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All sources NASA NTRS DOE OSTI

DOE OSTI2021

A Scalable Semi-Implicit Barotropic Mode Solver for the MPAS-Ocean

A scalable semi-implicit barotropic mode solver for the ocean component of the model for prediction across scales has been implemented as a competitor to an existing explicit-subcycling scheme to allow faster and more stable simulations while not sacrificing accuracy. The semi-implicit solver adopts the pipelined preconditioned bi-conjugate gradient stabilization algorithm as an iterative solver in conjunction with the restricted additive Schwarz preconditioner that accelerates the convergence rate of the iterative solver. The preconditioner is constructed from a linearized barotropic system that also reorders the system for optimal performance, while the semi-implicit solver deals with the fully nonlinear barotropic system that requires reassembly of the coefficient matrix for every time step. Several numerical experiments, from simple one-dimensional tests to three-dimensional real-world tests, demonstrate that the semi-implicit solver has almost the same accuracy and better parallel scalability compared with the existing scheme while allowing faster and more stable simulations. Furthermore, the semi-implicit solver accelerates the barotropic mode up to 2.9 times faster than the existing scheme on 16,320 processors, leading to an overall runtime speedup of 1.9.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Mathematical solutions in internal dose assessment: A comparison of Python-based differential equation solvers in biokinetic modeling

Abstract In biokinetic modeling systems employed for radiation protection, biological retention and excretion have been modeled as a series of discretized compartments representing the organs and tissues of the human body. Fractional retention and excretion in these organ and tissue systems have been mathematically governed by a series of coupled first-order ordinary differential equations (ODEs). The coupled ODE systems comprising the biokinetic models are usually stiff due to the severe difference between rapid and slow transfers between compartments. In this study, the capabilities of solving a complex coupled system of ODEs for biokinetic modeling were evaluated by comparing different Python programming language solvers and solving methods with the motivation of establishing a framework that enables multi-level analysis. The stability of the solvers was analyzed to select the best performers for solving the biokinetic problems. A Python-based linear algebraic method was also explored to examine how the numerical methods deviated from an analytical or semi-analytical method. Results demonstrated that customized implicit methods resulted in an enhanced stable solution for the inhaled 60 Co (Type M) and 131 I (Type F) exposure scenarios for the inhalation pathway of the International Commission on Radiological Protection (ICRP) Publication 130 Human Respiratory Tract Model (HRTM). The customized implementation of the Python-based implicit solvers resulted in approximately consistent solutions with the Python-based matrix exponential method ( expm ). The differences generally observed between the implicit solvers and expm are attributable to numerical precision and the order of numerical approximation of the numerical solvers. This study provides the first analysis of a list of Python ODE solvers and methods by comparing their usage for solving biokinetic models using the ICRP Publication 130 HRTM and provides a framework for the selection of the most appropriate ODE solvers and methods in Python language to implement for modeling the distribution of internal radioactivity.

61 RADIATION PROTECTION AND DOSIMETRY↗

NASA NTRS1998

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Source record↗

NASA NTRS1990

Linear iterative solvers for implicit ODE methods

The numerical solution of stiff initial value problems, which lead to the problem of solving large systems of mildly nonlinear equations are considered. For many problems derived from engineering and science, a solution is possible only with methods derived from iterative linear equation solvers. A common approach to solving the nonlinear equations is to employ an approximate solution obtained from an explicit method. The error is examined to determine how it is distributed among the stiff and non-stiff components, which bears on the choice of an iterative method. The conclusion is that error is (roughly) uniformly distributed, a fact that suggests the Chebyshev method (and the accompanying Manteuffel adaptive parameter algorithm). This method is described, also commenting on Richardson's method and its advantages for large problems. Richardson's method and the Chebyshev method with the Mantueffel algorithm are applied to the solution of the nonlinear equations by Newton's method.

