Unstructured mesh generation and adaptivity
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1995-01-01
An overview of current unstructured mesh generation and adaptivity techniques is given. Basic building blocks taken from the field of computational geometry are first described. Various practical mesh generation techniques based on these algorithms are then constructed and illustrated with examples. Issues of adaptive meshing and stretched mesh generation for anisotropic problems are treated in subsequent sections. The presentation is organized in an education manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.
Adaptive triangular mesh generation
NASA Technical Reports Server (NTRS)
Erlebacher, G.; Eiseman, P. R.
1984-01-01
A general adaptive grid algorithm is developed on triangular grids. The adaptivity is provided by a combination of node addition, dynamic node connectivity and a simple node movement strategy. While the local restructuring process and the node addition mechanism take place in the physical plane, the nodes are displaced on a monitor surface, constructed from the salient features of the physical problem. An approximation to mean curvature detects changes in the direction of the monitor surface, and provides the pulling force on the nodes. Solutions to the axisymmetric Grad-Shafranov equation demonstrate the capturing, by triangles, of the plasma-vacuum interface in a free-boundary equilibrium configuration.
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Adaptive mesh generation for viscous flows using Delaunay triangulation
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1988-01-01
A method for generating an unstructured triangular mesh in two dimensions, suitable for computing high Reynolds number flows over arbitrary configurations is presented. The method is based on a Delaunay triangulation, which is performed in a locally stretched space, in order to obtain very high aspect ratio triangles in the boundary layer and the wake regions. It is shown how the method can be coupled with an unstructured Navier-Stokes solver to produce a solution adaptive mesh generation procedure for viscous flows.
Adaptive mesh generation for edge-element finite element method
NASA Astrophysics Data System (ADS)
Tsuboi, Hajime; Gyimothy, Szabolcs
2001-06-01
An adaptive mesh generation method for two- and three-dimensional finite element methods using edge elements is proposed. Since the tangential component continuity is preserved when using edge elements, the strategy of creating new nodes is based on evaluation of the normal component of the magnetic vector potential across element interfaces. The evaluation is performed at the middle point of edge of a triangular element for two-dimensional problems or at the gravity center of triangular surface of a tetrahedral element for three-dimensional problems. At the boundary of two elements, the error estimator is the ratio of the normal component discontinuity to the maximum value of the potential in the same material. One or more nodes are set at the middle points of the edges according to the value of the estimator as well as the subdivision of elements where new nodes have been created. A final mesh will be obtained after several iterations. Some computation results of two- and three-dimensional problems using the proposed method are shown.
NASA Astrophysics Data System (ADS)
Papadakis, A. P.; Georghiou, G. E.; Metaxas, A. C.
2008-12-01
A new adaptive mesh generator has been developed and used in the analysis of high-pressure gas discharges, such as avalanches and streamers, reducing computational times and computer memory needs significantly. The new adaptive mesh generator developed, uses normalized error indicators, varying from 0 to 1, to guarantee optimal mesh resolution for all carriers involved in the analysis. Furthermore, it uses h- and r-refinement techniques such as mesh jiggling, edge swapping and node addition/removal to develop an element quality improvement algorithm that improves the mesh quality significantly and a fast and accurate algorithm for interpolation between meshes. Finally, the mesh generator is applied in the characterization of the transition from a single electron to the avalanche and streamer discharges in high-voltage, high-pressure gas discharges for dc 1 mm gaps, RF 1 cm point-plane gaps and parallel-plate 40 MHz configurations, in ambient atmospheric air.
Lee, W; Kim, T-S; Cho, M; Lee, S
2005-01-01
In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.
Unstructured and adaptive mesh generation for high Reynolds number viscous flows
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1991-01-01
A method for generating and adaptively refining a highly stretched unstructured mesh suitable for the computation of high-Reynolds-number viscous flows about arbitrary two-dimensional geometries was developed. The method is based on the Delaunay triangulation of a predetermined set of points and employs a local mapping in order to achieve the high stretching rates required in the boundary-layer and wake regions. The initial mesh-point distribution is determined in a geometry-adaptive manner which clusters points in regions of high curvature and sharp corners. Adaptive mesh refinement is achieved by adding new points in regions of large flow gradients, and locally retriangulating; thus, obviating the need for global mesh regeneration. Initial and adapted meshes about complex multi-element airfoil geometries are shown and compressible flow solutions are computed on these meshes.
Lee, W H; Kim, T-S; Cho, M H; Ahn, Y B; Lee, S Y
2006-12-01
In studying bioelectromagnetic problems, finite element analysis (FEA) offers several advantages over conventional methods such as the boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropic conductivity. For FEA, mesh generation is the first critical requirement and there exist many different approaches. However, conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes (cMeshes), resulting in numerous nodes and elements in modelling the conducting domain, and thereby increasing computational load and demand. In this work, we present efficient content-adaptive mesh generation schemes for complex biological volumes of MR images. The presented methodology is fully automatic and generates FE meshes that are adaptive to the geometrical contents of MR images, allowing optimal representation of conducting domain for FEA. We have also evaluated the effect of cMeshes on FEA in three dimensions by comparing the forward solutions from various cMesh head models to the solutions from the reference FE head model in which fine and equidistant FEs constitute the model. The results show that there is a significant gain in computation time with minor loss in numerical accuracy. We believe that cMeshes should be useful in the FEA of bioelectromagnetic problems.
