An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography

Abstract

[1] A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving position-fixed meshes, the iteration process of the AFMV scheme moves a fewer number of the meshes adaptively in response to flow variables calculated in prior solutions and then simulates their posterior values on the new meshes. At each time step of the simulation, the AMFV scheme consists of three parts: an adaptive mesh movement to shift the vertices position, a geometrical conservative interpolation to remap the flow variables by summing the total mass over old meshes to avoid the generation of spurious waves, and a partial differential equations(PDEs) discretization to update the flow variables for a new time step. Five different test cases are presented to verify the computational advantages of the proposed scheme over nonadaptive methods. The results reveal three attractive features: (i) the AMFV scheme could preserve still water equilibrium and positivity of water depth within both mesh movement and PDE discretization steps; (ii) it improved the shockcapturing capability for handling topographic source terms and wet-dry interfaces by moving triangular meshes to approximate the spatial distribution of time-variant flood processes; (iii) it was able to solve the shallow water equations with a relatively higher accuracy and spatial-resolution with a lower computational cost.

An Indirect Simulation-Optimization Model for Determining Optimal TMDL Allocation under Uncertainty

“…jl x ± is the pollutant removal rate for pollutant l from sub-watershed j, calculated as the difference between baseline loadings ( Carolina water-quality standards and other references [28,29]. Three Chl-a criteria scenarios had been set as [12,15], [13,15] and [14,15] μg/L; max l x is the maximum removal level of the BMPs' performance for pollutant l, which was set at 80% according to the American Society of Civil Engineers' (ASCE) national BMP database; was set as zero, indicating that no nutrient load was removed; …”

“…To increase the financial and technical feasibility of implementation, the U.S. Environmental Protection Agency [1] suggested that process-oriented simulation models could be directly integrated into an optimization framework to develop optimal TMDL allocations at the least cost while risk must be identified. Either traditional nonlinear optimization or modern heuristic global search algorithms can be applied in the direct simulation-optimization model (SOM) framework [6][7][8][9][10][11][12][13]; however, this direct SOM approach is rarely applied in practice, primarily due to the prohibitive computational cost and the neglect of uncertainties in both simulation modeling and the optimization process [7,14].…”

Performance study of the multiwavelet discontinuous Galerkin approach for solving the Green‐Naghdi equations

“…25 Moreover, most of the available AMR developments lack a general adaptivity sensor, so that they either need separate criteria for refinement/coarsening 26,27 or problem specific criteria 28,29 or are reported to be highly dependent on the type of refinement criteria. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes.…”

“…30 In addition, deploying a classical AMR method dictates extra corrections in the numerical scheme to address the loss of well-balancedness property for the case of the NSW equations. 24,[31][32][33] Multiscale methods based on the multiresolution analysis (MRA) of wavelets provide an alternative that can preserve the quality of numerical methods on adaptive meshes. [34][35][36][37][38] Theoretical analyses show that only one error threshold value is needed with this category of adaptive solvers in order to bound the accumulated errors and preserve the accuracy of the reference uniform solver at the finest resolution grid.…”

Preface Special Issue “Advances in Numerical Modelling of Hydrodynamics”

“…Developments in numerical methods and computing power continue to grow, to cite just a few (Caviedes-Voullième and , Sanders et al 2010, Dawson et al 2013, Cao et al 2015, George 2011, Smith and Liang 2013, Lacasta et al 2013, Zhou et al 2013, Donat et al 2014, Zanotti et al 2015, Delis et al 2011, Juez et al 2014, Jian et al 2015, Ran et al 2015, Murillo and Garcia-Navarro 2010, Marsooli and Wu 2015, Swartenbroekx et al 2013, Guan et al 2014, Kim et al 2014. This growth has opened-up opportunities to increase the accuracy, robustness and computational complexity of latest simulation models, and to address issues of practical relevance for modelling hydrodynamic processes.…”