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NASA NTRS1996

The Effects of Dissipation and Coarse Grid Resolution for Multigrid in Flow Problems

The objective of this paper is to investigate the effects of the numerical dissipation and the resolution of the solution on coarser grids for multigrid with the Euler equation approximations. The convergence is accomplished by multi-stage explicit time-stepping to steady state accelerated by FAS multigrid. A theoretical investigation is carried out for linear hyperbolic equations in one and two dimensions. The spectra reveals that for stability and hence robustness of spatial discretizations with a small amount of numerical dissipation the grid transfer operators have to be accurate enough and the smoother of low temporal accuracy. Numerical results give grid independent convergence in one dimension. For two-dimensional problems with a small amount of numerical dissipation, however, only a few grid levels contribute to an increased speed of convergence. This is explained by the small numerical dissipation leading to dispersion. Increasing the mesh density and hence making the problem over resolved increases the number of mesh levels contributing to an increased speed of convergence. If the steady state equations are elliptic, all grid levels contribute to the convergence regardless of the mesh density.

Eliasson, Peter↗

NASA NTRS1985

Stability of interfaces with mesh refinement

A study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite-difference approximations. First, a root condition which implies stability for the initial-boundary value problem for this type of interface is derived. From the root condition, the stability of several interface equations is proved, using the maximum principle. In some cases, the final verification steps can be done analytically; in other cases, a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle. Using this method, stability for Lax-Wendroff with all the interface conditions considered, and for Leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved.

Berger, M. J.↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

Venkatakrishnan, V.↗

NASA NTRS2000

A Contaminant Ice Visualization Experiment in a Glass Pulse Tube

Results are presented from pulse tube experiments designed to investigate the effect of 400 parts per million water vapor contamination of the helium working gas. The experiments were conducted in a glass pulse tube to enable visualization of ice formation on internal surfaces. Photographs of this ice formation were taken along with simultaneous coldtip temperature and compressor power measurements. Four types of regenerator elements were tested in various combinations: 200- and 400-mesh stainless steel screens, 1.6 mm diameter glass beads, and 1.6 mm thick perforated plastic plates. Internal spacers were also used to provide clear fields of view into the regenerator stack. Substantial water-ice formation was observed at the cold end of the regenerator and on the inside wall of pulse tube; it appeared to be highly porous, like snow, and was seen to accumulate only in a very localized region at the coldest end, despite changing the cold tip temperature across a range of 150 to 235 K. Ice formation degraded pulse tube thermal performance only in cases where screen regenerators were used at the regenerator cold end. It was concluded that flow blockage was the mechanism by which contaminants affected performance; coarse regenerator elements were largely immune over the tested time scale of a few days. Substantially reduced ice formation and minimal performance loss were also observed in repeated tests where the contaminated gas was reused after warming up and melting of the accumulated internal ice. Significant adsorption of the liquid water onto the regenerator was inferred, a process that depleted the gas phase concentration of water.

Hall, J. L.↗

DOE OSTI2022

Large-Eddy Simulation of a wind turbine using a Filtered Actuator Line Model

When dealing with multirotor devices such as quadcopters or wind farms, the cost of blade-resolved large-eddy simulation (LES) becomes prohibitive. Combining LES with a family of lower-fidelity models, called actuator line models (ALMs), has grown in popularity in the past decade. ALM replaces full blade resolution with an array of actuator points or lines parameterized by aerodynamic lift/drag polar plots along the blades. Body forces computed based on these actuator points are then projected onto the LES flow mesh, mimicking the effect of rotating blades on the flow. However, the optimal projection radius and the associated LES grid size is often too restrictive for multirotor simulations. Recently, a new tip-correction-based filtered ALM (F-ALM) was proposed by Martinez-Tossas and Meneveau (2019), which allows coarser-than-optimal grids by avoiding the associated overprediction of thrust. In this work, F-ALM is implemented into a high-order, in-house LES code to simulate National Renewable Energy Laboratory Phase VI wind turbine. It is then followed by a comparison between the baseline ALM and the newly implemented F-ALM in terms of instantaneous and time-averaged flow fields and blade loads, revealing the advantages of F-ALM in preventing the overprediction of power on coarse grids. Finally, this encourages accurate and affordable simulations of multirotor devices in the future.

