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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Adaptive enriched Galerkin methods for miscible displacement problems with entropy residual stabilization

Here we present a novel approach to the simulation of miscible displacement by employing adaptive enriched Galerkin finite element methods (EG) coupled with entropy residual stabilization for transport. In particular, numerical simulations of viscous fingering instabilities in heterogeneous porous media and Hele–Shaw cells are illustrated. EG is formulated by enriching the conforming continuous Galerkin finite element method (CG) with piecewise constant functions. The method provides locally and globally conservative fluxes, which are crucial for coupled flow and transport problems. Moreover, EG has fewer degrees of freedom in comparison with discontinuous Galerkin (DG) and an efficient flow solver has been derived which allows for higher order schemes. Dynamic adaptive mesh refinement is applied in order to reduce computational costs for large-scale three dimensional applications. In addition, entropy residual based stabilization for high order EG transport systems prevents spurious oscillations. Numerical tests are presented to show the capabilities of EG applied to flow and transport.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Uniform Subspace Correction Preconditioners for Discontinuous Galerkin Methods with hp-Refinement

In this paper, we develop subspace correction preconditioners for discontinuous Galerkin (DG) discretizations of elliptic problems with hp-refinement. These preconditioners are based on the decomposition of the DG finite element space into a conforming subspace, and a set of small nonconforming edge spaces. The conforming subspace is preconditioned using a matrix-free low-order refined technique, which in this work, we extend to the hp-refinement context using a variational restriction approach. The condition number of the resulting linear system is independent of the granularity of the mesh h, and the degree of the polynomial approximation p. The method is amenable to use with meshes of any degree of irregularity and arbitrary distribution of polynomial degrees. Furthermore, numerical examples are shown on several test cases involving adaptively and randomly refined meshes, using both the symmetric interior penalty method and the second method of Bassi and Rebay (BR2).

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1974

A finite-element method for lifting surfaces in steady incompressible subsonic flow

The problem of potential steady subsonic flow for lifting surfaces is considered. This problem requires the solution of an integral equation relating the value of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface is divided into small (quadrilateral hyperboloidal) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each element and equal to their values at the centroids of the elements. This yields a set of linear algebraic equations. Numerical results are in good agreement with existing ones.

Morino, L.↗
NASA NTRS1991

Compatible thermal and structural elements for the analysis of beam and plate structures

Energy methods are used to formulate steady-state thermal elements which are compatible with structural beam and plate elements. Comparisons of energy method results with finite element results indicate that the energy methods achieve similar accuracy with fewer degrees of freedom. Limitations of energy methods with regard to discontinuous functions and computational overflow are noted. Thermal stress calculations are simplified by the use of similar formulations for the thermal and structural elements. The advantages that these energy-based elements offer to high-temperature structural optimization are discussed.

Vause, R. F.↗
DOE OSTI2019

A Comparison of Classical and Aggregation-Based Algebraic Multigrid Preconditioners for High-Fidelity Simulation of Wind Turbine Incompressible Flows

This paper presents a comparison of parallel strong scaling performance of classical and aggregation algebraic multigrid (AMG) preconditioners in the context of wind turbine simulations. Fluid motion is governed by the incompressible Navier--Stokes equations, discretized in space with control-volume finite elements and in time with an inexact projection scheme using an implicit integrator. A discontinuous-Galerkin sliding-mesh algorithm captures rotor motion. The momentum equations are solved with iterative Krylov methods, preconditioned by symmetric Gauss--Seidel (SGS) in Trilinos and $\ell_1$ SGS in hypre. The mass-continuity equation is solved with GMRES preconditioned by AMG and can account for the majority of simulation time. Reducing this continuity solve time is crucial. Wind turbine simulations present two unique challenges for AMG preconditioned solvers: the computational meshes include strongly anisotropic elements, and mesh motion requires matrix reinitialization and computation of preconditioners at each time step. Detailed timing profiles are presented and analyzed, and best practices are discussed for both classical and aggregation-based AMG. Results are presented for simulations of two different wind turbines with up to 6 billion grid points on two different computer architectures. For moving mesh problems that require linear-system reinitialization, the well-established strategy of amortizing preconditioner setup costs over a large number of time steps to reduce the solve time is no longer valid. Instead, results show that faster time to solution is achieved by reducing preconditioner setup costs at the expense of linear-system solve costs. Standard smoothed aggregation with Chebyshev relaxation was found to perform poorly when compared with classical AMG in terms of solve time and robustness. However, plain aggregation was comparable to classical AMG.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1995

Sensitivity analysis for the dynamic response of viscoplastic shells of revolution

