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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
NASA NTRS1987

Multigrid solution of the Euler equations on unstructured and adaptive meshes

A multigrid algorithm has been developed for solving the steady-state Euler equations in two dimensions on unstructured triangular meshes. The method assumes the various coarse and fine grids of the multigrid sequence to be independent of one another, thus decoupling the grid generation procedure from the multigrid algorithm. The transfer of variables between the various meshes employs a tree-search algorithm which rapidly identifies regions of overlap between coarse and fine grid cells. Finer meshes are obtained either by regenerating new globally refined meshes, or by adaptively refining the previous coarser mesh. For both cases, the observed convergence rates are comparable to those obtained with structured multigrid Euler solvers. The adaptively generated meshes are shown to produce solutions of higher accuracy with fewer mesh points.

Mavriplis, Dimitri↗
NASA NTRS1992

Adaptive mesh strategies for the spectral element method

An adaptive spectral method was developed for the efficient solution of time dependent partial differential equations. Adaptive mesh strategies that include resolution refinement and coarsening by three different methods are illustrated on solutions to the 1-D viscous Burger equation and the 2-D Navier-Stokes equations for driven flow in a cavity. Sharp gradients, singularities, and regions of poor resolution are resolved optimally as they develop in time using error estimators which indicate the choice of refinement to be used. The adaptive formulation presents significant increases in efficiency, flexibility, and general capabilities for high order spectral methods.

Mavriplis, Catherine↗
NASA NTRS2018

Using Adaptive Mesh Refinement to Study Grid Resolution Effects for Shock-Boundary Layer Interactions

Adaptive Mesh Refinement (AMR) promises a much more computationally efficient means to obtain a discrete approximation to a continuous boundary value problem of a specified accuracy than classic isotropic grid refinement. The AMR capability of OVERFLOW (a computational fluid dynamics (CFD) code) is utilized to provide estimates of the exact analytical solutions to problems of interest to turbulence modeling. Predictions of surface pressure and skin friction, essentially the state of stress at the surface, shows little difference with grids believed to be "grid resolved." Velocity profiles, on the other hand, show marked differences in flows with shocks. The AMR method, as implemented in OVERFLOW 2.2k, appears to provide the ability to produce arbitrarily accurate solutions at a predictable cost much smaller than classic uniform mesh refinement.

Turbulence Modeling↗
NASA NTRS1999

Adaptive Mesh Refinement for Microelectronic Device Design

Finite element and finite volume methods are used in a variety of design simulations when it is necessary to compute fields throughout regions that contain varying materials or geometry. Convergence of the simulation can be assessed by uniformly increasing the mesh density until an observable quantity stabilizes. Depending on the electrical size of the problem, uniform refinement of the mesh may be computationally infeasible due to memory limitations. Similarly, depending on the geometric complexity of the object being modeled, uniform refinement can be inefficient since regions that do not need refinement add to the computational expense. In either case, convergence to the correct (measured) solution is not guaranteed. Adaptive mesh refinement methods attempt to selectively refine the region of the mesh that is estimated to contain proportionally higher solution errors. The refinement may be obtained by decreasing the element size (h-refinement), by increasing the order of the element (p-refinement) or by a combination of the two (h-p refinement). A successful adaptive strategy refines the mesh to produce an accurate solution measured against the correct fields without undue computational expense. This is accomplished by the use of a) reliable a posteriori error estimates, b) hierarchal elements, and c) automatic adaptive mesh generation. Adaptive methods are also useful when problems with multi-scale field variations are encountered. These occur in active electronic devices that have thin doped layers and also when mixed physics is used in the calculation. The mesh needs to be fine at and near the thin layer to capture rapid field or charge variations, but can coarsen away from these layers where field variations smoothen and charge densities are uniform. This poster will present an adaptive mesh refinement package that runs on parallel computers and is applied to specific microelectronic device simulations. Passive sensors that operate in the infrared portion of the spectrum as well as active device simulations that model charge transport and Maxwell's equations will be presented.

