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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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Generalized Korn’s inequalities for piecewise $H¹$ and $H²$ vector fields

The purpose of this paper is to construct a new class of discrete generalized Korn’s inequalities for piecewise $H^1$ vector fields and piecewise $H^2$ vector fields in three-dimensional space. The resulting Korn’s inequalities are different from the standard Korn’s inequalities, as they involve the trace-free symmetric gradient operator, in place of the usual symmetric gradient operator. Furthermore, it is anticipated that the new generalized Korn’s inequalities will be useful for the analysis of a broad range of finite element methods, including mixed finite element methods and discontinuous Galerkin methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

An Advanced Meso-Scale Peridynamic Modeling Technology using High-Performance Computing for Cost-Effective Product Design and Testing of Carbon Fiber Reinforced Polymer Composites in Light-weight Vehicles

We study a peridynamic composite modeling technology based on the discontinuous Galerkin finite element method, implemented in the commercial LS-DYNA software, for modeling and prediction of failure in carbon fiber reinforced polymer composites. The proposed technology is developed for the material failure analysis at the meso-scale, which provides the prevailing fiber-matrix interaction mechanism, without adoption of the representative volume element method and thus avoiding complicated numerical calibration procedures. Three types of experimental tests—in-plane coupon test, out-of-plane coupon test, and a component crash test—are simulated in a high-performance computing environment to assess the performance of the proposed peridynamic composite modeling technology.

36 MATERIALS SCIENCE↗
NASA NTRS2004

A-Posteriori Error Estimation for Hyperbolic Conservation Laws with Constraint

This lecture considers a-posteriori error estimates for the numerical solution of conservation laws with time invariant constraints such as those arising in magnetohydrodynamics (MHD) and gravitational physics. Using standard duality arguments, a-posteriori error estimates for the discontinuous Galerkin finite element method are then presented for MHD with solenoidal constraint. From these estimates, a procedure for adaptive discretization is outlined. A taxonomy of Green's functions for the linearized MHD operator is given which characterizes the domain of dependence for pointwise errors. The extension to other constrained systems such as the Einstein equations of gravitational physics are then considered. Finally, future directions and open problems are discussed.

Barth, Timothy↗
NASA NTRS2018

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Carton De Wiart, Corentin↗
DOE OSTI2021

An IIPG-Based Finite Element Framework in MOOSE for Modeling Fiber Reinforced Composite Failure Governed by Extrinsic Cohesive Laws

Many material and structure failures are initiated at the interface between two distinctive materials, such as the debonding of interfaces of matrix/fiber of composites or bulk matrix/inclusion in metals at micro-scales. Accurate and robust modeling of these interface failures is critical to the design of novel material and structure with improved functionality. This paper presents a robust implementation of a discontinuous Galerkin finite element method in MOOSE based on the Incomplete Interior Penalty Galerkin scheme for modeling material interface behavior. This DG-based interface method naturally accommodates important extrinsic cohesive zone material models and is capable of modeling the failures of material interfaces across which material properties are highly distinctive. We demonstrate a good performance of the proposed method using single fiber and multiple fiber debonding problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

FIERRO V.X

FIERRO is a modern C++ code intended to simulate quasi-static solid mechanics problems and transient, compressible material dynamic problems with Lagrangian methods, which have meshes with constant mass elements that move with the material. FIERRO is designed to aid a) material model research that has historically been done using commercial implicit and explicit finite element codes, b) numerical methods research, and c) computer science research. FIERRO supports user developed material models that adhere to several industry standard formats by using a C++ to Fortran interface to couple the model to the numerical solvers. FIERRO is built on the ELEMENTS library that supports a diverse suite of element types, including high-order elements, and quadrature rules. The mesh class within the ELEMENTS library is designed for efficient calculations on unstructured meshes and to minimize memory usage. FIERRO is designed to readily accommodate a range of numerical methods including continuous finite element, finite volume, and discontinuous Galerkin methods. FIERRO is designed to support explicit and implicit time integration methods. FIERRO only supports a single material in an element. No physical data exists within the code.