Saylor, Paul E.↗

DOE OSTI2020

Exact and locally implicit source term solvers for multifluid-Maxwell systems

Recently, a family of models that couple multifluid systems to the full Maxwell equations have been used in laboratory, space, and astrophysical plasma modeling. These models are more complete descriptions of the plasma than reduced models like magnetohydrodynamic (MHD) since they are derived more closely from the full kinetic Vlasov-Maxwell system, without assumptions like quasi-neutrality, negligible electron mass, etc. Thus these models naturally retain non-ideal MHD effects like electron inertia, Hall term, pressure anisotropy/nongyrotropy, displacement current, among others. One obstacle to broader application of these model is that an explicit treatment of their source terms leads to the need to resolve rapid processes like plasma oscillation and electron cyclotron motion, even when these are not important. In this paper, we suggest two ways to address this issue. First, we derive the analytic solutions to the source update equations, which can be implemented as a practical, but less generic solver. We then develop a time-centered, locally implicit algorithm to update the source terms, allowing stepping over the fast kinetic time-scales. For a plasma with S species, the locally implicit algorithm involves inverting a local (3 S + 3) × (3 S + 3) matrix only, thus is very efficient. The performance can be further increased by using the direct update formulas to skip null calculations. In this paper, we present benchmarks illustrating the exact energy-conservation of the locally implicit solver, as well as its efficiency and robustness for both small-scale, idealized problems and largescale, complex systems. The locally implicit algorithm can be also easily extended to include other local sources, like collisions and ionization, which are difficult to solve analytically.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Domain Aware Deep-learning Algorithms Integrated with Scientific-computing Technologies (DADAIST)

This technical report summarized the contribution of the DADAIST project funded by the Data Model Convergence Initiative via the Laboratory Directed Research and Development (LDRD) investments at Pacific Northwest National Laboratory (PNNL). Specifically, we report the development of the NeuroMANCER (Neural Modules with Adaptive Nonlinear Constraints and Efficient Regularizations), a new open-source Scientific Machine Learning library for formulating and solving parametric constrained optimization problems, physics-informed system identification, and parametric optimal control problems. NeuroMANCER is using differentiable programming to combine modern data-driven models and optimization modeling language into a coherent algorithmic and software framework. NeuroMANCER is a Pytorch-based framework and adopts much of its philosophy focused on research and development, rapid prototyping, and streamlined deployment. Strong emphasis is given to extensibility, interoperability with the PyTorch ecosystem, and quick adaptability to custom domain problems. Neuromancer repository contains a comprehensive library of differentiable modules, including custom activation functions, matrix factorizations, deep learning architectures, neural differential equations, differential equation solvers, implicit layers such as iterative solvers, high-level API for symbolic expressions, API for modeling and control of dynamical systems, and extensive set of tutorial code examples in the form of python scripts and jupyter notebooks.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

An implicit barotropic mode solver for MPAS-ocean using a modern Fortran solver interface

Here, we demonstrate use of a modern Fortran solver interface to manage solver algorithms for an implicit barotropic mode solver in the Model for Predictions Across Scales-Ocean (MPAS-O). ForTrilinos, a Fortran interface to Trilinos that contains a large collection of solver capabilities written in C++, has been implemented in MPAS-O to provide access to a suite of linear solver options. By virtue of the simplified wrapper and interface generator (SWIG) automation tool that generates modern Fortran interfaces to C++ code, we were able to implement the Fortran solver interface in MPAS-O using a familiar Fortran coding style while minimizing performance degradation. The ForTrilinos solver interface is written within MPAS-O’s time stepping modules as a subroutine in conjunction with MPAS-O code. Applied to an idealized ocean and a high-resolution realistic ocean test case, parallel performance of ForTrilinos solvers is examined. It is found that parallel scalability of the ForTrilinos solvers is highly dependent on the number of global synchronization points per solver iteration in each iterative solver algorithm. ForTrilinos solvers perform best compared to the Fortran hand-crafted (FHC) solver when the amount of work per processor is large enough. However, parallel scalability is better with the FHC solver and so when the work per core is modest FHC outperforms ForTrilinos. The intercomparison between the ForTrilinos and FHC solvers reveals that this performance hit in the ForTrilinos solver mostly comes from the global synchronization process, while suggesting that the matrix-vector multiplication process in the FHC solver needs to be optimized for better performance.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Numerical Behaviour of a Smooth Local Correlation-based Transition Model in a Newton-Krylov Flow Solver

