flux is shown to be superior to the IP closure. The transient dissipation term is essential in reproducing the effect of obstacles and microtopography. Distinguishing between the building wall- and building roof-induced friction is seen to be essential. The model is validated successfully against a scale model experimental dataset for the submersion of a coastal urban area by a tsunami wave.

A critical assessment of flux and source term closures in shallow water models with porosity for urban flood simulations

The validity of flux and source term formulae used in shallow water models with porosity for urban flood simulations is assessed by solving the two-dimensional shallow water equations over computational domains representing periodic building layouts. The models under assessment are the Single Porosity (SP), the Integral Porosity (IP) and the Dual Integral Porosity (DIP) models. 9 different geometries are considered. 18 two-dimensional initial value problems and 6 two-dimensional boundary value problems are defined. This results in a set of 96 fine grid simulations. Analysing the simulation results leads to the following conclusions: (i) the DIP flux and source term models outperform those of the SP and IP models when the Riemann problem is aligned with the main street directions, (ii) all models give erroneous flux closures when is the Riemann problem is not aligned with one of the main street directions or when the main street directions are not orthogonal, (iii) the solution of the Riemann problem is self-similar in space-time when the street directions are orthogonal and the Riemann problem is aligned with one of them, (iv) a momentum balance confirms the existence of the transient momentum dissipation model presented in the DIP model, (v) none of the source term models presented so far in the literature allows all flow configurations to be accounted for(vi) future laboratory experiments aiming at the validation of flux and source term closures should focus on the high-resolution, two-dimensional monitoring of both water depth and flow velocity fields.

Dual integral porosity shallow water model for urban flood modelling

With CPU times 2 to 3 orders of magnitude smaller than classical shallow water-based models, the shallow water equations with porosity are a promising tool for large-scale modelling of urban floods. In this paper, a new model formulation called the Dual Integral Porosity (DIP) model is presented and examined analytically and computationally with a series of benchmark tests. The DIP model is established from an integral mass and momentum balance whereby both porosity and flow variables are defined separately for control volumes and boundaries, and a closure scheme is introduced to link control volume- and boundary-based flow variables. Previously developed Integral Porosity (IP) models were limited to a single set of flow variables. A new transient momentum dissipation model is also introduced to account for the effects of sub-grid scale wave action on porosity model solutions, effects which are validated by fine-grid solutions of the classical shallow-water equations and shown to be important for achieving similarity in dam-break solutions. One-dimensional numerical test cases show that the proposed DIP model outperforms the IP model, with significantly improved wave propagation speeds, water depths and discharge calculations. A two-dimensional field scale test case shows that the DIP model performs better than the IP model in mapping the floods extent and is slightly better in reproducing the anisotropy of the flow field when momentum dissipation parameters are calibrated.