The uniform convergence of finite element approximations based on a modified Hu-Washizu formulation for the nearly incompressible linear elasticity is analyzed. We show the optimal and robust convergence of the displacement-based discrete formulation in the nearly incompressible case with the choice of approximations based on quadrilateral and hexahedral elements. These choices include bases th...

The well-balanced, positivity-preserving scheme of Audusse et al, 2004, for the solution of the Saint-Venant equations with wetting and drying, is generalised to an adaptive quadtree spatial discretisation. The scheme is validated using an analytical solution for the oscillation of a fluid in a parabolic container, as well as the classic Monai tsunami laboratory benchmark. An efficient database...

Rating curves relating stream discharge to water-surface stage are traditionally established empirically through many measurements of discharge and concurrent stage. However, discharge measurements typically scatter and do not show a unique relation to the stage because the underlying physics are usually not reflected in the rating. Examining the relationship of stage versus discharge in open c...

We develop well-balanced finite-volume central schemes on overlapping cells for the SaintVenant shallow water system and its variants. The main challenge in deriving the schemes is related to the fact that the Saint-Venant system contains a geometric source term due to nonflat bottom topography and therefore a delicate balance between the flux gradients and source terms has to be preserved. We ...

A two-stage physically-based detention model has been developed for green roof systems. Vertical flow in the substrate is represented by Richards equation, and horizontal underlying drainage layer modeled Saint Venant equation. This (2SPB) stormwater management (SWMM) low impact development control (SWMM-GR) were validated using measured runoff profiles from two contrasting systems: a conventio...