A computational procedure is presented for evaluating the sensitivity coefficients of the dynamic axisymmetric response of viscoplastic shells of revolution. The analytical formulation is based on Reissner's large deformation shell theory with the effects of transverse shear deformation, rotatory inertia and moments turning around the normal to the middle surface included. The material model is chosen to be isothermal viscoplasticity, and an associated flow rule is used with a von Mises effective stress. A mixed formulation is used with the fundamental unknowns consisting of six stress resultants, three generalized displacements and three velocity components. Spatial discretization is performed using finite elements, with discontinuous stress resultants across element interfaces. The temporal integration is performed by using an explicit central difference scheme (leap-frog method) with an implicit constitutive update. The sensitivity coefficients are evaluated using a direct differentiation approach. Numerical results are presented for a spherical cap subjected to step loading, and a circular plate subjected to impulsive loading. The sensitivity coefficients are generated by evaluating the derivatives of the response quantities with respect to thickness, mass density, Young's modulus, and two of the material parameters characterizing the viscoplastic response. Time histories of the response and sensitivity coefficients are presented, along with spatial distributions of these quantities at selected times.

Kulkarni, Makarand↗
DOE OSTI2018

Numerical experiments with the extended virtual element method for the Laplace problem with strong discontinuities

The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes. In the VEM, the basis functions are implicit (virtual) — they are not known nor do they need to be computed within the problem domain. Suitable projection operators are used to decompose the bilinear form at the element-level into two parts: a consistent term that reproduces a given polynomial space and a correction term that ensures stability. In this study, we consider a low-order extended virtual element method (X-VEM) that is in the spirit of the extended finite element method for crack problems. Herein, we focus on the two-dimensional Laplace crack problem. In the X-VEM, we enrich the standard virtual element space with additional discontinuous functions through the framework of partition-of-unity. The nodal basis functions in the VEM are chosen as the partition-of-unity functions, and we study means to stabilize the standard and enriched sub-matrices that constitute the element stiffness matrix. Numerical experiments are performed on the problem of a cracked membrane under mode III loading to affirm the accuracy, and to establish the optimal convergence in energy of the method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Robust Approaches to Handling Complex Geometries with Galerkin Difference Methods

The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite-difference-like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using a tensor product construction on quadrilateral elements. The GD basis can be used to define the solution space for a discontinuous Galerkin finite element discretization of partial differential equations. In this work we propose two approaches to handling complex geometries within this setting: (1) using nonconforming, curvilinear GD elements and (2) coupling affine GD elements with curvilinear simplicial elements. In both cases the (semidiscrete) discontinuous Galerkin method is provably energy stable even when variational crimes are committed. Additionally, for both element types a weight-adjusted mass matrix is used, which ensures that only the reference mass matrix must be inverted. We also present sufficient conditions on the treatment of metric terms for the curvilinear, nonconforming GD elements to ensure that the scheme is both constant preserving and conservative. Numerical experiments confirm the stability results and demonstrate the accuracy of the coupled schemes.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗
NASA NTRS2001

The Applicability of the Generalized Method of Cells for Analyzing Discontinuously Reinforced Composites

The paper begins with a short overview of the recent work done in the field of discontinuous reinforced composites, focusing on the different parameters which influence the material behavior of discontinuous reinforced composites, as well as the various analysis approaches undertaken. Based on this overview it became evident, that in order to investigate the enumerated effects in an efficient and comprehensive manner, an alternative approach to the computationally intensive finite-element based micromechanics approach is required. Therefore, an investigation is conducted to demonstrate the utility of utilizing the generalized method of cells (GMC), a semi-analytical micromechanics-based approach, to simulate the elastic and elastoplastic material behavior of aligned short fiber composites. The results are compared with (1) simulations using other micromechanical based mean field models and finite element (FE) unit cell models found in the literature given elastic material behavior, as well as (2) finite element unit cell and a new semianalytical elastoplastic shear lag model in the inelastic range. GMC is shown to definitely have a window of applicability when simulating discontinuously reinforced composite material behavior.

Pahr, D. H.↗
DOE OSTI2023

Modeling diffusion and types I-V sorption of water vapor in heterogeneous systems

Here, a sorption and diffusion model is developed using a mobile-immobile decomposition of the vapor concentration. Henry’s mode represents the mobile species which diffuses through the solid, while Langmuir and pooling modes represent possible immobilization processes that cause nonlinearities in sorption capacity. The model can simulate the five classical sorption types and can incorporate additional dynamics compared to models based on thermodynamic equilibrium. Additionally, the framework allows for discontinuities in material properties encountered in multi-material systems. The resulting non-linear coupled equations are solved by employing a finite element method to discretize in space, and a backward Euler method to discretize in time. The discretized system of equations is solved via a Newton-type iteration scheme at each time-step. Four different materials are parameterized for the model, which are then used in examples to demonstrate the model’s ability to capture complex sorption processes in multi-material systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Finite Element Method for Electrochemical Transport

This code provides Finite Element solvers for Electrochemical Transport. A few examples from the literature are reproduced, with a focus on CO2 electrolysis. The Discontinuous Galerkin scheme for the electroneutral Nernst-Planck equations is from Roy, T., Andrej, J. and Beck, V.A., 2021. A scalable DG solver for the electroneutral Nernst-Planck equations. arXiv preprint arXiv:2112.09271. This work also includes a scalable preconditioner.