The numerical behaviour of transport-equation-based transition models, including both iterative and grid convergence, is influenced by the source terms. Transition models contain source terms that are large and highly nonlinear, and can be destabilizing in a strong implicit solver. Linearization strategies with varying levels of coupling are evaluated in conjunction with a source-term time step restriction to determine best-practices for solving the SA-sLM2015smooth local correlation-based transition model in an implicit Newton-Krylov flow solver. Achieving deep iterative convergence facilitates a detailed investigation of the grid convergence of these free-transition simulations, which are evaluated relative to fully-turbulent simulations performed using the Spalart-Allmaras turbulence model. Simulations of the NLF0416 general aviation airfoil, VA-2 supercritical airfoil, and NASA CRM-NLF wing-body geometry are performed over a range of grid levels. The results demonstrate that both a fully-coupled linearization strategy and a source-term time step restriction improve nonlinear convergence as the complexity of the free-transition simulations increases. In general, additional grid resolution is required for free-transition simulations relative to fully-turbulent simulations in order to achieve a similar level of accuracy, with the grid convergence of free-transition simulations sensitive to the streamwise grid spacings in the transition regions.

AATT↗

DOE OSTI2020

Implicit fast sweeping method for hyperbolic systems of conservation laws

Implicit time-accurate methods are often used to integrate stiff problems where explicit schemes impose severe time step restrictions. This paper presents an efficient numerical framework based on the Fast Sweeping Method (FSM) for solving linear and nonlinear hyperbolic systems of conservation laws. The solution at each discrete location is computed by sweeping the numerical domain in several predetermined directions that follow the causality of the characteristic families. The use of a fractional step strategy eliminates the need for a solution selection criterion while one-sided stencils limit the number of sweeps to at most 2 d for d space dimensions. This work focuses on the first-order implicit upwind method since it constitutes the building block for high-order conservative schemes. For problems where the degree of stiffness evolves over time, implicit-explicit hybridization can be accomplished with the same algorithm by simply switching the stencil at each time level. As opposed to traditional implicit solvers, the sweeping method does not require a local time linearization of the fluxes thereby preserving the nonlinear stability properties of the original implicit scheme. It also avoids the large computational and memory requirements associated with solving large block-diagonal systems of equations. Here, a series of one- and two-dimensional test cases are presented for the inviscid Burgers' equation and the reactive Euler equations. The results indicate that the implicit FSM can allow a major reduction in the number of time steps even in the presence of discontinuous solution profiles.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS1999

Implicit Space-Time Conservation Element and Solution Element Schemes

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Chang, Sin-Chung↗

DOE OSTI2025

A physics-constrained neural ordinary differential equations approach for robust learning of stiff chemical kinetics

The high computational cost associated with solving for detailed chemistry poses a significant challenge for predictive computational fluid dynamics (CFD) simulations of turbulent reacting flows. While deep learning techniques have been explored to develop faster surrogate models, they often fail to integrate reliably with CFD solvers. This instability arises because traditional deep learning approaches optimize for training error without ensuring compatibility with ordinary differential equation (ODE) solvers, resulting in accumulation of errors over time. Recently, neuralODE (NODE) based approaches have been shown to be a promising technique to emulate and accelerate detailed chemistry computations. Here, in the present work, we extend this NODE framework for stiff chemical kinetics by incorporating mass conservation constraints directly into the loss function during training. This ensures that the total mass as well as the individual elemental species masses are conserved in an a-posteriori manner. Proof-of-concept studies are performed with the novel physics-constrained NODE (PC-NODE) approach for homogeneous autoignition of hydrogen-air mixture over a range of composition and thermodynamic conditions. It is demonstrated that the PC-NODE framework not only improves the physical consistency of the resulting data-driven model with respect to mass conservation criteria, but also improves training efficiency. PC-NODE is shown to achieve 2–100× speedup relative to the hydrogen-air detailed chemical mechanism depending on the type of the ODE solver (implicit or explicit) used during autoregressive inference tests. Lastly, a-posteriori studies are performed wherein the trained PC-NODE model is coupled with a CFD solver. It is shown that higher accuracy is achieved with PC-NODE relative to the purely data-driven NODE approach. Moreover, PC-NODE also exhibits robustness and generalizability to unseen initial conditions from within (interpolative capability) as well as outside (extrapolative capability) the training regime.

computational combustion↗

DOE OSTI2023

An implicit, conservative and asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas in uniform magnetic fields