17 WIND ENERGY↗

DOE OSTI2025

Enhanced Interfacial Bonding of Graft Copolymers

To understand how thermoplastic welding strength can be tuned through chemical modifications and macromolecular topology, we combined coarse-grained molecular dynamics (MD) simulations with experimental validation. Our simulations examined the diffusion dynamics of both linear and graft polymers across representative interfaces, revealing that diffusion-controlled interdigitation follows a power law, with the exponent decreasing from 0.34 to 0.11 as grafting density increases from 7.5 to 196% (with side chains grafted to both sides of a monomer unit). The addition of side chains enhances welding efficiency, as dense bottlebrush polymers with high grafting density reach maximum rupture strength faster than linear polymers. However, their saturated rupture strength is lower. This observation is subsequently corroborated by experimental lap-shear tests comparing linear polyethylene with octene grafted polyethylene elastomers. Our MD simulations show that unlike linear polymers, where backbone entanglements dominate, the grafted side chains introduce mechanisms in addition to entanglement dilution. The rapid interdigitation of side chains creates a dense mesh of entropic van der Waals contacts, which can also enhance the film welding. Furthermore, our MD simulations reveal a brittle rupture behavior in linear and comb-like (mildly grafted) polymers, while bottlebrush (densely grafted) polymers display elastomeric behavior with a pronounced stress plateau prior to fracture. Our simulations deconvolute the influence of polymer topology on deformation behavior. The rate of polymer deformation becomes lower than the applied strain rate prior to rupture, and the onset of this deviation is progressively delayed from linear to bottlebrush polymers. This trend highlights the critical role of molecular architecture in governing the mechanical response. In conclusion, these results provide deeper insight into the underlying welding mechanisms of topological polymers and present a potential approach for mitigating the interface anisotropy that is inherent in advanced manufacturing techniques such as fused filament fabrication.

graft copolymers↗

DOE OSTI2021

Stratigraphic Identification with Airborne Electromagnetic Methods at the Hanford Site, Washington

Stratigraphic units can influence the fate and transport of subsurface contaminants within groundwater. Units having coarse-grained sediments act as preferential flow pathways, and therefore can accelerate the transport of contaminants to reach human and ecological receptors. At legacy waste sites, detailed knowledge of subsurface stratigraphy can be used for effective monitoring and remediation planning to help minimize risk to human health and the environment. Airborne electromagnetic (AEM) methods can non-invasively provide information on kilometer-scale or larger subsurface stratigraphic features and fill informational gaps in directly sampled data from sparsely located boreholes. In this paper, we present inversion results of a 412 line-km frequency-domain AEM survey to delineate subsurface stratigraphic features at the Hanford Site, located in southeastern Washington State. The inversion was performed using a massively parallel 3D electromagnetic modeling and inversion code, where the modeling is based on solving frequency-domain Maxwell’s equations using an unstructured-mesh finite-element method and the inversion employs a Gauss-Newton optimization scheme. The results are compared to an underlying geologic framework model (GFM), built by interpolating contact depths of stratigraphic units interpreted from site borehole datasets. In areas with good borehole coverage, the inversion results show a good match with the GFM to a depth of about 60 m. Outside of these areas, the inversion results exhibit inconsistencies from the assumptions made to create the GFM, demonstrating that the AEM survey results can be used to improve the understanding of the geological conceptual model.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Technical descriptions of the experimental dynamical downscaling simulations over North America by the CAM–MPAS variable-resolution model