Cwik, Tom↗
NASA NTRS2001

Highly parallel structured adaptive mesh refinement using parallel language-based approaches

Adaptive mesh refinement (AMR) calculations carried out on structured meshes play an exceedingly important role in several areas of science and engineering. A strategy for using Fortran 90 in an object-oriented fashion is presented. This permits AMR applications to be expressed in terms of familiar abstractions that are natural to the process of solving AMR hierarchies. The OpenMP features that are useful for parallel processing of AMR hierarchies in a load balanced fashion on multiprocessors is described.

computational↗
NASA NTRS1992

Multigrid solution of internal flows using unstructured solution adaptive meshes

This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.

Smith, Wayne A.↗
NASA NTRS2014

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Schwing, Alan M.↗
NASA NTRS1990

Turbulent flow calculations using unstructured and adaptive meshes

A method of efficiently computing turbulent compressible flow over complex two dimensional configurations is presented. The method makes use of fully unstructured meshes throughout the entire flow-field, thus enabling the treatment of arbitrarily complex geometries and the use of adaptive meshing techniques throughout both viscous and inviscid regions of flow-field. Mesh generation is based on a locally mapped Delaunay technique in order to generate unstructured meshes with highly-stretched elements in the viscous regions. The flow equations are discretized using a finite element Navier-Stokes solver, and rapid convergence to steady-state is achieved using an unstructured multigrid algorithm. Turbulence modeling is performed using an inexpensive algebraic model, implemented for use on unstructured and adaptive meshes. Compressible turbulent flow solutions about multiple-element airfoil geometries are computed and compared with experimental data.

Mavriplis, Dimitri J.↗
DOE OSTI2023

Multi-Objective Adaptive Mesh Refinement Using Reinforcement Learning

Finite element methods approximate the solution to a partial differential equation (PDE) on a mesh consisting of many elements. In general, using more, smaller elements results in a lower error in the approximation. However, it is often possible to lower the error substantially by only refining, or decreasing the size of, the few elements in the mesh that have the highest error. Adaptive mesh refinement (AMR) is a process that selectively refines regions of a mesh with high error to achieve a desired accuracy in as few degrees of freedom (DOFs) as possible. AMR is favorable compared to uniform refinement, which refines all elements of the mesh equally, because it can often achieve the same accuracy without wasting extra computation time on refinement of elements that already have low error. However, it is difficult to know which elements to refine. In this report we explore ways to choose which elements to refine such that we minimize both the resulting error and the cumulative DOFs used in computation. In particular, we introduce a Pareto-front learning algorithm that trains a policy to give the optimal refinement actions to minimize the cumulative DOFs used to achieve a given target error. Such a policy is useful because it can be deployed on many different problem types where different accuracy levels are desired. Furthermore, training a single policy for a range of target errors allows us to use transfer learning to reduce the required training time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Comparison Study of Conventional and Adaptive Mesh Refinement in Organic Material Decomposition Models

This study compares conventional mesh refinement techniques, specifically Uniform Mesh Refinement (UMR), with a new Adaptive Mesh Refinement (AMR) method, applied to Organic Material Decomposition (OMD) models. The proposed benefit of AMR is that only areas that require refinement, based on minimizing a specific field gradient, are refined thus decreasing model wall time compared to conventional UMR methods. This work specifically focuses on comparing UMR and AMR methods on decomposing (both No-Flow and Porous-Flow material models) Polymeric Methylene Diisocyanate (PMDI) polyurethane foam. Throughout the work, the geometry increased in complexity to assess the refinement methods performance at varying levels geometric intricacy. While AMR has been shown to work well in a variety of applications, the UMR approach proved to be computationally faster, for many of the geometries and foam decomposition models, than AMR. However, it was observed that at higher levels of refinement, greater than 3 UMR, AMR begins to be computationally better. Additionally, the settings used to perform AMR greatly impact its performance, and lessons learned, in terms of OMD models, are shared. Due to physics involved in material decomposition, specifically the evolution of state variables, these problems don’t fully benefit from the advantages of AMR.

36 MATERIALS SCIENCE↗
NASA NTRSDate not supplied

Improvements to the LAURA Mesh Adaptation Algorithm

This paper describes recent improvements to the LAURA code that removes the requirementof unbroken body-normal lines when using the automated mesh adaptation algorithm inLAURA responsible for mesh alignment with shock and adjusting near-wall mesh spacing. Fornon-simple geometry, restricting block topologies such that blocks span the domain from thesurface wall boundaries to domain inflow boundary can be difficult or impossible. Removing thisrequirement enables novel block topologies that simplify the meshing workflow for LAURA users.The new adaptation algorithm implementation in LAURA is described and several examples ofthe adaptation are presented to demonstrate the efficacy of the adaptation algorithm.