Here, we introduce a new electrostatic particle-in-cell algorithm capable of using large timesteps compared to particle gyro-period under a uniform external magnetic field. The algorithm extends earlier electrostatic fully implicit PIC implementations with a new asymptotic-preserving particle-push scheme that allows timesteps much larger than particle gyroperiods. In the large-timestep limit, the integrator preserves all particle drifts, while recovering the full orbit for small timesteps. The scheme allows for a seamless, efficient treatment of particles with coexisting magnetized and unmagnetized species, and conserves energy and charge exactly without spoiling implicit solver performance. We demonstrate by numerical experiment with several problems of variable species magnetization (diocotron instability, modified two-stream instability, and drift instability) that orders of magnitude wall-clock-time speedups vs. the standard fully implicit electrostatic PIC algorithm are possible without sacrificing solution accuracy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRSDate not supplied

Improved Benchmarking of Cohesive Elements in Abaqus Standard for Predicting Disbond and Delamination in Composite Structures

Traditional approaches for aircraft certification require the assumption of an initial flaw condition, either represented as barely visible impact damage (BVID) or through inclusion of a Teflon insert to serve as surrogate damage. Based on the initial composite damage state, the structure must be shown to demonstrate structural durability and damage tolerance (DaDT) according to the following criteria: a. Damage displays no detrimental growth under cyclic loading b. The structure is able to sustain design limit load (DLL) Currently, the only available manner for validating structural performance is through test. Since damage can occur over a wide variety of areas within a structure, this approach has proven to be increasingly expensive and time consuming for composite airframes and acreage structure within the design-test-certification building block. A further complicating factor is the requirement to accurately capture the most critical damage morphologies as a starting condition. To understand the severity of the damage, it is either required to experimentally determine the most critical areas at tremendous expense or rely on legacy data of similar structural testing, which limits design space expansion. A preferred solution is to use advanced analysis to provide improved understanding of load margins for critical locations based on a wide variety of potential starting damage conditions. The standard industry approach for DaDT certification adheres to the use of the traditional virtual crack closure technique (VCCT) method. VCCT is generally a preferred method because it conforms to the current certification principles of damage from a known flaw, and when used correctly, can be effective at predicting delamination propagation under static and cyclic loading. The VCCT method requires the inclusion of an initial flaw in the finite element (FE) model requiring a-priori knowledge of the flaw location. This in turn requires a plethora of analysis cases to be examined to cover a reasonable span of potential damage states. Additionally, the VCCT approach requires node-to-node connectivity rendering it incompatible with the best practices and approaches for using continuum damage mechanics (CDM) based progressive damage and failure analysis (PDFA) tools within a typical FE solver. Alternatives to VCCT have emerged in the form of cohesive elements which utilize the cohesive zone model (CZM). Unlike VCCT which models linear elastic fracture mechanics, cohesive elements couples continuum and fracture based responses through the use of bilinear traction separation laws. These laws are defined based on a penalty stiffness, a cohesive strength, and a strain energy release rate. The approach can be mesh regularized with native cohesive elements within many FE solvers such as Abaqus and LS-DYNA. In Phase I of the NASA Advanced Composites Consortium (ACC) post-buckled stiffened panel with BVID, Strength and Life [1], the performance of cohesive elements were benchmarked in comparison to VCCT and LEFM solutions and showed good agreement using Abaqus explicit [2]. To realize savings on current and future programs, it is still necessary to close technical gaps related to the use of cohesive elements with Abaqus Standard. Within a program environment, standard finite element analysis is the preferred analytical capability for quasi-static loading as it eliminates uncertainty due to oscillatory behavior commonly seen with explicit analysis. This oscillatory behavior creates difficulties in writing margins of safety based on the analysis. The use of negative tangent stiffness material models complicates convergence which typically requires the use of numerical controls such as viscous damping to overcome. To date, there has not been a comprehensive study on how to establish best practices for cohesive element convergence for predictive capability within the Abaqus implicit solver. In pursuit of these goals, under the NASA ACC program, several numerical benchmark problems were proposed including pure mode I (double cantilevered beam – DCB), pure mode II (end notch flexure – ENF), and symmetric/unsymmetric evolving mixed mode (single leg bend – SLB). This paper focuses on the use of cohesive elements to model the delamination through the use of CZM. Specifically, finite element models for the DCB, ENF, symmetric SLB, and unsymmetric SLB, are developed and various solution controls for convergence are studied to develop a best practice. Once the best practice has been developed, the predictive capability of the objective CZM model is used to analyze the hat pull-off strength of a standard hat stiffened configuration under various loading conditions.