Morgan, Nathaniel↗
DOE OSTI2016

Nonnegative methods for bilinear discontinuous differencing of the S N equations on quadrilaterals

Historically, matrix lumping and ad hoc flux fixups have been the only methods used to eliminate or suppress negative angular flux solutions associated with the unlumped bilinear discontinuous (UBLD) finite element spatial discretization of the two-dimensional S N equations. Though matrix lumping inhibits negative angular flux solutions of the S N equations, it does not guarantee strictly positive solutions. In this paper, we develop and define a strictly nonnegative, nonlinear, Petrov-Galerkin finite element method that fully preserves the bilinear discontinuous spatial moments of the transport equation. Additionally, we define two ad hoc fixups that maintain particle balance and explicitly set negative nodes of the UBLD finite element solution to zero but use different auxiliary equations to fully define their respective solutions. We assess the ability to inhibit negative angular flux solutions and the accuracy of every spatial discretization that we consider using a glancing void test problem with a discontinuous solution known to stress numerical methods. Though significantly more computationally intense, the nonlinear Petrov-Galerkin scheme results in a strictly nonnegative solution and is a more accurate solution than all the other methods considered. One fixup, based on shape preserving, results in a strictly nonnegative final solution but has increased numerical diffusion relative to the Petrov-Galerkin scheme and is less accurate than the UBLD solution. The second fixup, which preserves as many spatial moments as possible while setting negative values of the unlumped solution to zero, is less accurate than the Petrov-Galerkin scheme but is more accurate than the other fixup. However, it fails to guarantee a strictly nonnegative final solution. As a result, the fully lumped bilinear discontinuous finite element solution is the least accurate method, with significantly more numerical diffusion than the Petrov-Galerkin scheme and both fixups.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
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↗
NASA NTRS2014

DNS of Flows over Periodic Hills using a Discontinuous-Galerkin Spectral-Element Method

Direct numerical simulation (DNS) of turbulent compressible flows is performed using a higher-order space-time discontinuous-Galerkin finite-element method. The numerical scheme is validated by performing DNS of the evolution of the Taylor-Green vortex and turbulent flow in a channel. The higher-order method is shown to provide increased accuracy relative to low-order methods at a given number of degrees of freedom. The turbulent flow over a periodic array of hills in a channel is simulated at Reynolds number 10,595 using an 8th-order scheme in space and a 4th-order scheme in time. These results are validated against previous large eddy simulation (LES) results. A preliminary analysis provides insight into how these detailed simulations can be used to improve Reynoldsaveraged Navier-Stokes (RANS) modeling

DNS↗
DOE OSTI2018

Deploy production sliding mesh capability with linear solver benchmarking.

Wind applications require the ability to simulate rotating blades. To support this use-case, a novel design-order sliding mesh algorithm has been developed and deployed. The hybrid method combines the control volume finite element methodology (CVFEM) with concepts found within a discontinuous Galerkin (DG) finite element method (FEM) to manage a sliding mesh. The method has been demonstrated to be design-order for the tested polynomial basis (P=1 and P=2) and has been deployed to provide production simulation capability for a Vestas V27 (225 kW) wind turbine. Other stationary and canonical rotating ow simulations are also presented. As the majority of wind-energy applications are driving extensive usage of hybrid meshes, a foundational study that outlines near-wall numerical behavior for a variety of element topologies is presented. Results indicate that the proposed nonlinear stabilization operator (NSO) is an effective stabilization methodology to control Gibbs phenomena at large cell Peclet numbers. The study also provides practical mesh resolution guidelines for future analysis efforts. Application-driven performance and algorithmic improvements have been carried out to increase robustness of the scheme on hybrid production wind energy meshes. Specifically, the Kokkos-based Nalu Kernel construct outlined in the FY17/Q4 ExaWind milestone has been transitioned to the hybrid mesh regime. This code base is exercised within a full V27 production run. Simulation timings for parallel search and custom ghosting are presented. As the low-Mach application space requires implicit matrix solves, the cost of matrix reinitialization has been evaluated on a variety of production meshes. Results indicate that at low element counts, i.e., fewer than 100 million elements, matrix graph initialization and preconditioner setup times are small. However, as mesh sizes increase, e.g., 500 million elements, simulation time associated with \setup-up" costs can increase to nearly 50% of overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Deploy production sliding mesh capability with linear solver benchmarking (ECP Milestone Report, Ver. 1.0)

