Search NASA⌕ Search

SEARCH · Search NASA

Results for “interface problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

Interface PINNs (I-PINNs): A physics-informed neural networks framework for interface problems

Here, we present a novel physics-informed neural networks (PINNs) framework for modeling interface problems, termed Interface PINNs (I-PINNs). I-PINNs uses different neural networks for any two subdomains separated by a sharp interface such that the neural networks differ only through their activation functions while the other parameters remain identical. The performance of I-PINNs, conventional PINNs, and other existing domain-decomposition PINNs methods such as extended PINNs (XPINNs) and multi-domain PINN (M-PINN) is compared through several one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems. The results demonstrate that I-PINNs provides a root-mean-square-error accuracy, at least two orders of magnitude better than conventional PINNs and XPINNs at approximately one-tenth of the computational cost of conventional PINNs and half the cost of XPINNs. Additionally, while I-PINNs and M-PINN provide comparable accuracies, M-PINN is found to be approximately 50% more expensive.

42 ENGINEERING↗

A variational mimetic finite difference method for elliptic interface problems on non-matching polytopal meshes with geometric interface inconsistencies

A new variational mimetic finite difference method for elliptic interface problems with perfect and imperfect thermal contacts on non-matching polytopal meshes with geometric interface inconsistencies is developed and analyzed theoretically and numerically. The method is defined on multiple non-matching submeshes with gaps and overlaps along their interfaces. The discrete equations are derived from a minimization problem for the augmented Dirichlet functional. For a perfect thermal contact, the functional uses a modified mimetic gradient with extended stencil which couples unknowns from both sides of an interface, as well as penalty terms to enforce weak continuity of temperature across the interface. The method leads to a symmetric positive definite matrix for any scaling of the penalty terms. For an imperfect thermal contact, the Dirichlet functional is supplemented with a quadratic jump term along the interface related to the interface thermal resistance. We prove that the method conserves the total heat flux across each interface. In conclusion, the obtained results are verified with numerical experiments showing convergence in the discrete L 2 and L ∞ norms.

97 MATHEMATICS AND COMPUTING↗

An Asymptotically Compatible Coupling Formulation for Nonlocal Interface Problems with Jumps

Here, we introduce a mathematically rigorous formulation for a nonlocal interface problem with jumps and propose an asymptotically compatible finite element discretization for the weak form of the interface problem. After proving the well-posedness of the weak form, we demonstrate that solutions to the nonlocal interface problem converge to the corresponding local counterpart when the nonlocal data are appropriately prescribed. Several numerical tests in one and two dimensions show the applicability of our technique, its numerical convergence to exact nonlocal solutions, its convergence to the local limit when the horizons vanish, and its robustness with respect to the patch test.

97 MATHEMATICS AND COMPUTING↗

Adaptive Interface-PINNs (AdaI-PINNs): An Efficient Physics-Informed Neural Networks Framework for Interface Problems

Here, we present an efficient physics-informed neural networks (PINNs) framework, termed Adaptive Interface-PINNs (AdaI-PINNs), to improve the modeling of interface problems with discontinuous coefficients and/or interfacial jumps. This framework is an enhanced version of its predecessor, Interface PINNs or I-PINNs (Sarma et al.; https://doi.org/10.1016/j.cma.2024.117135), which involves domain decomposition and assignment of different predefined activation functions to the neural networks in each subdomain across a sharp interface, while keeping all other parameters of the neural networks identical. In AdaI-PINNs, the activation functions vary solely in their slopes, which are trained along with the other parameters of the neural networks. This makes the AdaI-PINNs framework fully automated without requiring preset activation functions. Comparative studies on one-dimensional, two-dimensional, and three-dimensional benchmark elliptic interface problems reveal that AdaI-PINNs outperform I-PINNs, reducing computational costs by 2-6 times while producing similar or better accuracy.

97 MATHEMATICS AND COMPUTING↗

A high order Cartesian grid, finite volume method for elliptic interface problems

We present a higher-order finite volume method for solving elliptic PDEs with jump conditions on interfaces embedded in a 2D Cartesian grid. Second, fourth, and sixth order accuracy is demonstrated on a variety of tests including problems with high-contrast and spatially varying coefficients, large discontinuities in the source term, and complex interface geometries. We include a generalized truncation error analysis based on cell-centered Taylor series expansions, which then define stencils in terms of local discrete solution data and geometric information. In the process, we develop a simple method based on Green's theorem for computing exact geometric moments directly from an implicit function definition of the embedded interface. This approach produces stencils with a simple bilinear representation, where spatially-varying coefficients and jump conditions can be easily included and finite volume conservation can be enforced.

97 MATHEMATICS AND COMPUTING↗

A fractional model for anomalous diffusion with increased variability: Analysis, algorithms and applications to interface problems

Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. Here, we introduce a new fractional operator characterized by a doubly-variable fractional order and possibly truncated interactions. Under certain conditions on the model parameters and on the regularity of the fractional order we show that the corresponding Poisson problem is well-posed. Additionally, we introduce a finite element discretization and describe an efficient implementation of the finite-element matrix assembly in the case of piecewise constant fractional order. Through several numerical tests, we illustrate the improved descriptive power of this new operator across media interfaces. Furthermore, we present one-dimensional and two-dimensional h-convergence results that show that the variable-order model has the same convergence behavior as the constant-order model.

