Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “shallow water”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Dynamics of electrified liquid metal surface using shallow water model

A shallow water model that incorporates surface tension and electric field effects is developed to investigate the dynamics of an electrified liquid surface. The computational model is verified against the Zakharov–Kuznetsov equation and is applied to study the growth and damping of the electrified liquid surface. A linear wave analysis is performed under a shallow water theory assuming an analytic solution of the electric field, similar to the Tonks–Frenkel instability. The electrified liquid surface grows or dampens based on the balance of the electric field, surface tension, and gravitational forces. As a result, the numerical results obtained from the electrified shallow water solver are in good agreement with the theoretical analysis.

Computational models↗
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A GPU-based 2D shallow water quality model

In this paper, a 2D shallow water flow solver integrated with a water quality model is presented. The interaction between the main water quality constituents included is based on the Water Quality Analysis Simulation Program. Efficiency is achieved by computing with a combination of a Central Processing Unit (CPU) and a Graphics Processing Unit (GPU) device. This technique is intended to provide robust and accurate simulations with high computation speedups with respect to a single-core CPU in real events. The proposed numerical model is evaluated in cases that include the transport and reaction of water quality components over irregular bed topography and dry–wet fronts, verifying that the numerical solution in these situations conserves the required properties (C-property and positivity). The model can operate in any steady or unsteady form allowing an efficient assessment of the environmental impact of water flows. The field data from an unsteady river reach test case are used to show that the model is capable of predicting the measured temporal distribution of dissolved oxygen and water temperature, proving the robustness and computational efficiency of the model, even in the presence of noisy signals such as wind speed.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗
DOE OSTI2020

Multigrid-Reduction-in-Time for the Rotating Shallow Water Equations

We consider multilevel time-parallel methods for the numerical solution of the rotating shallow water equations. In particular, the multigrid-reduction-in-time (MGRIT) algorithm is used for the parallel time integration. An asymptotic model is used at the coarse levels while the full model is employed at the finer levels. The asymptotic model is well-suited for highly oscillatory partial differential equations like the rotating shallow water equations because it can accurately and stably take the required large time-steps on coarse levels. Our work exploits the flexibility of the MGRIT algorithm in terms of the number of levels and relaxation schemes to show some computational benefits, especially with respect to FCF-relaxation and data reuse.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparison of exponential integrators and traditional time integration schemes for the shallow water equations

We report the time integration scheme is probably one of the most fundamental choices in the development of an ocean model. In this paper, we investigate several time integration schemes when applied to the shallow water equations. This set of equations is accurate enough for the modeling of a shallow ocean and is also relevant to study as it is the one solved for the barotropic (i.e. vertically averaged) component of a three dimensional ocean model. We analyze different time stepping algorithms for the linearized shallow water equations. High order explicit schemes are accurate but the time step is constrained by the Courant-Friedrichs-Lewy stability condition. Implicit schemes can be unconditionally stable but, in practice lack accuracy when used with large time steps. In this paper we propose a detailed comparison of such classical schemes with exponential integrators. The accuracy and the computational costs are analyzed in different configurations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A self-consistent electrostatic electrified shallow water model for charged liquid surface dynamics

The dynamics of an electrified liquid surface are investigated using a shallow water model that is self-consistently coupled with an electrostatic solver. To account for the spatiotemporal variation of a curved liquid surface, the electric field on curved surfaces is calculated by solving a two-dimensional electrostatic equation using the weighted least squares (WLSQ) interpolation method. First, the WLSQ implementation is verified with analytical theory obtained from a Laplace solution assuming a half-cylinder liquid surface profile. Then, the coupled electrified shallow water model is used to study the instability of liquid surface perturbation as a function of the potential drop between an electrode and conducting liquid, surface tension, and gravity. We present a linear dispersion theory of liquid surface instability for long-wavelength perturbations, including the effects of liquid viscosity. Furthermore, the effects of multiple sinusoidal surface perturbations on the electrified liquid surface instability are investigated.

