Search NASA⌕ Search

SEARCH · Search NASA

Results for “all-at-once system”

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.

7 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

A low-rank solver for the stochastic unsteady Navier–Stokes problem

Here we study a low-rank iterative solver for the unsteady Navier–Stokes equations for incompressible flows with a stochastic viscosity. The equations are discretized using the stochastic Galerkin method, and we consider an all-at-once formulation where the algebraic systems at all the time steps are collected and solved simultaneously. The problem is linearized with Picard’s method. To efficiently solve the linear systems at each step, we use low-rank tensor representations within the Krylov subspace method, which leads to significant reductions in storage requirements and computational costs. Combined with effective mean-based preconditioners and the idea of inexact solve, we show that only a small number of linear iterations are needed at each Picard step. The proposed algorithm is tested with a model of flow in a two-dimensional symmetric step domain with different settings to demonstrate the computational efficiency.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2016

Uncertainty Reduction using Bayesian Inference and Sensitivity Analysis: A Sequential Approach to the NASA Langley Uncertainty Quantification Challenge

This paper presents a computational framework for uncertainty characterization and propagation, and sensitivity analysis under the presence of aleatory and epistemic un- certainty, and develops a rigorous methodology for efficient refinement of epistemic un- certainty by identifying important epistemic variables that significantly affect the overall performance of an engineering system. The proposed methodology is illustrated using the NASA Langley Uncertainty Quantification Challenge (NASA-LUQC) problem that deals with uncertainty analysis of a generic transport model (GTM). First, Bayesian inference is used to infer subsystem-level epistemic quantities using the subsystem-level model and corresponding data. Second, tools of variance-based global sensitivity analysis are used to identify four important epistemic variables (this limitation specified in the NASA-LUQC is reflective of practical engineering situations where not all epistemic variables can be refined due to time/budget constraints) that significantly affect system-level performance. The most significant contribution of this paper is the development of the sequential refine- ment methodology, where epistemic variables for refinement are not identified all-at-once. Instead, only one variable is first identified, and then, Bayesian inference and global sensi- tivity calculations are repeated to identify the next important variable. This procedure is continued until all 4 variables are identified and the refinement in the system-level perfor- mance is computed. The advantages of the proposed sequential refinement methodology over the all-at-once uncertainty refinement approach are explained, and then applied to the NASA Langley Uncertainty Quantification Challenge problem.

Uncertainty↗
DOE OSTI2021

KKT Preconditioners for PDE-Constrained Optimization with the Helmholtz Equation

This paper considers preconditioners for the linear systems that arise from optimal control and inverse problems involving the Helmholtz equation. Specifically, we explore an all-at-once approach. The main contribution centers on the analysis of two block preconditioners. Variations of these preconditioners have been proposed and analyzed in prior works for optimal control problems where the underlying partial differential equation is a Laplace-like operator. In this paper, we extend some of the prior convergence results to Helmholtz-based optimization applications. Our analysis examines situations where control variables and observations are restricted to subregions of the computational domain. We prove that solver convergence rates do not deteriorate as the mesh is refined or as the wavenumber increases. More specifically, for one of the preconditioners we prove accelerated convergence as the wavenumber increases. Additionally, in situations where the control and observation subregions are disjoint, we observe that solver convergence rates have a weak dependence on the regularization parameter. We give a partial analysis of this behavior. We illustrate the performance of the preconditioners on control problems motivated by acoustic testing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Influence of Agricultural Managed Aquifer Recharge (AgMAR) and Stratigraphic Heterogeneities on Nitrate Reduction in the Deep Subsurface

Agricultural managed aquifer recharge (AgMAR) is a strategy whereby surface water is used to intentionally flood croplands to recharge underlying aquifers. However, nitrate (NO 3 - ) contamination in agriculturally intensive regions poses a threat to groundwater resources under AgMAR. We use a reactive transport model to understand the effects of AgMAR management strategies (i.e., by varying the frequency, duration between flooding events, and amount of water) on NO 3 - leaching to groundwater under different stratigraphic configurations and antecedent moisture conditions. We examine the potential of denitrification and nitrogen retention in deep vadose zone sediments (~15 m) using variable AgMAR application rates on two-dimensional representations of differently textured soils, soils with discontinuous bands/channels, and with preferential flow paths characteristic of agricultural fields. Simulations indicate finer textured sediments, alone or embedded within/adjacent to high flow regions, are important reducing zones providing conditions needed for denitrification. Simulation results suggest that applying water all-at-once rather than in increments transports higher concentrations of NO 3 - deeper into the profile, which may exacerbate groundwater quality. This transport into deeper depths can be aggravated by wetter antecedent soil moisture conditions. However, applying water all-at-once also increases denitrification within the vadose zone by promoting anoxic conditions. We conclude that AgMAR can be designed to enhance denitrification in the subsurface and reduce NO 3 - leaching to groundwater, while specifically accounting for lithologic heterogeneity, antecedent soil moisture conditions, and depth to the water table. Our findings are potentially relevant to other systems that experience flooding inundation such as floodplains and dedicated recharge basins.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Influence of Agricultural Managed Aquifer Recharge (AgMAR) and Stratigraphic Heterogeneities on Nitrate Reduction in the Deep Subsurface