Wind applications require the ability to simulate rotating blades. To support this use-case, a novel design-order sliding mesh algorithm has been developed and deployed. The hybrid method combines the control volume finite element methodology (CVFEM) with concepts found within a discontinuous Galerkin (DG) finite element method (FEM) to manage a sliding mesh. The method has been demonstrated to be design-order for the tested polynomial basis (P=1 and P=2) and has been deployed to provide production simulation capability for a Vestas V27 (225 kW) wind turbine. Other stationary and canonical rotating flow simulations are also presented. As the majority of wind-energy applications are driving extensive usage of hybrid meshes, a foundational study that outlines near-wall numerical behavior for a variety of element topologies is presented. Results indicate that the proposed nonlinear stabilization operator (NSO) is an effective stabilization methodology to control Gibbs phenomena at large cell Peclet numbers. The study also provides practical mesh resolution guidelines for future analysis efforts. Application-driven performance and algorithmic improvements have been carried out to increase robustness of the scheme on hybrid production wind energy meshes. Specifically, the Kokkos-based Nalu Kernel construct outlined in the FY17/Q4 ExaWind milestone has been transitioned to the hybrid mesh regime. This code base is exercised within a full V27 production run. Simulation timings for parallel search and custom ghosting are presented. As the low-Mach application space requires implicit matrix solves, the cost of matrix reinitialization has been evaluated on a variety of production meshes. Results indicate that at low element counts, i.e., fewer than 100 million elements, matrix graph initialization and preconditioner setup times are small. However, as mesh sizes increase, e.g., 500 million elements, simulation time associated with "setup-up" costs can increase to nearly 50% of overall simulation time when using the full Tpetra solver stack and nearly 35% when using a mixed Tpetra- Hypre-based solver stack. The report also highlights the project achievement of surpassing the 1 billion element mesh scale for a production V27 hybrid mesh. A detailed timing breakdown is presented that again suggests work to be done in the setup events associated with the linear system. In order to mitigate these initialization costs, several application paths have been explored, all of which are designed to reduce the frequency of matrix reinitialization. Methods such as removing Jacobian entries on the dynamic matrix columns (in concert with increased inner equation iterations), and lagging of Jacobian entries have reduced setup times at the cost of numerical stability. Artificially increasing, or bloating, the matrix stencil to ensure that full Jacobians are included is developed with results suggesting that this methodology is useful in decreasing reinitialization events without loss of matrix contributions. With the above foundational advances in computational capability, the project is well positioned to begin scientific inquiry on a variety of wind-farm physics such as turbine/turbine wake interactions.

Domino, Stefan P.↗
DOE OSTI2016

A hybridizable discontinuous Galerkin method for modeling fluid–structure interaction

This study presents a novel application of the hybridizable discontinuous Galerkin (HDG) finite element method to the multi-physics simulation of coupled fluid–structure interaction (FSI) problems. Recent applications of the HDG method have primarily been for single-physics problems including both solids and fluids, which are necessary building blocks for FSI modeling. Utilizing these established models, HDG formulations for linear elastostatics, a nonlinear elastodynamic model, and arbitrary Lagrangian–Eulerian Navier–Stokes are derived. The elasticity formulations are written in a Lagrangian reference frame, with the nonlinear formulation restricted to hyperelastic materials. With these individual solid and fluid formulations, the remaining challenge in FSI modeling is coupling together their disparate mathematics on the fluid–solid interface. This coupling is presented, along with the resultant HDG FSI formulation. Verification of the component models, through the method of manufactured solutions, is performed and each model is shown to converge at the expected rate. The individual components, along with the complete FSI model, are then compared to the benchmark problems proposed by Turek and Hron [1]. The solutions from the HDG formulation presented in this work trend towards the benchmark as the spatial polynomial order and the temporal order of integration are increased.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A family of independent Variable Eddington Factor methods with efficient preconditioned iterative solvers

