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At least 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Implementation of a Mesh refinement algorithm into the quasi-static PIC code QuickPIC

Plasma-based acceleration (PBA) has emerged as a promising candidate for the accelerator technology used to build a future linear collider and/or an advanced light source. In PBA, a trailing or witness particle beam is accelerated in the plasma wave wakefield (WF) created by a laser or particle beam driver. The WF is often nonlinear and involves the crossing of plasma particle trajectories in real space and thus particle-in-cell methods are used. The distance over which the drive beam evolves is several orders of magnitude larger than the wake wavelength. This large disparity in length scales is amenable to the quasi-static approach. Three-dimensional (3D), quasi-static (QS), particle-in-cell (PIC) codes, e.g., QuickPIC, have been shown to provide high fidelity simulation capability with 2-4 orders of magnitude speedup over 3D fully explicit PIC codes. In PBA, the witness beam needs to be matched to the focusing forces of the WF to reduce the emittance growth. In some linear collider designs, the matched spot size of the witness beam can be 2 to 3 orders of magnitude smaller than the spot size (and wavelength) of the wakefield. Such an additional disparity in length scales is ideal for mesh refinement where the WF within the witness beam is described on a finer mesh than the rest of the WF. A mesh refinement scheme is described that has been implemented into the 3D QS PIC code, QuickPIC. Very fine (high) resolution is used in a small spatial region that includes the witness beam and progressively coarser resolutions in the rest of the simulation domain. A fast multigrid Poisson solver has been implemented for the field solve on the refined meshes and a Fast Fourier Transform (FFT) based Poisson solver is used for the coarse mesh. The code has been parallelized with both MPI and OpenMP, and the parallel scalability has also been improved by using pipelining. A preliminary adaptive mesh refinement technique is described to optimize the computational time for simulations with an evolving witness beam size. Several test problems are used to verify that the mesh refinement algorithm provides accurate results. Additionally, the results are benchmarked against highly resolved simulations exhibiting near-azimuthal symmetry, performed using QPAD—a novel hybrid QS PIC code that uses a PIC description in the coordinates (r, ct – z) and a gridless description in the azimuthal angle, Φ.

Linear collider↗
DOE OSTI2022

Volumetric Rendering on Wavelet-Based Adaptive Grid

Numerical modeling of physical phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last two decades, the advancements in wavelet-based numerical methodologies to solve partial differential equations, combined with the unique properties of wavelet analysis to resolve localized structures of the solution on dynamically adaptive computational meshes, make it feasible to perform large-scale numerical simulations of a variety of physical systems on a dynamically adaptive computational mesh that changes both in space and time. Volumetric visualization of the solution is an essential part of scientific computing, yet the existing volumetric visualization techniques do not take full advantage of multi-resolution wavelet analysis and are not fully tailored for visualization of a compressed solution on the wavelet-based adaptive computational mesh. Our objective is to explore the alternatives for the visualization of time-dependent data on space-time varying adaptive mesh using volume rendering while capitalizing on the available sparse data representation. Two alternative formulations are explored. The first one is based on volumetric ray casting of multi-scale datasets in wavelet space. Rather than working with the wavelets at the finest possible resolution, a partial inverse wavelet transform is performed as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a solution in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these coarse scaling functions. Additional details are added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet coefficient magnitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. The second approach is based on complementing of wavelet-based adaptive mesh to the traditional Adaptive Mesh Refinement (AMR) mesh. Both algorithms are illustrated and compared to the existing volume visualization software for Rayleigh-Benard thermal convection and electron density data sets in terms of rendering time and visual quality for different data compression of both wavelet-based and AMR adaptive meshes.

Vezolainen, Alexei V.↗
NASA NTRS1992

r-adaptive methods based on element-level error indicators for parallel analysis of plates and shells

The formulation and application of element-level error indicators based on parametrized variational principles are investigated. These indicators are ideally suited to drive adaptive mesh refinment on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such estimators are not affected by physical jumps at wavefronts or interfaces. An estimator derived from the higher-order element energy is applied to r adaptation of meshes in plates and shell structures where the exact solution is known.