Capillary waves↗
DOE OSTI2024

A high-order explicit Runge-Kutta approximation technique for the shallow water equations

Here, we introduce a high-order space–time approximation of the Shallow Water Equations with sources that is invariant-domain preserving (IDP), well-balanced with respect to rest states, and employs a novel explicit Runge–Kutta (ERK) introduced in Ern and Guermond (SIAM J. Sci. Comput. 44(5), A3366–A3392, 2022) for systems of non-linear conservation equations. The resulting method is then numerically illustrated through verification and validation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Shallow-Water Habitat in the Lower Columbia River Estuary: A Highly Altered System

Abstract Decreases in shallow-water habitat area (SWHA) in the Lower Columbia River and Estuary (LCRE) have adversely affected salmonid populations. We investigate the causes by hindcasting SWHA from 1928 to 2004, system-wide, based on daily higher high water (HHW) and system hypsometry. Physics-based regression models are used to represent HHW along the system as a function of river inflow, tides, and coastal processes, and hypsometry is used to estimate the associated SWHA. Scenario modeling is employed to attribute SWHA losses to levees, flow regulation, diversion, navigational development, and climate-induced hydrologic change, for subsidence scenarios of up to 2 m, and for 0.5 m fill. For zero subsidence, the system-wide annual-average loss of SWHA is 55 ± 5%, or 51 × 10 5 ha/year; levees have caused the largest decrease ( $${54}_{-14}^{+5}$$ 54 - 14 + 5 %, or ~ 50 × 10 5 ha/year). The loss in SWHA due to operation of the hydropower system is small, but spatially and seasonally variable. During the spring freshet critical to juvenile salmonids, the total SWHA loss was $${63}_{-3}^{+2}$$ 63 - 3 + 2 %, with the hydropower system causing losses of 5–16% (depending on subsidence). Climate change and navigation have caused SWHA losses of $${5}_{-5}^{+16}$$ 5 - 5 + 16 % and $${4}_{-6}^{+14}$$ 4 - 6 + 14 %, respectively, but with high spatial variability; irrigation impacts have been small. Uncertain subsidence causes most of the uncertainty in estimates; the sum of the individual factors exceeds the total loss, because factors interact. Any factor that reduces mean or peak flows (reservoirs, diversion, and climate change) or alters tides and along-channel slope (navigation) becomes more impactful as assumed historical elevations are increased to account for subsidence, while levees matter less.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

A mass conservative, well balanced, tangency preserving and energy decaying method for the shallow water equations on a sphere

Here a fully discrete surface finite element method is proposed for solving the viscous shallow water equations in a bounded Lipschitz domain on the sphere based on a general triangular mesh. The method consists of a modified Crank–Nicolson method in time and a Galerkin surface finite element method in space for the fluid thickness H and the fluid velocity u. A finite element space tangential to the sphere at all finite element nodes is proposed to approximate the fluid velocity u. The proposed method has second-order accuracy in time and first-order accuracy in space, and preserves mass conservation, well balancedness, tangency of velocity to the sphere, and energy decay. Numerical experiments are presented to illustrate the accuracy of the proposed method and the preservation of the physical properties, including mass conservation, well balancedness, and energy decay. A numerical simulation of ocean mesoscale activity on a circular basin with a continental shelf is provided.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

SERGHEI (SERGHEI-SWE) v1.0: a performance-portable high-performance parallel-computing shallow-water solver for hydrology and environmental hydraulics

The Simulation EnviRonment for Geomorphology, Hydrodynamics, and Ecohydrology in Integrated form (SERGHEI) is a multi-dimensional, multi-domain, and multi-physics model framework for environmental and landscape simulation, designed with an outlook towards Earth system modelling. At the core of SERGHEI's innovation is its performance-portable high-performance parallel-computing (HPC) implementation, built from scratch on the Kokkos portability layer, allowing SERGHEI to be deployed, in a performance-portable fashion, in graphics processing unit (GPU)-based heterogeneous systems. In this work, we explore combinations of MPI and Kokkos using OpenMP and CUDA backends. In this contribution, we introduce the SERGHEI model framework and present with detail its first operational module for solving shallow-water equations (SERGHEI-SWE) and its HPC implementation. This module is designed to be applicable to hydrological and environmental problems including flooding and runoff generation, with an outlook towards Earth system modelling. Its applicability is demonstrated by testing several well-known benchmarks and large-scale problems, for which SERGHEI-SWE achieves excellent results for the different types of shallow-water problems. Finally, SERGHEI-SWE scalability and performance portability is demonstrated and evaluated on several TOP500 HPC systems, with very good scaling in the range of over 20 000 CPUs and up to 256 state-of-the art GPUs.

