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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. Furthermore, we believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1994

Investigation of finite element: ABC methods for electromagnetic field simulation

The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.

Chatterjee, A.↗
NASA NTRS1992

Unstructured grid methods for compressible flows

The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.

Morgan, K.↗
DOE OSTI2023

Multi-fidelity microstructure-induced uncertainty quantification by advanced Monte Carlo methods

Quantifying uncertainty associated with the microstructure variation of a material can be a computationally daunting task, especially when dealing with advanced constitutive models and fine mesh resolutions in the crystal plasticity finite element method (CPFEM). Numerous studies have been conducted regarding the sensitivity of material properties and performance to the mesh resolution and choice of constitutive model. However, a unified approach that accounts for various fidelity parameters, such as mesh resolutions, integration time-steps and constitutive models simultaneously is currently lacking. Further, this paper proposes a novel uncertainty quantification (UQ) approach for computing the properties and performance of homogenized materials using CPFEM, that exploits a hierarchy of approximations with different levels of fidelity. In particular, we illustrate how multi-level sampling methods, such as multi-level Monte Carlo (MLMC) and multi-index Monte Carlo (MIMC), can be applied to assess the impact of variations in the microstructure of polycrystalline materials on the predictions of homogenized materials properties. We show that by adaptively exploiting the fidelity hierarchy, we can significantly reduce the number of microstructures required to reach a certain prescribed accuracy. Finally, we show how our approach can be extended to a multi-fidelity framework, where we allow the underlying constitutive model to be chosen from either a phenomenological plasticity model or a dislocation-density-based model.

36 MATERIALS SCIENCE↗
NASA NTRS2000

Stress Recovery and Error Estimation for Shell Structures

The Penalized Discrete Least-Squares (PDLS) stress recovery (smoothing) technique developed for two dimensional linear elliptic problems is adapted here to three-dimensional shell structures. The surfaces are restricted to those which have a 2-D parametric representation, or which can be built-up of such surfaces. The proposed strategy involves mapping the finite element results to the 2-D parametric space which describes the geometry, and smoothing is carried out in the parametric space using the PDLS-based Smoothing Element Analysis (SEA). Numerical results for two well-known shell problems are presented to illustrate the performance of SEA/PDLS for these problems. The recovered stresses are used in the Zienkiewicz-Zhu a posteriori error estimator. The estimated errors are used to demonstrate the performance of SEA-recovered stresses in automated adaptive mesh refinement of shell structures. The numerical results are encouraging. Further testing involving more complex, practical structures is necessary.

Yazdani, A. A.↗
NASA NTRS2018

Tetrahedral-Mesh Simulations of Shock-Turbulence Interaction

Despite decades of development of unstructured mesh methods, direct numerical simulations (DNS) of turbulent flows are still predominantly performed on structured or unstructured hexahedral meshes with high-order finite-difference methods, weighted essentially nonoscillatory (WENO) schemes, or hybrid schemes formed by their combinations. Tetrahedral meshes offer easy mesh generation and adaptation around complex geometries and the potential of an orientation-free grid that would benefit the isotropic nature of small-scale dissipation, as well as the solution accuracy of intermediate scales. To advance the state of the art of unstructured-mesh simulation capabilities for shock/turbulence interaction, DNS using pure tetrahedral meshes are carried out with the space-time conservation element, solution element (CESE) method in this research. By its design, the CESE method is constructed based on a non-dissipative scheme and is a genuinely multidimensional numerical framework that is free from the use of an approximate Riemann-solver. The numerical framework also provides the ability to add numerical dissipation (the nondissipative scheme acts as the reference state like that of the reversible state in thermodynamics) when needed (with justification from mathematics/physics). The above-mentioned features along with the CESE method's consistent shock-capturing approach and strong enforcement of flux conservation in spacetime offers a novel method to accurately simulate turbulent flows and their interaction with shocks using tetrahedral meshes. Two canonical problems, namely, isotropic turbulence interaction with a normal shock and a Mach 2.9 turbulent boundary layer flow over a 24deg compression corner are investigated in this study. Computational results show reasonably good agreement with experimental data and results from structured-mesh, high-order simulations available in the literature. Successful validation of these canonical problems demonstrated here paves the way for future high-fidelity supersonic flow simulations involving complex-geometries.

Venkatachari, Balaji Shankar↗
DOE OSTI2021

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1989

Mesh refinement in finite element analysis by minimization of the stiffness matrix trace

Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.

Kittur, Madan G.↗
NASA NTRS2014

Using SpaceClaimTD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractor's thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces/solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing/repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the "mark-up" of that geometry. These so-called "mark-ups" control how finite element (FE) meshes are to be generated through the "tagging" of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. "Domain-tags" were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine the objects each time as one would if using TDMesher. The use of SpaceClaim/TD Direct helps simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It also saves time and effort in the subsequent analysis.

Power Systems↗
DOE OSTI2024

Leveraging a Neural Network-Enhanced Reproducing Kernel Particle Method for Multiphysics Degradation Modeling of Energy Storage Materials

