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Results for “Stefan problem”

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.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Analytical Modeling of Metal Foam Composite Phase Change Materials (PCM) in Thermal Energy Storage Using Asymptotic Analysis

The use of phase change materials (PCMs) for thermal energy storage can release or absorb a significant amount of latent heat during the freezing or melting process, offering a higher energy storage density. One of the main drawbacks of PCMs is their low thermal conductivity, resulting in poor thermal performance. Recent research has attempted to enhance heat transfer and increase the thermal conductivity of PCMs, including the use of metal foams. However, modeling the metal foam composite PCM using conventional methods is computationally expensive. This paper proposes an asymptotic solution for a Stefan-like problem subject to a convective boundary for outward solidification in a hollow cylinder, capable of predicting the freeze-melt cycle of the metal foam composite PCM. Specifically, three temporal regimes and four spatial layers are considered in the asymptotic analysis for each phase change process. The thermal conductivity is calculated by a theoretical three-dimensional tetrakaidecahedron model, while other thermophysical properties are obtained using the method of volume averaging. The results are verified with numerical data and validated against experimental data in the literature. The presented analytical modeling framework could have the potential to be applied to other types of composite PCMs with considerably lower computational costs compared with conventional methods.

analytical model↗
DOE OSTI2023

A level-set immersed boundary method for reactive transport in complex topologies with moving interfaces

A simulation framework based on the level-set and the immersed boundary methods (LS-IBM) has been developed for reactive transport problems in porous media involving a moving solid-fluid interface. The interface movement due to surface reactions is tracked by the level-set method, while the immersed boundary method captures the momentum and mass transport at the interface. The proposed method is capable of accurately modeling transport near evolving boundaries in Cartesian grids. The framework formulation guarantees second order accuracy in space. Since the interface velocity is only defined at the moving boundary, an interface velocity propagation method is also proposed. The method can be applied to other moving interface problems of the “Stefan” type. Here, we validate the proposed LS-IBM both for flow and transport close to an immersed object with reactive boundaries as well as for crystal growth. Lastly, the proposed method provides a powerful tool to model more realistic problems involving moving reactive interfaces in complex domains.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Gravity and conduction driven melting in a sphere

In the Stefan and Neumann problems fundamentally characterizing melting, unmolten portions of a solid undergoing phase changes within spherical containers are assumed to remain stationary. An approach to these issues that is related to the theories of lubrication and film condensation is presently employed in conjunction with an approximate, closed-form solution of melting within spheres. It is shown that a group of dimensionless parameters containing Prandtl, Archimides and Stefan numbers can describe the melting process. Also given are the results of fundamental heat transfer experiments performed on the melting of a phase-change medium in a spherical shell.

Bahrami, P. A.↗
NASA NTRS1993

The p-version of the finite element method in incremental elasto-plastic analysis

Whereas the higher-order versions of the finite elements method (the p- and hp-version) are fairly well established as highly efficient methods for monitoring and controlling the discretization error in linear problems, little has been done to exploit their benefits in elasto-plastic structural analysis. Aspects of incremental elasto-plastic finite element analysis which are particularly amenable to improvements by the p-version is discussed. These theoretical considerations are supported by several numerical experiments. First, an example for which an analytical solution is available is studied. It is demonstrated that the p-version performs very well even in cycles of elasto-plastic loading and unloading, not only as compared to the traditional h-version but also in respect to the exact solution. Finally, an example of considerable practical importance - the analysis of a cold-worked lug - is presented which demonstrates how the modeling tools offered by higher-order finite element techniques can contribute to an improved approximation of practical problems.

Holzer, Stefan M.↗
NASA NTRS1996

Schwarz Methods: To Symmetrize or not to Symmetrize

A preconditioning theory for Schwarz methods is presented. The theory establishes sufficient conditions for multiplicative and additive Schwarz algorithms to yield self-adjoint positive definite preconditioners. It allows for the analysis and use of non-variational and non-convergent linear methods as preconditioners for conjugate gradient methods, and it is applied to domain decomposition and multigrid. This paper illustrates why symmetrizing may be a bad idea for linear methods. Numerical examples are presented for a test problem.