Militello, Carmelo↗
NASA NTRS2010

Exploring Discretization Error in Simulation-Based Aerodynamic Databases

This work examines the level of discretization error in simulation-based aerodynamic databases and introduces strategies for error control. Simulations are performed using a parallel, multi-level Euler solver on embedded-boundary Cartesian meshes. Discretization errors in user-selected outputs are estimated using the method of adjoint-weighted residuals and we use adaptive mesh refinement to reduce these errors to specified tolerances. Using this framework, we examine the behavior of discretization error throughout a token database computed for a NACA 0012 airfoil consisting of 120 cases. We compare the cost and accuracy of two approaches for aerodynamic database generation. In the first approach, mesh adaptation is used to compute all cases in the database to a prescribed level of accuracy. The second approach conducts all simulations using the same computational mesh without adaptation. We quantitatively assess the error landscape and computational costs in both databases. This investigation highlights sensitivities of the database under a variety of conditions. The presence of transonic shocks or the stiffness in the governing equations near the incompressible limit are shown to dramatically increase discretization error requiring additional mesh resolution to control. Results show that such pathologies lead to error levels that vary by over factor of 40 when using a fixed mesh throughout the database. Alternatively, controlling this sensitivity through mesh adaptation leads to mesh sizes which span two orders of magnitude. We propose strategies to minimize simulation cost in sensitive regions and discuss the role of error-estimation in database quality.

Aftosmis, Michael J.↗
NASA NTRS1993

Implementation of a mesh adaptive scheme based on an element-level error indicator

We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.

Keating, Scott↗
NASA NTRS1995

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field.

South, Jerry C., Jr.↗
NASA NTRS2004

Toward Effective Shell Modeling of Wrinkled Thin-Film Membranes Exhibiting Stress Concentrations

Geometrically nonlinear shell finite element analysis has recently been applied to solar-sail membrane problems in order to model the out-of-plane deformations due to structural wrinkling. Whereas certain problems lend themselves to achieving converged nonlinear solutions that compare favorably with experimental observations, solutions to tensioned membranes exhibiting high stress concentrations have been difficult to obtain even with the best nonlinear finite element codes and advanced shell element technology. In this paper, two numerical studies are presented that pave the way to improving the modeling of this class of nonlinear problems. The studies address the issues of mesh refinement and stress-concentration alleviation, and the effects of these modeling strategies on the ability to attain converged nonlinear deformations due to wrinkling. The numerical studies demonstrate that excessive mesh refinement in the regions of stress concentration may be disadvantageous to achieving wrinkled equilibrium states, causing the nonlinear solution to lock in the membrane response mode, while totally discarding the very low-energy bending response that is necessary to cause wrinkling deformation patterns. An element-level, strain-energy density criterion is suggested for facilitating automated, adaptive mesh refinements specifically aimed at the modeling of thin-film membranes undergoing wrinkling deformations.

Tessler, Alexander↗
DOE OSTI2025

Three-dimensional modeling of hyphal fusion, branching, and nutrient transport in filamentous fungi

Fungi exhibit behaviors distinct from other microbes. Filamentous fungi grow by extending complex networks of branched filaments collectively referred to as the mycelium. These networks can expand over large distances and traverse low-nutrient areas by translocating nutrients through the filament network. This spatial characteristic makes filamentous fungi crucial for soil ecosystems, supporting stable microbial communities and promoting plant growth. However, simulating these behaviors is complex. The elongated nature of fungal compartments results in different mechanical interactions compared to the commonly modeled spherical bacteria. These detailed hyphal mechanics require specialized consideration and are often excluded from conventional fungal simulation packages. Additionally, the extensive fungal networks in nature demand computationally intensive simulations, necessitating high-performance algorithms. Therefore, realistic fungi simulations require specialized software. Here, we introduce a fungal modeling expansion to the high-performance biological modelling and interface exchange (bmx) software suite. bmx leverages adaptive mesh refinement in AMReX for chemical diffusion and incorporates a full mechanical model for bacterial cells, accelerated by GPUs. By extending bmx to model filamentous particles, we demonstrate the formation of complex filament networks through interactions like hyphal branching and fusion (anastomosis). We show that the networks produced match real-world fungal structures through various metrics. This work supports computational studies of fungal growth dynamics and can be adapted to investigate the growth of other filamentous structures in biology or materials science. The expanded-BMX package is open-sourced and is available online.

