USGS Science⌕ Search
Home/Archive/USGS

USGS · 70021094

Parallel iterative solution for h and p approximations of the shallow water equations

E. J. Barragy·R. A. Walters
View original source ↗Export metadata ↓

Abstract

A p finite element scheme and parallel iterative solver are introduced for a modified form of the shallow water equations. The governing equations are the three-dimensional shallow water equations. After a harmonic decomposition in time and rearrangement, the resulting equations are a complex Helmholz problem for surface elevation, and a complex momentum equation for the horizontal velocity. Both equations are nonlinear and the resulting system is solved using the Picard iteration combined with a preconditioned biconjugate gradient (PBCG) method for the linearized subproblems. A subdomain-based parallel preconditioner is developed which uses incomplete LU factorization with thresholding (ILUT) methods within subdomains, overlapping ILUT factorizations for subdomain boundaries and under-relaxed iteration for the resulting block system. The method builds on techniques successfully applied to linear elements by introducing ordering and condensation techniques to handle uniform p refinement. The combined methods show good performance for a range of p (element order), h (element size), and N (number of processors). Performance and scalability results are presented for a field scale problem where up to 512 processors are used.

Explore related subjects

Advances in Water ResourcesArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

E. J. Barragy, R. A. Walters. 1998. Parallel iterative solution for h and p approximations of the shallow water equations. https://doi.org/10.1016/s0309-1708(97)00006-7

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2025

Karhunen–Loève deep learning method for surrogate modeling and approximate Bayesian parameter estimation

We evaluate the performance of the Karhunen–Loève Deep Neural Network (KL-DNN) framework for surrogate modeling and approximate Bayesian parameter estimation in partial differential equation models. In the surrogate model, the Karhunen–Loève (KL) expansions are used for the dimensionality reduction of the number of unknown parameters and variables, and a deep neural network is employed to relate the reduced space of parameters to that of the state variables. The KL-DNN surrogate model is used to formulate a maximum-a-posteriori-like least-squares problem, which is randomized to draw samples of the posterior distribution of the parameters. We test the proposed framework for a hypothetical unconfined aquifer via comparison with the forward MODFLOW and inverse PEST++ iterative ensemble smoother (IES) solutions as well as the state-of-the-art Fourier neural operator (FNO) and deep operator networks (DeepONets) operator learning surrogate models. Our results show that the KL-DNN surrogate model outperforms FNO and DeepONet for forward predictions. For solving inverse problems, the randomized algorithm provides the same or more accurate Bayesian predictions of the parameters than IES as evidenced by the higher log predictive probability of both the estimated parameter field and the forecast hydraulic head. The posterior mean obtained from the randomized algorithm is closer to the reference parameter field than that obtained with FNO as the maximum a posteriori estimate.

Advances in Water Resources↗
USGS2025

The acoustic-Doppler current profiler (ADCP): A comprehensive tool for river-reach hydromorphodynamics

This paper introduces the use of acoustic Doppler current profiler (ADCP) measurements as input for the Acoustic Mapping Velocimetry (AMV) method, a technique for characterizing the dynamics of riverine bedforms. The performance of this new approach, ADCP-AMV, is compared with input from a multibeam echosounder through a field study conducted on the Mississippi River (USA). A virtual ADCP tool has been created to support the ADCP-AMV measurements with optimal data density predictions. To the authors’ knowledge, this is the first time ADCP measurements have been used in conjunction with the AMV dune-tracking method. Subsequently, the paper discusses the coupling of ADCP-AMV measurements with ancillary data extracted from the ADCP. These ancillary data are processed using previously developed protocols to characterize hydrodynamics and the suspended sediment distribution in the water column. This paper emphasizes the capability of ADCPs to characterize open-channel river hydromorphodynamic parameters with high spatiotemporal resolution. Recommendations to accurately and efficiently acquire these multi-variable measurements and derived datasets are discussed.

Tennessee↗
USGS2024

Precipitation uncertainty estimation and rainfall-runoff model calibration using iterative ensemble smoothers

The introduction of iterative ensemble smoothers (IES) for parameter calibration opens avenues for expanding parameter space in surface water hydrologic modeling. Here, we have introduced independent parameters into a model calibration experiment to estimate errors in rainfall forcing data. This approach has the potential to estimate rainfall errors using other hydrological observations and to improve model calibration. Using high-resolution rain gauge data, we estimated “real” rainfall errors across the Turkey River watershed at storm and daily scales. Tests on synthetic and real-world scenarios successfully estimated errors correlated with observed values – even at daily scales. However, a bias remained from model parameter compensation, and identifying errors was challenging for low precipitation and snowfall. Despite synthetic results showing good error correlation, the biases in parameter identification masked potential improvements in hydrological calibration. This study highlights the potential of IES to provide additional information on rainfall errors, even only using streamflow observations.

Advances in Water Resources↗