Abstract. Comprehensive assessment of climate datasets is important for communicating model projections and associated uncertainties to stakeholders. Uncertainties can arise not only from assumptions and biases within the model but also from external factors such as computational constraint and data processing. To understand sources of uncertainties in global variable-resolution (VR) dynamical downscaling, we produced a regional climate dataset using the Model for Prediction Across Scales (MPAS; dynamical core version 4.0) coupled to the Community Atmosphere Model (CAM; version 5.4), which we refer to as CAM–MPAS hereafter. This document provides technical details of the model configuration, simulations, computational requirements, post-processing, and data archive of the experimental CAM–MPAS downscaling data. The CAM–MPAS model is configured with VR meshes featuring higher resolutions over North America as well as quasi-uniform-resolution meshes across the globe. The dataset includes multiple uniform- (240 and 120 km) and variable-resolution (50–200, 25–100, and 12–46 km) simulations for both the present-day (1990–2010) and future (2080–2100) periods, closely following the protocol of the North American Coordinated Regional Climate Downscaling Experiment. A deviation from the protocol is the pseudo-warming experiment for the future period, using the ocean boundary conditions produced by adding the sea surface temperature and sea-ice changes from the low-resolution version of the Max Planck Institute Earth System Model (MPI-ESM-LR) in the Coupled Model Intercomparison Project Phase 5 to the present-day ocean state from a reanalysis product. Some unique aspects of global VR models are evaluated to provide background knowledge to data users and to explore good practices for modelers who use VR models for regional downscaling. In the coarse-resolution domain, strong resolution sensitivity of the hydrological cycles exists over the tropics but does not appear to affect the midlatitude circulations in the Northern Hemisphere, including the downscaling target of North America. The pseudo-warming experiment leads to similar responses of large-scale circulations to the imposed radiative and boundary forcings in the CAM–MPAS and MPI-ESM-LR models, but their climatological states in the historical period differ over various regions, including North America. Such differences are carried to the future period, suggesting the importance of the base state climatology. Within the refined domain, precipitation statistics improve with higher resolutions, and such statistical inference is verified to be negligibly influenced by horizontal remapping during post-processing. Limited (≈50 % slower) throughput of the current code is found on a recent many-core/wide-vector high-performance computing system, which limits the lengths of the 12–46 km simulations and indirectly affects sampling uncertainty. Our experience shows that global and technical aspects of the VR downscaling framework require further investigations to reduce uncertainties for regional climate projection.

58 GEOSCIENCES↗

DOE OSTI2022

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. In this study, two-level generalized Dryja--Smith--Widlund (GDSW)--type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the message passing interface (MPI)--parallel implementation of multilevel Schwarz preconditioners provided by the package FROSch (fast and robust Schwarz) from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To the best of our knowledge, this is the first time two-level Schwarz preconditioners have been applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The preconditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the subdomains. Additionally, several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as nonuniform meshes for the Greenland ice sheet. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32,K processor cores (8,K MPI ranks and 4 OpenMP threads) and 566,M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4,K processor cores (and MPI ranks) and 68,M degrees of freedom for the coupled problem.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

FROSch Preconditioners for Land Ice Simulations of Greenland and Antarctica

Numerical simulations of Greenland and Antarctic ice sheets involve the solution of large-scale highly nonlinear systems of equations on complex shallow geometries. This work is concerned with the construction of Schwarz preconditioners for the solution of the associated tangent problems, which are challenging for solvers mainly because of the strong anisotropy of the meshes and wildly changing boundary conditions that can lead to poorly constrained problems on large portions of the domain. Here, two-level GDSW (Generalized Dryja–Smith–Widlund) type Schwarz preconditioners are applied to different land ice problems, i.e., a velocity problem, a temperature problem, as well as the coupling of the former two problems. We employ the MPI-parallel implementation of multi-level Schwarz preconditioners provided by the package FROSch (Fast and Robust Schwarz)from the Trilinos library. The strength of the proposed preconditioner is that it yields out-of-the-box scalable and robust preconditioners for the single physics problems. To our knowledge, this is the first time two-level Schwarz preconditioners are applied to the ice sheet problem and a scalable preconditioner has been used for the coupled problem. The pre-conditioner for the coupled problem differs from previous monolithic GDSW preconditioners in the sense that decoupled extension operators are used to compute the values in the interior of the sub-domains. Several approaches for improving the performance, such as reuse strategies and shared memory OpenMP parallelization, are explored as well. In our numerical study we target both uniform meshes of varying resolution for the Antarctic ice sheet as well as non uniform meshes for the Greenland ice sheet are considered. We present several weak and strong scaling studies confirming the robustness of the approach and the parallel scalability of the FROSch implementation. Among the highlights of the numerical results are a weak scaling study for up to 32 K processor cores (8 K MPI-ranks and 4 OpenMP threads) and 566 M degrees of freedom for the velocity problem as well as a strong scaling study for up to 4 K processor cores (and MPI-ranks) and 68 M degrees of freedom for the coupled problem.