Cell mechanics↗
DOE OSTI2022

Conservative and Accurate Solution Transfer Between High-Order and Low-Order Refined Finite Element Spaces

Here, in this paper, we introduce general transfer operators between high-order and low-order refined finite element spaces that can be used to couple high-order and low-order simulations. Under natural restrictions on the low-order refined space we prove that both the high-to-low-order and low-to-high-order linear mappings are conservative, constant preserving, and high-order accurate. While the proof holds for affine geometries, numerical experiments indicate that the results hold for more general curved meshes. We present several numerical results confirming our analysis and demonstrate the utility of the new mappings in the context of adaptive mesh refinement and conservative multidiscretization coupling.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2001

Multiresolution Wavelet Based Adaptive Numerical Dissipation Control for Shock-Turbulence Computations

The recently developed essentially fourth-order or higher low dissipative shock-capturing scheme of Yee, Sandham and Djomehri (1999) aimed at minimizing nu- merical dissipations for high speed compressible viscous flows containing shocks, shears and turbulence. To detect non smooth behavior and control the amount of numerical dissipation to be added, Yee et al. employed an artificial compression method (ACM) of Harten (1978) but utilize it in an entirely different context than Harten originally intended. The ACM sensor consists of two tuning parameters and is highly physical problem dependent. To minimize the tuning of parameters and physical problem dependence, new sensors with improved detection properties are proposed. The new sensors are derived from utilizing appropriate non-orthogonal wavelet basis functions and they can be used to completely switch to the extra numerical dissipation outside shock layers. The non-dissipative spatial base scheme of arbitrarily high order of accuracy can be maintained without compromising its stability at all parts of the domain where the solution is smooth. Two types of redundant non-orthogonal wavelet basis functions are considered. One is the B-spline wavelet (Mallat & Zhong 1992) used by Gerritsen and Olsson (1996) in an adaptive mesh refinement method, to determine regions where re nement should be done. The other is the modification of the multiresolution method of Harten (1995) by converting it to a new, redundant, non-orthogonal wavelet. The wavelet sensor is then obtained by computing the estimated Lipschitz exponent of a chosen physical quantity (or vector) to be sensed on a chosen wavelet basis function. Both wavelet sensors can be viewed as dual purpose adaptive methods leading to dynamic numerical dissipation control and improved grid adaptation indicators. Consequently, they are useful not only for shock-turbulence computations but also for computational aeroacoustics and numerical combustion. In addition, these sensors are scheme independent and can be stand alone options for numerical algorithm other than the Yee et al. scheme.

Sjoegreen, B.↗
NASA NTRSDate not supplied

Multiscale Mesh Adaptation for Transonic Aeroelastic Flutter Problems

This work applies multiscale mesh adaptation with refine to reduce spatial discretization error of aeroelastic computational fluid dynamics (CFD) simulations. Benchmark flutter models, such as the pitch and plunge NACA64A-010 airfoil and the benchmark supercritical wing, are studied with both a linearized frequency-domain solver and time-marching CFD coupled to a modal structural solver in FUN3D. The undeformed NASA Common Research Model (CRM), an aeroelastic jig shape variant of the CRM, is also studied with the linearized frequency-domain approach. For these cases, the adaptation process converges to comparable flutter predictions to hand-generated meshes but with smaller node counts. However the additional disciplines of the linearized frequency-domain analysis, the mesh deformation, and the unsteady finite-volume solver create robustness challenges that need to be addressed before it can be applied as a fully automated process for complex transonic aeroelastic problems. In particular, negative volumes are observed to be an issue for FUN3D’s linear elasticity mesh deformation solver when moving the adapted meshes.

Aeroelasticity↗
NASA NTRS1999

Innovative Language-Based & Object-Oriented Structured AMR Using Fortran 90 and OpenMP

Parallel adaptive mesh refinement (AMR) is an important numerical technique that leads to the efficient solution of many physical and engineering problems. In this paper, we describe how AMR programing can be performed in an object-oreinted way using the modern aspects of Fortran 90 combined with the parallelization features of OpenMP.

software↗
NASA NTRS2011

Overview of the Helios Version 2.0 Computational Platform for Rotorcraft Simulations

This article summarizes the capabilities and development of the Helios version 2.0, or Shasta, software for rotary wing simulations. Specific capabilities enabled by Shasta include off-body adaptive mesh refinement and the ability to handle multiple interacting rotorcraft components such as the fuselage, rotors, flaps and stores. In addition, a new run-mode to handle maneuvering flight has been added. Fundamental changes of the Helios interfaces have been introduced to streamline the integration of these capabilities. Various modifications have also been carried out in the underlying modules for near-body solution, off-body solution, domain connectivity, rotor fluid structure interface and comprehensive analysis to accommodate these interfaces and to enhance operational robustness and efficiency. Results are presented to demonstrate the mesh adaptation features of the software for the NACA0015 wing, TRAM rotor in hover and the UH-60A in forward flight.