LAURA↗
NASA NTRSDate not supplied

Improvements to the LAURA Mesh Adaptation Algorithm

This paper describes recent improvements to the LAURA code that removes the requirementof unbroken body-normal lines when using the automated mesh adaptation algorithm inLAURA responsible for mesh alignment with shock and adjusting near-wall mesh spacing. Fornon-simple geometry, restricting block topologies such that blocks span the domain from thesurface wall boundaries to domain inflow boundary can be difficult or impossible. Removing thisrequirement enables novel block topologies that simplify the meshing workflow for LAURA users.The new adaptation algorithm implementation in LAURA is described and several examples ofthe adaptation are presented to demonstrate the efficacy of the adaptation algorithm.

LAURA↗
NASA NTRS1983

Intrinsic adaptive mesh techniques

An alternating direction adaptive grid movement code was developed and a thesis adaptive angular meshes was directed. The alternating direction code was also established on the NASA Langley computer system and is available for use there. In essence, grid points are moved on an abstract surface above physical space by means of alternating coordinate directions. The abstract surface is formed with the salient solution properties if they can be extracted by a priori physical reasoning; or otherwise, in the absence of such reasoning, by the use of error estimates in some chosen norm. Upon formulation, all important driving properties for adaptive purposes are consolidated into one object - the abstract surface. At a basic level, a uniform distribution of surface points is equivalent to gradient resolution. This arises from a projection back down into physical space. At a higher level, a more accurate view of the abstract surface is obtained when changes in surface direction are also resolved. The appropriate measure for direction changes is normal curvature. It is defined as the rate of change of surface tangent planes as a surface coordinate curve is transversed in uniform increments of arc length.

Eiseman, P. R.↗
NASA NTRS2023

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator model from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than fifty percent reduction in resource usage required to achieve the same level of accuracy as uniform and user constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

CST↗
NASA NTRS2023

Anisotropic Mach Cone Aligned Mesh Adaptation for Low Boom Simulations

An automated off-body Mach cone aligned structured curvilinear grid generation procedure is presented for near-field computational fluid dynamics simulations. This procedure combines output-based indicators and mesh redistribution to perform anisotropic mesh adaptation while maintaining Mach cone alignment. Automation is achieved through a novel direction-based adaptation indicator formulation. The adaptation procedure is demonstrated on the JAXA Wing Body geometry and X-59 C608 demonstrator model from the Second and Third AIAA Sonic Boom Prediction Workshops, respectively. It is demonstrated that anisotropic mesh adaptation may result in a greater than fifty percent reduction in resource usage required to achieve the same level of accuracy as uniform and user constructed Mach cone aligned grids for near-field pressure signatures, ground-level overpressure signatures, and loudness metrics.

CST↗
DOE OSTI2024

Learning Robust Marking Policies for Adaptive Mesh Refinement

Here in this work, we revisit the marking decisions made in the standard adaptive finite element method (AFEM). Experience shows that a naïve marking policy leads to inefficient use of computational resources for adaptive mesh refinement (AMR). Consequently, using AMR in practice often involves ad-hoc or time-consuming offline parameter tuning to set appropriate parameters for the marking subroutine. To address these practical concerns, we recast AMR as a Markov decision process in which refinement parameters can be selected on-the-fly at run time, without the need for pre-tuning by expert users. In this new paradigm, the refinement parameters are also chosen adaptively via a marking policy that can be optimized using methods from reinforcement learning. We use the Poisson equation to demonstrate our techniques on h- and hp-refinement benchmark problems, and our experiments suggest that superior marking policies remain undiscovered for many classical AFEM applications. Furthermore, an unexpected observation from this work is that marking policies trained on one family of PDEs are sometimes robust enough to perform well on problems far outside the training family. For illustration, we show that a simple hp-refinement policy trained on 2D domains with only a single re-entrant corner can be deployed on far more complicated 2D domains, and even 3D domains, without significant performance loss. For reproduction and broader adoption, we accompany this work with an open-source implementation of our methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1993

Dynamic mesh adaption for triangular and tetrahedral grids

The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.

Rupak Biswas↗