58 GEOSCIENCES↗

DOE OSTI2024

Multilevel well modeling in aggregation-based nonlinear multigrid for multiphase flow in porous media

A full approximation scheme (FAS) nonlinear multigrid solver for two-phase flow and transport problems driven by wells with multiple perforations is developed here. It is an extension to our previous work on FAS solvers for diffusion and transport problems. The solver is applicable to discrete problems defined on unstructured grids as the coarsening algorithm is aggregation-based and algebraic. To construct coarse basis that can better capture the radial flow near wells, coarse grids in which perforated well cells are not near the coarse-element interface are desired. This is achieved by an aggregation algorithm proposed in this paper that makes use of the location of well cells in the cell-connectivity graph. Numerical examples in which the FAS solver is compared against Newton's method on benchmark problems are given. In particular, for a refined version of the SAIGUP model, the FAS solver is at least 35% faster than Newton's method for time steps with a CFL number greater than 10.

58 GEOSCIENCES↗

DOE OSTI2021

Rapid prototyping of arbitrary 2D and 3D wireframe DNA origami

Wireframe DNA origami assemblies can now be programmed automatically from the top-down using simple wireframe target geometries, or meshes, in 2D and 3D, using either rigid, six-helix bundle (6HB) or more compliant, two-helix bundle (DX) edges. While these assemblies have numerous applications in nanoscale materials fabrication due to their nanoscale spatial addressability and high degree of customization, no easy-to-use graphical user interface software yet exists to deploy these algorithmic approaches within a single, standalone interface. Further, top-down sequence design of 3D DX-based objects previously enabled by DAEDALUS was limited to discrete edge lengths and uniform vertex angles, limiting the scope of objects that can be designed. Here, we introduce the open-source software package ATHENA with a graphical user interface that automatically renders single-stranded DNA scaffold routing and staple strand sequences for any target wireframe DNA origami using DX or 6HB edges, including irregular, asymmetric DX-based polyhedra with variable edge lengths and vertices demonstrated experimentally, which significantly expands the set of possible 3D DNA-based assemblies that can be designed. ATHENA also enables external editing of sequences using caDNAno, demonstrated using asymmetric nanoscale positioning of gold nanoparticles, as well as providing atomic-level models for molecular dynamics, coarse-grained dynamics with oxDNA, and other computational chemistry simulation approaches.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2021

Considering computational speed vs. accuracy: Choosing appropriate mesoscale RVE boundary conditions

Modeling a material’s microstructure using continuum theories allows for inspection of the relationship between coarse scale and fine scale behaviors. Computational limits generally require selection of a sub-volume from a bulk sample in order to directly model the microstructure. Boundary conditions are applied to the sub-volume to mimic the excluded bulk material. Appropriate selection of boundary conditions helps effectively determine the appropriate spatial scale required of the sub-volume. Applicable boundary conditions include direct displacement, periodic, and uniform traction. While direct displacement and periodic boundary conditions are commonly used, uniform traction boundary conditions have seen limited use due to rigid body stability issues in simulations of compression or shear deformation. A new application of uniform traction boundary conditions was developed through linear constraint equations, similar to approaches employed by direct displacement and periodic boundary conditions, to quench rigid body motions with minimal interference of the relative deformation of the model. These boundary conditions were tested by compressing several synthetically generated periodic microstructures using the finite element method. Evaluating the effective stiffness along the compression axis, the direct displacement boundary condition produced the stiffest response, whereas the uniform traction boundary condition produced the most compliant. Periodic boundary conditions produced the same response for all volumes analyzed and both the direct displacement and uniform traction boundary conditions trended toward the periodic response as the domain volume increased. Computational performance was also evaluated for each boundary condition using implicit and explicit solvers. Direct displacement boundary conditions presented the lowest computational cost of all of the boundary conditions followed by periodic then uniform traction. The computational expense of periodic and uniform traction boundary conditions limited the viable spatial scale and mesh resolutions able to be simulated. Selection of appropriate boundary conditions for specific uses need to be a balance between allowable computational expense and accuracy of the method. Techniques for evaluating which boundary conditions to use are discussed.

42 ENGINEERING↗