Holst, Michael↗
DOE OSTI2023

Increasing CO 2 Capture Rate in Liquid-Solvent Direct-Air Carbon Capture via Additive Manufacturing

Carbon capture is essential to meeting climate change mitigation goals. One approach currently being commercialized utilizes liquid-based solvents to capture CO 2 directly from the atmosphere but is limited by slow absorption of CO 2 into the liquid. Improved air/solvent liquid mixing increases CO 2 absorption rate, and this increased CO 2 absorption efficiency allows for smaller carbon capture systems with lower capital costs and better economic viability. In this project, we study the use of passive micromixers fabricated by metal additive manufacturing. The micromixer’s small-scale surface geometric features perturb and mix the liquid film to enhance mass transfer and CO 2 absorption. In this project, we evaluated this hypothesis through computational and experimental studies. Computational investigations focused on developing capabilities to simulate thin film (~ 100μm) fluid flow on rough surfaces. Such thin films are in a surface-tension dominated regime and simulations in this regime are prone to instabilities. Improvements to the Nalu code completed in this project resulted in a 10x timestep stability improvement for these problems.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗
DOE OSTI2023

Scalable DPG multigrid solver for Helmholtz problems: A study on convergence

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from $\mathscr{O}$(10 7 ) degrees of freedom (DOFs) to $\mathscr{O}$(10 9 ) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. Finally, the paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Simulations of plasmas and fluids using anti-symmetric models

ALMA (Anti-symmetric, Large-Moment, Accelerated) is a fast, flexible, and scalable toolkit designed to solve hyperbolic conservation law systems in hybrid supercomputers. Here this manuscript describes the theoretical background and implementation of ALMA, which uses the anti-symmetric formulation of fluids to obtain simple, robust, and easily paralellizable code. Practical GPU acceleration is realized on entire applications with an overall gain factor of 2 to 4. ALMA also provides a parallel, GPU accelerated sparse solver based on geometric multigrid, capable of diagonalizing linear systems with 239 unknowns. Here we demonstrate ALMA's scaling and performance in petascale supercomputers and use standard fluid models to verify the overall approach with canonical benchmark problems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

A fixed grid numerical methodology for phase change problems involving a moving heat source

A numerical method for solving phase change problems involving a moving heat source is presented and illustrated by a two-dimensional example. The method uses a fixed grid and does not require the implementation of the Stefan condition at the solid-liquid interface; the procedure can thus be easily implemented using existing fixed grid codes. The problem considered as an example involves natural convection flow in the molten metal during tungsten inert gas welding.

Prakash, C.↗
NASA NTRS1991

Numerical identification of boundary conditions on nonlinearly radiating inverse heat conduction problems

An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.

Murio, Diego A.↗
DOE OSTI2021

A method for convex black-box integer global optimization

Here we study the problem of minimizing a convex function on a nonempty, finite subset of the integer lattice when the function cannot be evaluated at noninteger points. We propose a new underestimator that does not require access to (sub)gradients of the objective; such information is unavailable when the objective is a blackbox function. Rather, our underestimator uses secant linear functions that interpolate the objective function at previously evaluated points. These linear mappings are shown to underestimate the objective in disconnected portions of the domain. Therefore, the union of these conditional cuts provides a nonconvex underestimator of the objective. We propose an algorithm that alternates between updating the underestimator and evaluating the objective function. We prove that the algorithm converges to a global minimum of the objective function on the feasible set. We present two approaches for representing the underestimator and compare their computational effectiveness. We also compare implementations of our algorithm with existing methods for minimizing functions on a subset of the integer lattice. We discuss the difficulty of this problem class and provide insights into why a computational proof of optimality is challenging even for moderate problem sizes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

PARMOO

ParMOO is a Python library for solving multiobjective simulation optimization problems, while exploiting problem structure. ParMOO stands for "parallel multiobjective optimization".