Energy storage materials exhibit strong electro-chemo-mechanical coupling and highly anisotropic material properties, contributing to the formation and propagation of micro-cracking during charge/discharge cycling and resulting in reduced performance and service life. A coupled electro-chemo-mechanical reproducing kernel particle method (RKPM) formulation has been developed to analyze this system. With microstructural images supplied by the National Renewable Energy Laboratory (NREL), pixel-based model construction by RKPM is used to represent the complex material microstructures that dictate the coupled physics of these systems. Traditional electro-chemo-mechanical models rely on mesh-based finite element methods, which can lead to difficulties in meshing such complex geometries and capturing crack propagation due to mesh dependency. Here, a neural network-enhanced reproducing kernel particle method (NN-RKPM) [1, 2] is introduced to effectively model damage and crack propagation in the material microstructures; the location, orientation, and solution transition near a localization are automatically captured by superimposed block-level NN optimizations. This NN enrichment approach allows for effective modeling of localizations via a fixed background discretization, relieving tedious efforts for adaptive refinement in traditional mesh-based methods. Applications to the heterogeneous microstructures of Li-ion battery cathodes will be presented to demonstrate the effectiveness of the proposed methods. NN-RKPM is additionally used to inform how crack opening and closure in turn affect the coupled chemical equations and material microstructure. Reference: [1] Baek, J., Chen, J. S., Susuki, K., "Neural Network enhanced Reproducing Kernel Particle Method for Modeling Localizations," International Journal for Numerical Methods in Engineering, Vol. 123, pp 4422-4454, https://doi.org/10.1002/nme.7040, 2022. [2] Baek, J., Chen, J. S., "A Neural Network-Based Enrichment of Reproducing Kernel Approximation for Modeling Brittle Fracture", Computer Methods in Applied Mechanics and Engineering Vol. 410, 116590, 2024.

degradation↗
NASA NTRS2014

Using SpaceClaim/TD Direct for Modeling Components with Complex Geometries for the Thermal Desktop-Based Advanced Stirling Radioisotope Generator Model

SpaceClaim/TD Direct has been used extensively in the development of the Advanced Stirling Radioisotope Generator (ASRG) thermal model. This paper outlines the workflow for that aspect of the task and includes proposed best practices and lessons learned. The ASRG thermal model was developed to predict component temperatures and power output and to provide insight into the prime contractors thermal modeling efforts. The insulation blocks, heat collectors, and cold side adapter flanges (CSAFs) were modeled with this approach. The model was constructed using mostly TD finite difference (FD) surfaces solids. However, some complex geometry could not be reproduced with TD primitives while maintaining the desired degree of geometric fidelity. Using SpaceClaim permitted the import of original CAD files and enabled the defeaturing repair of those geometries. TD Direct (a SpaceClaim add-on from CRTech) adds features that allowed the mark-up of that geometry. These so-called mark-ups control how finite element (FE) meshes were generated and allowed the tagging of features (e.g. edges, solids, surfaces). These tags represent parameters that include: submodels, material properties, material orienters, optical properties, and radiation analysis groups. TD aliases were used for most tags to allow analysis to be performed with a variety of parameter values. Domain-tags were also attached to individual and groups of surfaces and solids to allow them to be used later within TD to populate objects like, for example, heaters and contactors. These tools allow the user to make changes to the geometry in SpaceClaim and then easily synchronize the mesh in TD without having to redefine these objects each time as one would if using TD Mesher.The use of SpaceClaim/TD Direct has helped simplify the process for importing existing geometries and in the creation of high fidelity FE meshes to represent complex parts. It has also saved time and effort in the subsequent analysis.

Power Systems↗
NASA NTRS1990

Algebraic turbulence modeling for unstructured and adaptive meshes

An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.

Mavriplis, Dimitri J.↗
NASA NTRS1988

Nonconforming mortar element methods: Application to spectral discretizations

Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.

Maday, Yvon↗
DOE OSTI2021

AIR Algebraic Multigrid for a Space-Time Hybridizable Discontinuous Galerkin Discretization of Advection(-Diffusion)

This article investigates the efficiency, robustness, and scalability of approximate ideal restriction (AIR) algebraic multigrid as a preconditioner in the all-at-once solution of a space-time hybridizable discontinuous Galerkin discretization of advection-dominated flows. The motivation for this study is that the time-dependent advection-diffusion equation can be seen as a “steady” advection-diffusion problem in $(d+1)$-dimensions and AIR has been shown to be a robust solver for steady advection-dominated problems. Numerical examples demonstrate the effectiveness of AIR as a preconditioner for advection-diffusion problems on fixed and time-dependent domains, using both slab-by-slab and all-at-once space-time discretizations, and in the context of uniform and space-time adaptive mesh refinement. A closer look at the geometric coarsening structure that arises in AIR also explains why AIR can provide robust, scalable, space-time convergence on advective and hyperbolic problems, while most multilevel parallel-in-time schemes struggle with such problems.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1997

Multilevel methods for elliptic problems on unstructured grids

Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.

Chan, Tony F.↗
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 NTRSDate not supplied

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗
DOE OSTI2022

Active learning with multifidelity modeling for efficient rare event simulation

Here, while multifidelity modeling provides a cost-effective way to conduct uncertainty quantification with computationally expensive models, much greater efficiency can be achieved by adaptively deciding the number of required high-fidelity (HF) simulations, depending on the type and complexity of the problem and the desired accuracy in the results. We propose a framework for active learning with multifidelity modeling emphasizing the efficient estimation of rare events. Our framework works by fusing a low-fidelity (LF) prediction with an HF-inferred correction, filtering the corrected LF prediction to decide whether to call the high-fidelity model, and for enhanced subsequent accuracy, adapting the correction for the LF prediction after every HF model call. The framework does not make any assumptions as to the LF model type or its correlations with the HF model. In addition, for improved robustness when estimating smaller failure probabilities, we propose using dynamic active learning functions that decide when to call the HF model. We demonstrate our framework using several academic case studies (including some high-dimensional problems) and two finite element model case studies: estimating Navier-Stokes velocities using the Stokes approximation and estimating stresses in a transversely isotropic model subjected to displacements via a coarsely meshed isotropic model. Across these case studies, not only did the proposed framework estimate the failure probabilities accurately, but compared with either Monte Carlo or a standard variance reduction method, it also required only a small fraction of the calls to the HF model.

42 ENGINEERING↗