97 MATHEMATICS AND COMPUTING↗

Interface Problem Formulation Improvements with Application to Nuclear Fuel Performance Analysis

The U.S. Department of Energy’s Nuclear Energy Advanced Modeling and Simulation Program aims to develop predictive capabilities by applying computational methods to the analysis and design of advanced reactor and fuel cycle systems. This program has been providing engineering scale support for the development of BISON, a high-fidelity and high-resolution fuel performance tool. This report documents new developments and robustness improvements in mechanical and thermal (gap heat transfer) contact formulations. The improvements range from the migration of industrial level (“assessment”) nuclear fuel model setups to the usage of mortar formulations, the addition of frictional contact to one-dimensional layered representations of fuel and cladding components, and the addition of the Petrov-Galerkin approach to dual mortar, which improves performance on curved, relatively coarse meshes. In addition, the Lagrange-multiplier enforcement of mechanical mortar contact constraints has been extended to two additional types of enforcement: penalty and augmented Lagrange-Uzawa. We show that the latter approach yields the same interface results as dual mortar in the Multiphysics Object-Oriented Simulation Environment, with the advantage of not worsening the condition number of the system matrix—thereby enabling the use of some general implementations of iterative preconditioners, at the expense of additional system evaluations (i.e., augmentations).

42 ENGINEERING↗

Mathematical Foundations for Nonlocal Interface Problems: Multiscale Simulations of Heterogeneous Materials (Final LDRD Report)

Nonlocal models provide a much-needed predictive capability for important Sandia mission applications, ranging from fracture mechanics for nuclear components to subsurface flow for nuclear waste disposal, where traditional partial differential equations (PDEs) models fail to capture effects due to long-range forces at the microscale and mesoscale. However, utilization of this capability is seriously compromised by the lack of a rigorous nonlocal interface theory, required for both application and efficient solution of nonlocal models. To unlock the full potential of nonlocal modeling we developed a mathematically rigorous and physically consistent interface theory and demonstrate its scope in mission-relevant exemplar problems.

97 MATHEMATICS AND COMPUTING↗

Dynamic flux surrogate-based partitioned methods for interface problems

Loosely coupled partitioned methods for multiphysics problems treat each subproblem as a separate entity and advance them independently in time. In so doing these methods enable code reuse, increase concurrency and provide a convenient framework for plug-and-play multiphysics simulations. However, mathematically loosely coupled schemes are equivalent to a single step of an iterative solution method, which can compromise their accuracy and stability. We present a new data-driven partitioned method for coupled parametric PDEs that can improve upon the accuracy of traditional loosely coupled methods without incurring a performance penalty. To that end, we replace conventional field transfers across the interface by a surrogate for the dynamics of the interface flux exchanged between the subdomains. To develop this surrogate we apply dynamic mode decomposition to a non-standard staggered-in-time state, comprising the interface flux and small solution patches near the interface. The new approach shifts the main computational burden to an offline training phase, whereas application of the surrogate in the online phase amounts to a single matrix–vector multiplication. In conclusion, we provide stability analysis of the surrogate-based partitioned scheme and include numerical results that demonstrate its potential.

Dynamic mode decomposition (DMD)↗

Optimal local truncation error method for 3-D elasticity interface problems

The paper deals with a new effective numerical technique on unfitted Cartesian meshes for simulations of heterogeneous elastic materials. Here, we develop the optimal local truncation error method (OLTEM) with 27- point stencils (similar to those for linear finite elements) for the 3-D time-independent elasticity equations with irregular interfaces. Only displacement unknowns at each internal Cartesian grid point are used. The interface conditions are added to the expression for the local truncation error and do not change the width of the stencils. The unknown stencil coefficients are calculated by the minimization of the local truncation error of the stencil equations and yield the optimal second order of accuracy for OLTEM with the 27-point stencils on unfitted Cartesian meshes. A new post-processing procedure for accurate stress calculations has been developed. Similar to basic computations it uses OLTEM with the 27-point stencils and the elasticity equations. The post-processing procedure can be easily extended to unstructured meshes and can be independently used with existing numerical techniques (e.g., with finite elements). Numerical experiments show that at an accuracy of 0.1% for stresses, OLTEM with the new post-processing procedure significantly (by 10 5 -10 9 times) reduces the number of degrees of freedom compared to linear finite elements. OLTEM with the 27-point stencils yields even more accurate results than high-order finite elements with wider stencils.