We present a family of discretizations for the Variable Eddington Factor (VEF) equations that have high-order accuracy on curved meshes and efficient preconditioned iterative solvers. The VEF discretizations are combined with the Discontinuous Galerkin transport discretization from to form effective high-order, linear transport methods. The VEF discretizations are derived by extending the unified analysis of Discontinuous Galerkin methods for elliptic problems presented by Arnold et al. to the VEF equations. This framework is used to define analogs of the interior penalty, second method of Bassi and Rebay, minimal dissipation local Discontinuous Galerkin, and continuous finite element methods. The analysis of subspace correction preconditioners, which use a continuous operator to iteratively precondition the discontinuous discretization, is extended to the case of the non-symmetric VEF system. Numerical results demonstrate that the VEF discretizations have arbitrary-order accuracy on curved meshes, preserve the thick diffusion limit, and are effective on a proxy problem from thermal radiative transfer in both outer transport iterations and inner preconditioned linear solver iterations. We demonstrate that the VEF solution converges to the S N transport solution as the mesh is refined on both problems with smooth and non-smooth behavior in angle. Parallel performance studies show that the interior penalty VEF discretization's linear solve weak scales out to 1024 processors and strong scales well on a single node. Particular attention is paid to the parallel performance of the VEF algorithm when used in combination with a parallel block Jacobi transport sweep.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2002

A Discontinuous Galerkin Discretization of the Eikonal Equation on Curved Piecewise Isoparametric Triangulated Manifolds

This viewgraph presentation provides information on optimizing the travel distance between two points on a curved surface. The presentation addresses the single source shortest path problem, fast algorithms for estimating the eikonal equation, fast schemes and barrier theorems, and the discontinuous Galerkin method, including hyperbolic causality, finite element method, scalars, and marching the discontinuous Galerkin Eikonal approximation.

Barth, TIm↗
DOE OSTI2019

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗
NASA NTRS1991

The P1-RKDG method for two-dimensional Euler equations of gas dynamics

A class of nonlinearly stable Runge-Kutta local projection discontinuous Galerkin (RKDG) finite element methods for conservation laws is investigated. Two dimensional Euler equations for gas dynamics are solved using P1 elements. The generalization of the local projections, which for scalar nonlinear conservation laws was designed to satisfy a local maximum principle, to systems of conservation laws such as the Euler equations of gas dynamics using local characteristic decompositions is discussed. Numerical examples include the standard regular shock reflection problem, the forward facing step problem, and the double Mach reflection problem. These preliminary numerical examples are chosen to show the capacity of the approach to obtain nonlinearly stable results comparable with the modern nonoscillatory finite difference methods.

Cockburn, Bernardo↗
DOE OSTI2017

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for both the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.

nite element methods↗
DOE OSTI2016

Pellet Cladding Mechanical Interaction Modeling Using the Extended Finite Element Method

As a brittle material, the ceramic UO2 used as light water reactor fuel experiences significant fracturing throughout its life, beginning with the first rise to power of fresh fuel. This has multiple effects on the thermal and mechanical response of the fuel/cladding system. One such effect that is particularly important is that when there is mechanical contact between the fuel and cladding, cracks that extending from the outer surface of the fuel into the volume of the fuel cause elevated stresses in the adjacent cladding, which can potentially lead to cladding failure. Modeling the thermal and mechanical response of the cladding in the vicinity of these surface-breaking cracks in the fuel can provide important insights into this behavior to help avoid operating conditions that could lead to cladding failure. Such modeling has traditionally been done in the context of finite-element-based fuel performance analysis by modifying the fuel mesh to introduce discrete cracks. While this approach is effective in capturing the important behavior at the fuel/cladding interface, there are multiple drawbacks to explicitly incorporating the cracks in the finite element mesh. Because the cracks are incorporated in the original mesh, the mesh must be modified for cracks of specified location and depth, so it is difficult to account for crack propagation and the formation of new cracks at other locations. The extended finite element method (XFEM) has emerged in recent years as a powerful method to represent arbitrary, evolving, discrete discontinuities within the context of the finite element method. Development work is underway by the authors to implement XFEM in the BISON fuel performance code, and this capability has previously been demonstrated in simulations of fracture propagation in ceramic nuclear fuel. These preliminary demonstrations have included only the fuel, and excluded the cladding for simplicity. This paper presents initial results of efforts to apply XFEM to model stress concentrations induced by fuel fractures at the fuel/cladding interface during pellet cladding mechanical interaction (PCMI). This is accomplished by enhancing the thermal and mechanical contact enforcement algorithms employed by BISON to permit their use in conjunction with XFEM. The results from this methodology are demonstrated to be equivalent to those from using meshed discrete cracks. While the results of the two methods are equivalent for the case of a stationary crack, it is demonstrated that XFEM provides the additional flexibility of allowing arbitrary crack initiation and propagation during the analysis, and minimizes model setup effort for cases with stationary cracks.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