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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Modeling and analysis of mixed convection stagnation point flow of nanofluid towards a stretching surface: OHAM and FEM approach

A theoretical study of mixed convection stagnation point flow towards a stretching surface is presented. The governing boundary layer equations are transformed into a set of highly nonlinear ordinary differential equations using suitable similarity transforms. The semi-analytical solution is obtained using optimal homotopy analysis method (OHAM) and the numerical solution is obtained via finite element method (FEM). Solutions obtained via two different approaches are in excellent agreement, which validates the accuracy of present analysis. In a special case, the present OHAM solution is also validated with the earlier available results. Effect of pertinent flow parameters on the skin friction coefficient and Nusselt number is presented in tabular form, whereas the velocity, temperature and nanoparticle distribution are presented in graphical forms. Further, a quadratic multiple regression analysis on numeric data of skin friction coefficient and Nusselt number is performed. The findings suggest that velocity slip assists the fluid motion in presence of buoyancy forces, whereas it exhibits a retarding nature on fluid motion when no buoyancy forces exist.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Error analysis for semi-analytic displacement derivatives with respect to shape and sizing variables

Sensitivity analysis is fundamental to the solution of structural optimization problems. Consequently, much research has focused on the efficient computation of static displacement derivatives. As originally developed, these methods relied on analytical representations for the derivatives of the structural stiffness matrix (K) with respect to the design variables (b sub i). To extend these methods for use with complex finite element formulations and facilitate their implementation into structural optimization programs using the general finite element method analysis codes, the semi-analytic method was developed. In this method the matrix the derivative of K/the derivative b sub i is approximated by finite difference. Although it is well known that the accuracy of the semi-analytic method is dependent on the finite difference parameter, recent work has suggested that more fundamental inaccuracies exist in the method when used for shape optimization. Another study has argued qualitatively that these errors are related to nonuniform errors in the stiffness matrix derivatives. The accuracy of the semi-analytic method is investigated. A general framework was developed for the error analysis and then it is shown analytically that the errors in the method are entirely accounted for by errors in delta K/delta b sub i. Furthermore, it is demonstrated that acceptable accuracy in the derivatives can be obtained through careful selection of the finite difference parameter.

Fenyes, Peter A.↗
DOE OSTI2021

Multiscale simulations for multi-continuum Richards equations

In this paper, we study a multiscale method for simulating a dual-continuum unsaturated flow problem within complex heterogeneous fractured porous media. Mathematically, each of the dual continua is modeled by a multiscale Richards equation (for pressure head), and these equations are coupled to one another by transfer terms. On its own, Richards equation is already a nonlinear partial differential equation, and it is exceedingly difficult to solve numerically due to the extra nonlinear dependencies involving the soil water. To deal with multiple scales, our strategy is that starting from a microscopic scale, we upscale the coupled system of dual-continuum Richards equations via homogenization by the two-scale asymptotic expansion, to obtain a homogenized system, at an intermediate scale (level). Based on a hierarchical approach, the homogenization’s effective coefficients are computed through solving the arising cell problems. Furthermore, to tackle the nonlinearity, after time discretization, we use Picard iteration procedure for linearization of the homogenized Richards equations. At each Picard iteration, some degree of multiscale still remains from the intermediate level, so we utilize the generalized multiscale finite element method (GMsFEM) combining with a multi-continuum approach, to upscale the homogenized system to a macroscopic (coarse-grid) level. This scheme involves building uncoupled and coupled multiscale basis functions, which are used not only to construct coarse-grid solution approximation with high accuracy but also (with the coupled multiscale basis) to capture the interactions among continua. These prospects and convergence are demonstrated by several numerical results for the proposed method.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1998

The Role of Multiphysics Simulation in Multidisciplinary Analysis

This article describes the applications of the Spectrum(Tm) Solver in Multidisciplinary Analysis (MDA). Spectrum, a multiphysics simulation software based on the finite element method, addresses compressible and incompressible fluid flow, structural, and thermal modeling as well as the interaction between these disciplines. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena. Interaction constraints are enforced in a fully-coupled manner using the augmented-Lagrangian method. Within the multiphysics framework, the finite element treatment of fluids is based on Galerkin-Least-Squares (GLS) method with discontinuity capturing operators. The arbitrary-Lagrangian-Eulerian method is utilized to account for deformable fluid domains. The finite element treatment of solids and structures is based on the Hu-Washizu variational principle. The multiphysics architecture lends itself naturally to high-performance parallel computing. Aeroelastic, propulsion, thermal management and manufacturing applications are presented.