58 GEOSCIENCES↗
DOE OSTI2021

Local time stepping for the shallow water equations in MPAS

In this work we assess the performance of a set of local time-stepping (LTS) schemes for the shallow water equations implemented in the Model for Prediction Across Scales (MPAS). The goal of LTS is to speed up the simulation by allowing different time-steps on different regions of the computational grid. The LTS schemes considered here were originally introduced by Hoang et al. (2019) [26], who laid out the mathematical foundation of the methods. Here, the authors take on the task of presenting a fast, efficient and scalable parallel implementation of these LTS methods on high performance computing machines, with the aim to provide a recipe for other climate modeling groups that may be interested in employing LTS algorithms in their codes. As a matter of fact, even if MPAS is our framework of choice, our approach is general enough and could be of interest to other groups beyond the MPAS community. Due to their nature, LTS methods possess an inherent load imbalance that needs to be carefully addressed in order to obtain efficient scalability. Even more important is the far from trivial task of computing the right-hand side terms only on specific LTS regions during the time-stepping procedure. An inefficient handling of this task causes a drastic decay of the CPU time performance, making the LTS algorithms practically of no use. The emphasis of the present work is therefore on the computational and parallel aspects of the LTS methods, whose proper treatment is crucial to make the methods run faster against existing strategies, such as for instance high-order explicit global time-stepping schemes. This is in fact the ultimate goal of using an LTS procedure and it is the one to which we direct all our optimization efforts.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Monsoon Depression Amplification by Horizontal Shear and Humidity Gradients: A Shallow Water Perspective

Transient, synoptic-scale vortices produce a large fraction of total rainfall in most monsoon regions and are often associated with extreme precipitation. However, the mechanism of their amplification remains a topic of active research. For monsoon depressions, which are the most prominent synoptic-scale vortex in the Asian–Australian monsoon, recent work has suggested that meridional gradients in zonal wind in the vortex environment may produce growth through barotropic instability, while meridional gradients in environmental humidity have also been proposed to cause amplification through coupling with precipitating convection. Here, a two-dimensional shallow water model on a sphere with parameterized precipitation is used to examine the relative role played by these two environmental gradients. By systematically varying the meridional moisture gradient and meridional wind shear for both weak, quasi-linear waves and finite-amplitude isolated vortices, we show that rotational winds in the initial vortex are amplified most strongly by meridional shear of the environmental zonal wind, while vortex precipitation rates are most sensitive to environmental moisture gradients. The growth rate in the presence of both gradients is less than the sum of growth rates in the presence of isolated gradients, as the phase relation between moisture and vorticity anomalies becomes distorted with increasing shear. In conclusion, these results suggest that background meridional gradients in both zonal wind and environmental humidity can contribute to the amplification of vortices to monsoon depression strength, but with some degree of decoupling of the dry rotational flow and the moist convection.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Design and Analysis of a Floating-Wind Shallow-Water Mooring System Featuring Polymer Springs

This paper presents a mooring system design featuring polymer springs for the VolturnUS-S 15-MW reference floating wind turbine in site conditions for the New York Bight at a 50-m water depth. Polymer springs have a nonlinear stress-strain curve that allows a stiffer response at low loads and a more flexible response at higher loads, potentially reducing peak mooring line tensions. The mooring dynamics model MoorDyn has been extended to model springs with nonlinear tension-strain curves from a user-inputted look-up table. This MoorDyn modeling advancement is verified against OrcaFlex simulation results. Using MoorDyn's updated capabilities, a spring-equipped catenary mooring system is designed for the 15-MW floating system, along with a baseline catenary mooring system that does not use polymer springs. The floating wind turbine simulator OpenFAST is used to simulate the mooring systems in design-driving load cases to show the effect of polymer springs on key dynamic behaviours. The results show that the spring-equipped design reduces peak tensions by up to 60%, whereas the turbine offsets stay within a maximum of 7.2 m, which is still a reasonable offset limit for cable considerations. The reduction in peak tensions results in a significant decrease in damage equivalent loads - on the order of 50% for upwind lines in fully loaded conditions. These results show that polymer springs can effectively reduce peak tensions and fatigue loads in mooring systems at shallow water depths.