Sankaran, Venkateswaran↗
NASA NTRS1998

Case-Based Capture and Reuse of Aerospace Design Rationale

The goal of this project is to apply artificial intelligence techniques to facilitate capture and reuse of aerospace design rationale. The project applies case-based reasoning (CBR) and concept mapping (CMAP) tools to the task of capturing, organizing, and interactively accessing experiences or "cases" encapsulating the methods and rationale underlying expert aerospace design. As stipulated in the award, Indiana University and Ames personnel are collaborating on performance of research and determining the direction of research, to assure that the project focuses on high-value tasks. In the first five months of the project, we have made two visits to Ames Research Center to consult with our NASA collaborators, to learn about the advanced aerospace design tools being developed there, and to identify specific needs for intelligent design support. These meetings identified a number of task areas for applying CBR and concept mapping technology. We jointly selected a first task area to focus on: Acquiring the convergence criteria that experts use to guide the selection of useful data from a set of numerical simulations of high-lift systems. During the first funding period, we developed two software systems. First, we have adapted a CBR system developed at Indiana University into a prototype case-based reasoning shell to capture and retrieve information about design experiences, with the sample task of capturing and reusing experts' intuitive criteria for determining convergence (work conducted at Indiana University). Second, we have also adapted and refined existing concept mapping tools that will be used to clarify and capture the rationale underlying those experiences, to facilitate understanding of the expert's reasoning and guide future reuse of captured information (work conducted at the University of West Florida). The tools we have developed are designed to be the basis for a general framework for facilitating tasks within systems developed by the Advanced Design Technologies Testbed (ADTT) project at ARC. The tenets of our framework are (1) that the systems developed should leverage a designer's knowledge, rather than attempting to replace it; (2) that learning and user feedback must play a central role, so that the system can adapt to how it is used, and (3) that the learning and feedback processes must be as natural and as unobtrusive as possible. In the second funding period we will extend our current work, applying the tools to capturing higher-level design rationale.

Leake, David B.↗
DOE OSTI2025

An efficient second-order adaptive procedure for inserting CAD geometries into hexahedral meshes using volume fractions

Here, this paper is concerned with inserting three-dimensional computer-aided design (CAD) geometries into meshes composed of hexahedral elements using a volume fraction representation. An adaptive procedure for doing so is presented. The procedure consists of two steps. The first step performs spatial acceleration using a k-d tree. The second step involves subdividing individual hexahedra in an adaptive mesh refinement (AMR)-like fashion and approximating the CAD geometry linearly (as a plane) at the finest subdivision. The procedure requires only two geometric queries from a CAD kernel: determining whether or not a queried spatial coordinate is inside or outside the CAD geometry and determining the closest point on the CAD geometry’s surface from a given spatial coordinate. We prove that the procedure is second-order accurate for sufficiently smooth geometries and sufficiently refined background meshes. We demonstrate the expected order of accuracy is achieved with several verification tests and illustrate the procedure’s effectiveness for several exemplar CAD geometries.

Adaptive↗
DOE OSTI2022

Mesoflow: An Open-Source Reacting Flow Solver for Catalysis at Mesoscale

We present the capabilities and software performance metrics of our open-source continuum solver for catalysis, Mesoflow, developed specifically for modeling transport and chemistry at the mesoscale. Our solver utilizes Cartesian block-structured adaptive mesh refinement to resolve complex catalyst surface morphologies directly obtained from X-ray tomography data. An immersed boundary based formulation enables rapid representation of complex geometries prevalent in most mesoporous catalyst interfaces. The solver is developed on top of open-source performance portable library, AMReX, providing parallel execution capabilities on current and upcoming high-performance-computing (HPC) architectures. Our flexible software framework enables integration of complex chemical mechanisms at heterogenous interfaces and time-split algorithms for circumventing highly disparate reaction and flow time-scales. Our current studies indicate a ten-fold performance gain by using graphics-processing-units (GPUs) compared to a single processor for representative problem sizes (2 million cell mesh). We will also present a brief introduction on how to build and use this software for application problems pertaining to catalytic upgrading and gas transport within porous catalyst particles.