Rifai, Steven M.↗
DOE OSTI2017

AZTRAN and AZKIND verification with a BWR study case

The AZTLAN Platform project is a national initiative led by the National Institute of Nuclear Research which gather the main public institutions of higher education in Mexico: the National Polytechnic Institute, the National Autonomous University of Mexico and the Autonomous Metropolitan University. It consists in the development of a modeling platform for the analysis and design of nuclear reactors. This project aims to modernize, improve and integrate the neutronic, thermohydraulics and thermomechanical codes, developed in the national institutions, in a platform integrated and developed by Mexican experts. The development of AZTLAN Platform is divided technically into four working groups: neutronics, thermohydraulics, coupling and uncertainty analysis, and users group. The present work is the result of the activities of the Users Group focused on the follow-up, testing and use of the different codes (modules) being developed under the AZTLAN project; with the objective of providing feedback and to suggest development priorities to the team of developers, as well as to promote collaboration and synergy between the participating institutions. In particular, in this work, the AZTRAN and the AZKIND modules were verified and tested against the results of well-known codes of the nuclear industry for boiling water reactor (BWR) models. AZTRAN is a 3D transport code which solves numerically the multi-group time independent neutron transport equation in Cartesian geometry, based on the discrete ordinates (SN) method and the RTN-0 nodal scheme. AZKIND is a 3D diffusion code that solves numerically the time dependent neutron diffusion equations in Cartesian geometry, based on a Galerkin Finite Element Method using the RTN-0 polynomial nodal approximation.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Analysis of the weighted shifted boundary method for the Poisson and Stokes problems

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. Accuracy is maintained by properly shifting the location and values of the boundary conditions. This avoids integration over cut cells and the associated implementation issues. Recently, the Weighted SBM (WSBM) was proposed for the Navier-Stokes equations with free surfaces and the Stokes flow with moving boundaries. The attribute “weighted” in the name WSBM stems from the fact that its variational form is weighted with the elemental volume fraction of active fluid. The motivation for the development of the WSBM was the preservation of the volume of active fluid to a higher degree of accuracy, which in turn resulted in improved stability and robustness characteristics in moving-boundary, time-dependent simulations. In this article, we present the numerical analysis of the WSBM formulations for the Poisson and Stokes problems. We give mathematical conditions under which the bilinear forms defining the discrete variational formulations are uniformly coercive (Poisson problem) or inf-sup stable (Stokes problem). By these results, stability and optimal convergence is proven in the natural norm; L2-error estimates can also be derived.

Approximate domain boundaries↗
DOE OSTI2019

The Shifted Interface Method: A flexible approach to embedded interface computations

We propose a new embedded finite element method to simulate partial differential equations over domains with internal interfaces. Our approach belongs to the family of surrogate/approximate interface methods and relies on the idea of shifting the location and value of jump interface conditions. This choice has the goal of preserving optimal convergence rates while avoiding small cut cells and related problematic issues, typical of traditional embedded methods. The proposed approach is accurate, robust, efficient, and simple to implement. We apply this concept to internal interface computations in the context of the mixed Poisson problem, also known as the Darcy flow problem. An extensive set of numerical tests is provided to demonstrate the performance of the proposed approach.

42 ENGINEERING↗
DOE OSTI2016

Heat transfer in porous medium embedded with vertical plate: Non-equilibrium approach - Part B

This work is continuation of the paper Part A. Due to large number of results, the paper is divided into two section with section-A (Part A) discussing the effect of various parameters such as heat transfer coefficient parameter, thermal conductivity ratio etc. on streamlines and isothermal lines. Section-B highlights the heat transfer characteristics in terms of Nusselt number The Darcy model is employed to simulate the flow inside the medium. It is assumed that the heat transfer takes place by convection and radiation. The governing partial differential equations are converted into non-dimensional form and solved numerically using finite element method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Spectral element method for elastic and acoustic waves in frequency domain

Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1988

Probabilistic finite elements for fracture mechanics

The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

Besterfield, Glen↗
NASA NTRS1986

Adaptive computational methods for SSME internal flow analysis

Adaptive finite element methods for the analysis of classes of problems in compressible and incompressible flow of interest in SSME (space shuttle main engine) analysis and design are described. The general objective of the adaptive methods is to improve and to quantify the quality of numerical solutions to the governing partial differential equations of fluid dynamics in two-dimensional cases. There are several different families of adaptive schemes that can be used to improve the quality of solutions in complex flow simulations. Among these are: (1) r-methods (node-redistribution or moving mesh methods) in which a fixed number of nodal points is allowed to migrate to points in the mesh where high error is detected; (2) h-methods, in which the mesh size h is automatically refined to reduce local error; and (3) p-methods, in which the local degree p of the finite element approximation is increased to reduce local error. Two of the three basic techniques have been studied in this project: an r-method for steady Euler equations in two dimensions and a p-method for transient, laminar, viscous incompressible flow. Numerical results are presented. A brief introduction to residual methods of a-posterior error estimation is also given and some pertinent conclusions of the study are listed.