Abaqus↗

DOE OSTI2026

Vacuum Neutral Transport Model in UEDGE for Tokamak Far Scrape‐Off Layer

A model for neutral transport in the far scrape-off layer (SOL) vacuum region (vacuum neutral model) has been developed and implemented in UEDGE. Free-streaming neutral trajectories between the outermost UEDGE boundary and the vessel wall are preprocessed using DEGAS2 to construct a tele-transport matrix that captures non-local neutral relocation through the vacuum. Here, this matrix is then used in UEDGE as a non-local boundary condition for the neutral equations, preserving the robustness and convergence of the implicit solver without introducing statistical noise. Simulations of a DIII-D lower single-null configuration show that the vacuum neutral model relocates neutrals from the divertor to the upstream region, increasing the outer midplane separatrix density required for detachment onset by about 30%. However, the characteristic target temperature at detachment (T e, osp ~ 3 - 4eV) and the radiation front behavior remain unchanged.

DEGAS2↗

DOE OSTI2021

Sierra/SolidMechanics 5.0 Goodyear Specific

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional finite element analysis code for solids and structures subjected to extensive contact and large deformations, encompassing explicit and implicit dynamic as well as quasistatic loading regimes. This document supplements the primary Sierra/SM 5.0 User’s Guide, describing capabilities specific to Goodyear analysis use cases, including additional implicit solver options, material models, finite element formulations, and contact settings.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Sierra/SolidMechanics 4.56 Goodyear User's Guide

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional finite element analysis code for solids and structures subjected to extensive contact and large deformations, encompassing explicit and implicit dynamic as well as quasistatic loading regimes. This document supplements the primary Sierra/SM 4.56 User’s Guide, describing capabilities specific to Goodyear analysis use cases, including additional implicit solver options, material models, finite element formulations, and contact settings.

42 ENGINEERING↗

DOE OSTI2025

Dusty Gas Model for Solid Oxide Fuel Cell Fuel Electrode

This model applies the Dusty Gas Model simulate multi-component species transport in SOFC (solid oxide fuel cell) anodes which considers the pressure gradient across the fuel electrode. This studyhas been verified with the analytical solution for different fuel electrode thicknesses and with literature values. The model was developed using the VoronoiFVM platform in Julia which is a built in implicit and semi implicit solver that integrates electrochemical behavior, microstructural effects, and transient analysis for accurate prediction of species transport under varying conditions.

dusty gas model (DGM)↗

DOE OSTI2026

Improving the Performance of NEML2 with Modern Graph Compilation Backends

NEML2 vectorizes constitutive-model evaluation for large-scale multiphysics simulation, using PyTorch as its tensor backend so that a batch of material-point updates runs on CPU or GPU through a single implementation. In the two prior reports in this series it was a C++-native library, deployed through TorchScript tracing and just-in-time (JIT) compilation; it has since been rewritten from the ground up into a Python-native library deployed through Ahead-of-Time Inductor (AOTInductor), a modern PyTorch graph-compilation backend. The rewrite is driven by a persistent tension, not a language preference: NEML2 composes constitutive models at runtime from a registry of small, independently-authored pieces, and that flexibility is difficult to reconcile with the compile-time knowledge an efficient GPU kernel needs. This report documents the rewrite and the investment that accompanied it: the AOTInductor export pipeline that turns a Python-authored model into a portable, Python-free compiled artifact loadable from pure C++; the eager and compiled runtimes and the new implicit solver layer built on them; a head-to-head benchmark of legacy JIT against AOTInductor; the physics-model catalog and its worked examples; the developer tooling; and the corresponding overhaul of MOOSE’s NEML2 integration that lets MOOSE consume it. A central objective is to examine whether modern PyTorch graph-compilation backends are effective for MOOSE GPU integration. The benchmark answers directly: AOTInductor outperforms legacy JIT on every GPU scenario measured, by 1.0–4.5×. Modern graph-compilation backends are effective for MOOSE GPU integration, and AOTInductor specifically – not compilation in the abstract – is why.

Hu, Gary (Tianchen) [Argonne National Laboratory (↗