floating offshore wind↗
DOE OSTI2022

Design and Analysis of a Floating-Wind Shallow-Water Mooring System Featuring Polymer Springs: Preprint

In this paper, a mooring system featuring polymer springs is designed for the VolturnUS-S 15 MW reference floating wind turbine in site conditions for the New York Bight at a 50-m water depth. Polymer springs have a nonlinear stress-strain curve that allows a stiffer response at low loads and a more flexible response at higher loads, potentially reducing peak mooring line tensions. The mooring dynamics model MoorDyn has been extended to model springs with nonlinear tension-strain curves from a user-inputted look-up table. This MoorDyn modelling advancement is verified against OrcaFlex simulation results. Using MoorDyn's updated capabilities, a spring-equipped catenary mooring system is designed for the 15 MW floating system, along with a baseline catenary mooring system that does not use polymer springs. The floating wind turbine simulator OpenFAST is used to simulate the mooring systems in design-driving load cases to show the effect of polymer springs on key dynamic behaviours. The results show that the spring-equipped design reduces peak tensions by up to 60%, while the turbine offsets stay within a maximum of 7.2 m, which is still a reasonable offset limit for cable considerations. The reduction in peak tensions results in a significant decrease in damage equivalent loads, on the order of 50% for upwind lines in fully loaded conditions. These results show that polymer springs can effectively reduce peak tensions and fatigue loads in mooring systems at shallow water depths.

floating offshore wind↗
DOE OSTI2025

Uncertainties in Simulating Flooding During Hurricane Harvey Using 2D Shallow Water Equations

Abstract Flooding is one of the most impactful weather‐related natural hazards. Numerical models that solve the two dimensional (2D) shallow water equations (SWE) represent the first‐principles approach to simulate all types of spatial flooding, such as pluvial, fluvial, and coastal flooding, and their compound dynamics. High spatial resolution (e.g., () m) is needed in 2D SWE simulations to capture flood dynamics accurately, resulting in formidable computational challenges. Thus, relatively coarser spatial resolutions are used for large‐scale simulations of flooding, which introduce uncertainties in the results. It is unclear how the uncertainty associated with the model resolution compares to the uncertainties in precipitation data sets and assumptions regarding boundary conditions when channelized flows interact with other water bodies. In this study, we compare these three sources of uncertainties in 2D SWE simulations for the 2017 Houston flooding event. Our results show that precipitation uncertainty and mesh resolution have more significant impacts on the simulated streamflow and inundation dynamics than the choice of the downstream boundary condition at the watershed outlet. We point out the viability to confine the uncertainty of coarsening mesh resolution by using the variable resolution mesh (VRM) which refines critical topographic features with far fewer grid cells. Specifically, in simulations with VRM, the simulated inundation depths over the refined region are comparable to that use the finest uniform mesh. This study contributes to understanding the challenges and pathways for applying 2D SWE models to improve the realism of flood simulations over large scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A Shallow-Water Model for Convective Self-Aggregation

Randomly distributed convective storms can self-aggregate in the absence of large-scale forcings. Here we present a 1D shallow-water model to study the convective self-aggregation. This model simulates the dynamics of the planetary boundary layer and represents convection as a triggered process. Once triggered, convection lasts for finite time and occupies finite length. Here we show that the model can successfully simulate self-aggregation, and that the results are robust to a wide range of parameter values. In the simulations, convection excites gravity waves. The gravity waves then form a standing wave pattern, separating the domain into convectively active and inactive regions. We analyze the available potential energy (APE) budget and show that convection generates APE, providing energy for self-aggregation. By performing dimensional analysis, we develop a scaling theory for the size of convective aggregation, which is set by the gravity wave speed, damping time scale, and number density of convective storms. This paper provides a simple modeling framework to further study convective self-aggregation.

54 ENVIRONMENTAL SCIENCES↗