42 ENGINEERING↗

Interface Aspects in All‐Solid‐State Li‐Based Batteries Reviewed

Abstract Extensive efforts have been made to improve the Li‐ionic conductivity of solid electrolytes (SE) for developing promising all‐solid‐state Li‐based batteries (ASSB). Recent studies suggest that minimizing the existing interface problems is even more important than maximizing the conductivity of SE. Interfaces are essential in ASSB, and their properties significantly influence the battery performance. Interface problems, arising from both physical and (electro)chemical material properties, can significantly inhibit the transport of electrons and Li‐ions in ASSB. Consequently, interface problems may result in interlayer formation, high impedances, immobilization of moveable Li‐ions, loss of active host sites available to accommodate Li‐ions, and Li‐dendrite formation, all causing significant storage capacity losses and ultimately battery failures. The characteristic differences of interfaces between liquid‐ and solid‐type Li‐based batteries are presented here. Interface types, interlayer origin, physical and chemical structures, properties, time evolution, complex interrelations between various factors, and promising interfacial tailoring approaches are reviewed. Furthermore, recent advances in the interface‐sensitive or depth‐resolved analytical tools that can provide mechanistic insights into the interlayer formation and strategies to tailor the interlayer formation, composition, and properties are discussed.

25 ENERGY STORAGE↗

A framework for multirate time integration of interface-coupled problems

The research described here was performed as part of the DOE SciDAC project Coupling Approaches for Next Generation Architectures (CANGA). A framework was developed for the derivation of novel algorithms for the multirate time integration of two-component systems coupled across an interface between spatial domains. The multirate aspect means that different time steps are allowed by each component integrator. The framework provides a way to construct multirate integrators with desirable properties related to stability, accuracy and preservation of system invariants. This report describes the framework and summarizes the major results, examples and research products.

97 MATHEMATICS AND COMPUTING↗

A conservative discontinuous-Galerkin-in-time (DGiT) multirate time integration framework for interface-coupled problems with applications to solid–solid interaction and air–sea models

In this paper we extend the DGiT multirate framework, developed in Connors and Sockwell (2022) for scalar transmission problems, to a solid–solid interaction (SSI) problem involving two coupled elastic solids and a coupled air–sea model with the rotating, thermal shallow water equations. In so doing we aim to demonstrate the broad applicability of the mathematical theory and governing principles established in Connors and Sockwell (2022) to coupled problems characterized by subproblems evolving at different temporal scales. Further, multirate time integration algorithms employing different time steps, optimized for the dynamics of each subproblem, can significantly improve simulation efficiency for such coupled problems. However, development of multirate algorithms is a highly non-trivial task due to the coupling, which can impact accuracy, stability or other desired properties such as preservation of system invariants. DGiT provides a general template for multirate time integration that can achieve these properties. To elucidate the manner in which DGiT accomplishes this task, we fully detail each step in the application of the framework to the SSI and air–sea coupled problems. Numerical examples illustrate key properties of the resulting multirate schemes for both problems.

42 ENGINEERING↗

Implement and Test 3D Mortar Contact in BISON

We leverage the extension of the generation of mortar segment meshes to three dimensions in MOOSE’s framework to extend thermomechanical modeling capabilities to problems with three dimensions. A modular approach to gap heat transfer physics using the mortar finite element method was created and documented, mechanical contact was extended to three dimensions—including frictional behavior, performance and ease of use were improved, and steps towards scalability of solid mechanics problems involving contact were taken. Many of these new developments are demonstrated in the simulation of 3D light-water reactor (LWR) problems, where the thermomechanical interface problem is solved using the mortar finite element method. Usage of the mortar framework has improved convergence in 2D problems and has enabled employing friction in 3D problems, of which we show results of a short, local stack of 3D pellets. Consequently, the benefits of mortar in terms of solution convergence and quality are extended to three dimensions. Section 2 discusses fundamental developments that enabled the simulation of practical mortar problems in three dimensions and other general improvements, including the reduction of the derivative container size, the modification of dual basis computations when edge dropping (lack of secondary element projection) takes place, the improvement of conditioning when employing the VCP in-edge dropping conditions, and code usability and quality improvements. These latter code enhancements include the migration of tests using “old” mortar contact constraints to using dual mortar with a semi-smooth Newton solution strategy and the reuse of lower dimensional domains for straightforwardly setting up a mortar thermomechanical LWR problem, i.e. the MOOSE action is employed for mechanical contact and the thermal LWR action is employed to capture the gas conductance, contact, and radiation components of gap heat transfer physics. Independently of the mortar LWR thermal action, we developed a modular approach to gap heat transfer that resides in MOOSE and can be leveraged, e.g., in metallic fuel problems. This approach, whose code design based on MOOSE’s user objects to model specific physics was proposed by the maintenance activity, is detailed in Section 3. Based on the dual mortar finite element method, the frictional contact constraints were extended to three dimensions. A block sheared in two directions in and out of contact with a rigid plane is employed in Section 4 to show the way the approach handles changes in frictional states (e.g. stick to slip) within a competitive number of Newton iterations. Equations and numerical results on the use of the VCP with Cartesian Lagrange multipliers, whose combination enables their direct condensation, are described in Section 5.3. Two-dimensional and three-dimensional BISON LWR simulations are discussed in Section 6. Particularly, a stack of five eccentric pellets with a surface defect is simulated and the effect of pellet-cladding friction is assessed. Finally, conclusions are outlined in Section 7.

42 ENGINEERING↗

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