Oden, J. T.↗
DOE OSTI2016

Hybrid finite element and Brownian dynamics method for charged particles

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

A numerical method for the quasi-incompressible Cahn–Hilliard–Navier–Stokes equations for variable density flows with a discrete energy law

In this paper, we investigate numerically a diffuse interface model for the Navier–Stokes equation with fluid–fluid interface when the fluids have different densities [48]. Under minor reformulation of the system, we show that there is a continuous energy law underlying the system, assuming that all variables have reasonable regularities. It is shown in the literature that an energy law preserving method will perform better for multiphase problems. Thus for the reformulated system, we design a C{sup 0} finite element method and a special temporal scheme where the energy law is preserved at the discrete level. Such a discrete energy law (almost the same as the continuous energy law) for this variable density two-phase flow model has never been established before with C{sup 0} finite element. A Newton method is introduced to linearise the highly non-linear system of our discretization scheme. Some numerical experiments are carried out using the adaptive mesh to investigate the scenario of coalescing and rising drops with differing density ratio. The snapshots for the evolution of the interface together with the adaptive mesh at different times are presented to show that the evolution, including the break-up/pinch-off of the drop, can be handled smoothly by our numerical scheme. The discrete energy functional for the system is examined to show that the energy law at the discrete level is preserved by our scheme.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1987

Significance of foundation-soil separation in dynamic soil-structure interaction

THe dynamic response of flexible surface strip-foundations allowed to uplift is numerically obtained for externally applied forces of a transient time variation. The soil medium is represented by an isotropic, homogeneous and linear half-space. The soil is treated by a time domain boundary element method, while the flexible foundation is treated by the finite element method. It was concluded that intermediate relative stiffness leads to moderate deformations when uplift is permitted. Very flexible footings produce higher deformations in unilateral contact compared to bilateral contact, and thus should be considered in their design. Unilateral contact does not significantly increase deformations for stiff footings subjected to concentrated central loading. However, relatively large deformation differences occur when the loading is eccentric, necessitating consideration of uplift in their design.

Spyrakos, Constantine C.↗
NASA NTRS1996

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Manteuffel, Thomas A.↗
DOE OSTI2018

Hob Strength in Gear Cutting

The strength of gear hobs in cutting worm gears is calculated by the finite-element method, on the basis of SolidWorks/Simulation software.

42 ENGINEERING↗
DOE OSTI2014

Edge equilibrium code for tokamaks

The edge equilibrium code (EEC) described in this paper is developed for simulations of the near edge plasma using the finite element method. It solves the Grad-Shafranov equation in toroidal coordinate and uses adaptive grids aligned with magnetic field lines. Hermite finite elements are chosen for the numerical scheme. A fast Newton scheme which is the same as implemented in the equilibrium and stability code (ESC) is applied here to adjust the grids.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Compact feature-aware Hermite-style high-order surface reconstruction

High-order surface reconstruction is now a commonly used technique for mesh generation and adaptation, geometric and physical modeling, and high-order numerical methods for solving partial differential equations (PDEs). However, surface reconstruction from a relatively coarse mesh remained a challenging problem, especially for surfaces with sharp features. Here in this paper, we introduce a new method to address this challenge by improving the previous state of the art, including continuous moving frames (CMF) and weighted averaging of local fittings (WALF) (Eng Comput 28 (2012)), in two aspects. First, we significantly improve the robustness of reconstruction from coarse meshes using a Hermite-style least squares approximation to incorporate normals of the surface and tangents of the feature curves. Second, we ensure both G 0 continuity and high-order accuracy of the reconstruction near sharp features by generating parametric surface elements with an iterative feature-aware parameterization. We present the theoretical framework of our method and compare it against point-based methods in terms of accuracy and stability. We demonstrate the use of the proposed technique in generating high-order meshes for finite element methods, and show that it enables nearly identical solutions as using the meshes generated from exact geometry, while allowing additional flexibility.

42 ENGINEERING↗