adaptive meshing↗
DOE OSTI2023

Mesh refinement for anisotropic diffusion in magnetized plasmas

Highly accurate simulation of plasma transport is needed to drive the successful design and operation of magnetically confined fusion reactors. Unfortunately, the extreme anisotropy present in magnetized plasmas results in thin boundary layers that are expensive to resolve. Here, this work investigates how various mesh refinement strategies might reduce that expense to allow for more efficient simulation by comparing standard variable refinement approaches that use a field quantity to an adaptive approach that uses an error estimator. It is first verified that higher order discretization only realizes the proper rate of convergence once the mesh resolves the thin boundary layer, therefore motivating the focusing of refinement on the boundary layer. For three two-dimensional test cases that contain characteristic features of tokamak magnetic fields, an exponential refinement strategy based on the magnetic flux function, which is the standard refinement approach in the field, is compared to an adaptive strategy utilizing the established Zienwiekicz and Zhu error estimator. The adaptive mesh refinement strategy consistently achieves the same accuracy using orders of magnitude less degrees of freedom than either exponential or uniform refinement. This result makes the adaptive refinement strategy more efficient than the exponential refinement strategy while also being more generalizable to problems with complex magnetic geometries. Scaling laws are derived that quantify the improvement in cost of the adaptive refinement strategy over other refinement approaches in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1999

High Order Approximations for Compressible Fluid Dynamics on Unstructured and Cartesian Meshes

The development of high-order accurate numerical discretization techniques for irregular domains and meshes is often cited as one of the remaining challenges facing the field of computational fluid dynamics. In structural mechanics, the advantages of high-order finite element approximation are widely recognized. This is especially true when high-order element approximation is combined with element refinement (h-p refinement). In computational fluid dynamics, high-order discretization methods are infrequently used in the computation of compressible fluid flow. The hyperbolic nature of the governing equations and the presence of solution discontinuities makes high-order accuracy difficult to achieve. Consequently, second-order accurate methods are still predominately used in industrial applications even though evidence suggests that high-order methods may offer a way to significantly improve the resolution and accuracy for these calculations. To address this important topic, a special course was jointly organized by the Applied Vehicle Technology Panel of NATO's Research and Technology Organization (RTO), the von Karman Institute for Fluid Dynamics, and the Numerical Aerospace Simulation Division at the NASA Ames Research Center. The NATO RTO sponsored course entitled "Higher Order Discretization Methods in Computational Fluid Dynamics" was held September 14-18, 1998 at the von Karman Institute for Fluid Dynamics in Belgium and September 21-25, 1998 at the NASA Ames Research Center in the United States. During this special course, lecturers from Europe and the United States gave a series of comprehensive lectures on advanced topics related to the high-order numerical discretization of partial differential equations with primary emphasis given to computational fluid dynamics (CFD). Additional consideration was given to topics in computational physics such as the high-order discretization of the Hamilton-Jacobi, Helmholtz, and elasticity equations. This volume consists of five articles prepared by the special course lecturers. These articles should be of particular relevance to those readers with an interest in numerical discretization techniques which generalize to very high-order accuracy. The articles of Professors Abgrall and Shu consider the mathematical formulation of high-order accurate finite volume schemes utilizing essentially non-oscillatory (ENO) and weighted essentially non-oscillatory (WENO) reconstruction together with upwind flux evaluation. These formulations are particularly effective in computing numerical solutions of conservation laws containing solution discontinuities. Careful attention is given by the authors to implementational issues and techniques for improving the overall efficiency of these methods. The article of Professor Cockburn discusses the discontinuous Galerkin finite element method. This method naturally extends to high-order accuracy and has an interpretation as a finite volume method. Cockburn addresses two important issues associated with the discontinuous Galerkin method: controlling spurious extrema near solution discontinuities via "limiting" and the extension to second order advective-diffusive equations (joint work with Shu). The articles of Dr. Henderson and Professor Schwab consider the mathematical formulation and implementation of the h-p finite element methods using hierarchical basis functions and adaptive mesh refinement. These methods are particularly useful in computing high-order accurate solutions containing perturbative layers and corner singularities. Additional flexibility is obtained using a mortar FEM technique whereby nonconforming elements are interfaced together. Numerous examples are given by Henderson applying the h-p FEM method to the simulation of turbulence and turbulence transition.

Barth, Timothy↗