Beck, VictorA↗
DOE OSTI2024

A hybrid Monte Carlo, discontinuous Galerkin method for linear kinetic transport equations

Here we present a hybrid method for time-dependent particle transport problems that combines Monte Carlo (MC) estimation with deterministic solutions based on discrete ordinates. For spatial discretizations, the MC algorithm computes a piecewise constant solution and the discrete ordinates use bilinear discontinuous finite elements. From the hybridization of the problem, the resulting problem solved by Monte Carlo is scattering free, resulting in a simple, efficient solution procedure. Between time steps, we use a projection approach to “relabel” collided particles as uncollided particles. In conclusion, from a series of standard 2-D Cartesian test problems we observe that our hybrid method has improved accuracy and reduction in computational complexity of approximately an order of magnitude relative to standard discrete ordinates solutions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

A high-order staggered meshless method for elliptic problems

Here, we present a new meshless method for scalar diffusion equations, which is motivated by their compatible discretizations on primal-dual grids. Unlike the latter though, our approach is truly meshless because it only requires the graph of nearby neighbor connectivity of the discretization points. This graph defines a local primal-dual grid complex with a virtual dual grid, in the sense that specification of the dual metric attributes is implicit in the method's construction. Our method combines a topological gradient operator on the local primal grid with a generalized moving least squares approximation of the divergence on the local dual grid. We show that the resulting approximation of the div-grad operator maintains polynomial reproduction to arbitrary orders and yields a meshless method, which attains $O(h^{m})$ convergence in both $L^2$- and $H^1$-norms, similar to mixed finite element methods. We demonstrate this convergence on curvilinear domains using manufactured solutions in two and three dimensions. Application of the new method to problems with discontinuous coefficients reveals solutions that are qualitatively similar to those of compatible mesh-based discretizations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗
DOE OSTI2017

Continuum kinetic and multi-fluid simulations of classical sheaths

The kinetic study of plasma sheaths is critical, among other things, to understand the deposition of heat on walls, the effect of sputtering, and contamination of the plasma with detrimental impurities. The plasma sheath also provides a boundary condition and can often have a significant global impact on the bulk plasma. In this paper, kinetic studies of classical sheaths are performed with the continuum kinetic code, Gkeyll, which directly solves the Vlasov-Maxwell equations. The code uses a novel version of the finite-element discontinuous Galerkin scheme that conserves energy in the continuous-time limit. The fields are computed using Maxwell equations. Ionization and scattering collisions are included; however, surface effects are neglected. The aim of this work is to introduce the continuum kinetic method and compare its results with those obtained from an already established finite-volume multi-fluid model also implemented in Gkeyll. Novel boundary conditions on the fluids allow the sheath to form without specifying wall fluxes, so the fluids and fields adjust self-consistently at the wall. Our work demonstrates that the kinetic and fluid results are in agreement for the momentum flux, showing that in certain regimes, a multifluid model can be a useful approximation for simulating the plasma boundary. There are differences in the electrostatic potential between the fluid and kinetic results. Further, the direct solutions of the distribution function presented here highlight the non-Maxwellian distribution of electrons in the sheath, emphasizing the need for a kinetic model. The densities, velocities, and the potential show a good agreement between the kinetic and fluid results. But, kinetic physics is highlighted through higher moments such as parallel and perpendicular temperatures which provide significant differences from the fluid results in which the temperature is assumed to be isotropic. Besides decompression cooling, the heat flux is shown to play a role in the temperature differences that are observed, especially inside the collisionless sheath. Published by AIP Publishing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2018

A mesh-independent method for planar three-dimensional crack growth in finite domains: A mesh-independent method for crack growth in 3D finite domains

The discrete crack mechanics (DCM) method is a dislocation-based crack modeling technique where cracks are constructed using Volterra dislocation loops. The method allows for the natural introduction of displacement discontinuities, avoiding numerically expensive techniques. Mesh dependence in existing computational modeling of crack growth is eliminated by utilizing a superposition procedure. The elastic field of cracks in finite bodies is separated into two parts: the infinite-medium solution of discrete dislocations and an finite element method solution of a correction problem that satisfies external boundary conditions. In the DCM, a crack is represented by a dislocation array with a fixed outer loop determining the crack tip position encompassing additional concentric loops free to expand or contract. Solving for the equilibrium positions of the inner loops gives the crack shape and stress field. The equation of motion governing the crack tip is developed for quasi-static growth problems. Additionally, convergence and accuracy of the DCM method are verified with two- and three-dimensional problems with well-known solutions. Crack growth is simulated under load and displacement (rotation) control. In the latter case, a semicircular surface crack in a bent prismatic beam is shown to change shape as it propagates inward, stopping as the imposed rotation is accommodated.

42 ENGINEERING↗
NASA NTRS1988

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Kim, Sang-Wook↗