WILD, STEFAN↗
DOE OSTI2024

Stochastic minibatch approach to the ptychographic iterative engine

The ptychographic iterative engine (PIE) is a widely used algorithm that enables phase retrieval at nanometer-scale resolution over a wide range of imaging experiment configurations. By analyzing diffraction intensities from multiple scanning locations where a probing wavefield interacts with a sample, the algorithm solves a difficult optimization problem with constraints derived from the experimental geometry as well as sample properties. The effectiveness at which this optimization problem is solved is highly dependent on the ordering in which we use the measured diffraction intensities in the algorithm, and random ordering is widely used due to the limited ability to escape from stagnation in poor-quality local solutions. In this study, we introduce an extension to the PIE algorithm that uses ideas popularized in recent machine learning training methods, in this case minibatch stochastic gradient descent. Our results demonstrate that these new techniques significantly improve the convergence properties of the PIE numerical optimization problem.

47 OTHER INSTRUMENTATION↗
NASA NTRS2004

Fleet Assignment Using Collective Intelligence

Airline fleet assignment involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of an agent-based integer optimization algorithm to a "cold start" fleet assignment problem. Results show that the optimizer can successfully solve such highly- constrained problems (129 variables, 184 constraints).

Antoine, Nicolas E.↗
NASA NTRS2004

Fleet Assignment Using Collective Intelligence

Product distribution theory is a new collective intelligence-based framework for analyzing and controlling distributed systems. Its usefulness in distributed stochastic optimization is illustrated here through an airline fleet assignment problem. This problem involves the allocation of aircraft to a set of flights legs in order to meet passenger demand, while satisfying a variety of linear and non-linear constraints. Over the course of the day, the routing of each aircraft is determined in order to minimize the number of required flights for a given fleet. The associated flow continuity and aircraft count constraints have led researchers to focus on obtaining quasi-optimal solutions, especially at larger scales. In this paper, the authors propose the application of this new stochastic optimization algorithm to a non-linear objective cold start fleet assignment problem. Results show that the optimizer can successfully solve such highly-constrained problems (130 variables, 184 constraints).

Antoine, Nicolas E.↗
DOE OSTI2021

Tuning Multigrid Methods with Robust Optimization and Local Fourier Analysis

Local Fourier analysis is a useful tool for predicting and analyzing the performance of many efficient algorithms for the solution of discretized PDEs, such as multigrid and domain decomposition methods. The crucial aspect of local Fourier analysis is that it can be used to minimize an estimate of the spectral radius of a stationary iteration, or the condition number of a preconditioned system, in terms of a symbol representation of the algorithm. In practice, this is a “minimax” problem, minimizing with respect to solver parameters the appropriate measure of work, which involves maximizing over the Fourier frequency. Often, several algorithmic parameters may be determined by local Fourier analysis in order to obtain efficient algorithms. Analytical solutions to minimax problems are rarely possible beyond simple problems; the status quo in local Fourier analysis involves grid sampling, which is prohibitively expensive in high dimensions. In this paper, we propose and explore optimization algorithms to solve these problems efficiently. Finally, several examples, with known and unknown analytical solutions, are presented to show the effectiveness of these approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

A taxonomy of constraints in black-box simulation-based optimization

The types of constraints encountered in black-box simulation-based optimization problems differ significantly from those addressed in nonlinear programming. Here, we introduce a characterization of constraints to address this situation. We provide formal definitions for several constraint classes and present illustrative examples in the context of the resulting taxonomy. This taxonomy, denoted KARQ, is useful for modeling and problem formulation, as well as optimization software development and deployment. It can also be used as the basis for a dialog with practitioners in moving problems to increasingly solvable branches of optimization.

42 ENGINEERING↗