This data package contains input files for TOUGHREACT for a modeling study examining the effects of managed aquifer recharge on agricultural lands on nitrate cycling and transport in the Central Valley of CA near Modesto. The files contain all the geochemical species, reactions, and hydrological parameters for the model. The files are text files used for the TOUGH family of code created by LBNL. To use the files a license is required. https://tough.lbl.gov/licensing-download/toughreact-licensing-download/Accompanying Paper Abstract: Agricultural managed aquifer recharge (AgMAR) is a proposed management strategy whereby surface water flows are used to intentionally flood croplands with the purpose of recharging underlying aquifers. However, legacy nitrate (NO3-) contamination in agriculturally-intensive regions poses a threat to groundwater resources under AgMAR. To address these concerns, we use a reactive transport modeling framework to better understand the effects of AgMAR management strategies (i.e., by varying the frequency, duration between flooding events, and amount of water) on N leaching to groundwater under different stratigraphic configurations and antecedent moisture conditions. In particular, we examine the potential of denitrification and nitrogen retention in deep vadose zone sediments (~15 m) using variable AgMAR application rates on two-dimensional representations of differently textured soils, soils with discontinuous bands/channels, and soils with preferential flow paths characteristic of typical agricultural field sites. Our results indicate that finer textured sediments, such as silt loams, alone or embedded within high flow regions, are important reducing zones providing conditions needed for denitrification. Simulation results further suggest that applying water all-at-once rather than in increments for a fixed volume of recharge transports higher concentrations of NO3- deeper into the profile, which has the potential to exacerbate groundwater quality. This transport into deeper depths can be aggravated by wetter antecedent soil moisture conditions. However, applying water all-at-once also increases denitrification within the vadose zone by promoting anoxic conditions. We conclude that AgMAR management strategies can be designed to enhance denitrification in the subsurface and reduce N leaching to groundwater, while specifically accounting for lithologic heterogeneity, antecedent soil moisture conditions, and depth to the water table. Our findings are potentially relevant to other systems that experience flooding inundation such as riparian corridors, floodplains, wetlands, and other managed landscapes like dedicated recharge basins.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

FORCE-DISPATCHES Integration - Initial Demonstration

Integrated energy systems (IES) combine, in mutually beneficial ways, power from variable renewable energy sources and nuclear power plants (NPP) to improve economic viability under uncertain market and weather conditions. The open-source Framework for Optimization of Resources and Economics (FORCE) tool suite, developed at Idaho National Laboratory (INL), has enabled comprehensive modeling and simulation of IES. The capabilities within FORCE include grid portfolio optimization through the Holistic Energy Resource Optimization Network (HERON) and the transient process model analysis library HYBRID, among others. Continuous efforts and investments from the IES programs have been made to expand and improve the versatility of the FORCE toolset in fiscal year 2022. Code-coupling and cross-tool communication have been important methods for improving this versatility. This report focuses on an additional workflow in the HERON tool for capacity and dispatch stochastic optimization through integration with the external tool Design Integration and Synthesis Platform to Advance Tightly Coupled Hybrid Energy Systems (DISPATCHES). DISPATCHES was primarily developed by the National Energy Technology Laboratory, in collaboration with other national laboratories, which included INL, universities, and industry partners. It is coupled to a library of algebraic models for specific plant components, and to a framework for stochastic optimization different from that provided in the current Risk Analysis Virtual Environment (RAVEN)-running-RAVEN algorithm in HERON. HERON currently conducts stochastic optimization via an outer-inner loop: it optimizes over variable capacity on the outer loop, and at each step within the capacity parameter space, conducts an inner optimization over scenarios (of market signals, demand, and/or weather patterns) and hourly dispatch throughout a user-specified number of years. On the other hand, DISPATCHES conducts stochastic optimization via an “all-at-once” strategy in which capacity variables are optimized at the same level as dispatch variables, as all scenarios are considered at once. The latter method works especially well for projects of limited size and project length, as the necessary computational power and memory increases with the number of variables and scenarios. The new capability to use the DISPATCHES workflow in HERON enhances standalone simulations by leveraging FORCE tools—namely, the economic metrics from the Tool for Economic Analysis (TEAL) and reduced-order model (ROM) sampling from RAVEN. The initial demonstration of the DISPATCHES workflow simulates an existing nuclear-case flowsheet within the DISPATCHES repository—this models a NPP with a secondary revenue stream for hydrogen production. Electrical output from the plant is converted to hydrogen via a proton-exchange membrane (PEM) electrolyzer, hydrogen tanks are used for storage, and an additional turbine is added for hydrogen combustion. Continued work regarding this FORCE-DISPATCHES integration will include automatic generation of DISPATCHES models from HERON inputs, offering analysts the option of using either the RAVEN-runsRAVEN or DISPATCHES workflow to solve technoeconomic optimization problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