Lober, R.R.; Tautges, T.J.; Vaughan, C.T.
1997-03-01
Paving is an automated mesh generation algorithm which produces all-quadrilateral elements. It can additionally generate these elements in varying sizes such that the resulting mesh adapts to a function distribution, such as an error function. While powerful, conventional paving is a very serial algorithm in its operation. Parallel paving is the extension of serial paving into parallel environments to perform the same meshing functions as conventional paving only on distributed, discretized models. This extension allows large, adaptive, parallel finite element simulations to take advantage of paving`s meshing capabilities for h-remap remeshing. A significantly modified version of the CUBIT mesh generation code has been developed to host the parallel paving algorithm and demonstrate its capabilities on both two dimensional and three dimensional surface geometries and compare the resulting parallel produced meshes to conventionally paved meshes for mesh quality and algorithm performance. Sandia`s {open_quotes}tiling{close_quotes} dynamic load balancing code has also been extended to work with the paving algorithm to retain parallel efficiency as subdomains undergo iterative mesh refinement.
Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption.
Dresel, T; Beyerlein, M; Schwider, J
1996-12-10
Computer-generated phase-only holograms can be used for laser beam shaping, i.e., for focusing a given aperture with intensity and phase distributions into a pregiven intensity pattern in their focal planes. A numerical approach based on iterative finite-element mesh adaption permits the design of appropriate phase functions for the task of focusing into two-dimensional reconstruction patterns. Both the hologram aperture and the reconstruction pattern are covered by mesh mappings. An iterative procedure delivers meshes with intensities equally distributed over the constituting elements. This design algorithm adds new elementary focuser functions to what we call object-oriented hologram design. Some design examples are discussed.
Applications of automatic mesh generation and adaptive methods in computational medicine
Schmidt, J.A.; Macleod, R.S.; Johnson, C.R.; Eason, J.C.
1995-12-31
Important problems in Computational Medicine exist that can benefit from the implementation of adaptive mesh refinement techniques. Biological systems are so inherently complex that only efficient models running on state of the art hardware can begin to simulate reality. To tackle the complex geometries associated with medical applications we present a general purpose mesh generation scheme based upon the Delaunay tessellation algorithm and an iterative point generator. In addition, automatic, two- and three-dimensional adaptive mesh refinement methods are presented that are derived from local and global estimates of the finite element error. Mesh generation and adaptive refinement techniques are utilized to obtain accurate approximations of bioelectric fields within anatomically correct models of the heart and human thorax. Specifically, we explore the simulation of cardiac defibrillation and the general forward and inverse problems in electrocardiography (ECG). Comparisons between uniform and adaptive refinement techniques are made to highlight the computational efficiency and accuracy of adaptive methods in the solution of field problems in computational medicine.
Spherical geodesic mesh generation
Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
Cubit Adaptive Meshing Algorithm Library
2004-09-01
CAMAL (Cubit adaptive meshing algorithm library) is a software component library for mesh generation. CAMAL 2.0 includes components for triangle, quad and tetrahedral meshing. A simple Application Programmers Interface (API) takes a discrete boundary definition and CAMAL computes a quality interior unstructured grid. The triangle and quad algorithms may also import a geometric definition of a surface on which to define the grid. CAMALs triangle meshing uses a 3D space advancing front method, the quadmore » meshing algorithm is based upon Sandias patented paving algorithm and the tetrahedral meshing algorithm employs the GHS3D-Tetmesh component developed by INRIA, France.« less
2007-02-02
The CMG is a small, lightweight, structured mesh generation code. It features a simple text input parser that allows setup of various meshes via a small set of text commands. Mesh generation data can be output to text, the silo file format, or the API can be directly queried by applications. It can run serially or in parallel via MPI. The CMG includes the ability to specify varius initial conditions on a mesh via meshmore » tags.« less
Christon, M.; Hardin, D.; Compton, J.; Zosel, M.
1994-08-29
Building complex meshes for large-scale numerical simulations presents immense difficulties in exploiting high-performance computers. Industry and research leaders will describe the current state of the art for generating meshes for such large scientific problems. This will be followed by a panel and general audience discussion of the algorithmic and architectural issues surrounding the generation of meshes with10{sup 7} to 10{sup 9} grid points. (Note: The terms ``mesh`` and ``grid`` are used interchangeably in the literature.)
A GPU implementation of adaptive mesh refinement to simulate tsunamis generated by landslides
NASA Astrophysics Data System (ADS)
de la Asunción, Marc; Castro, Manuel J.
2016-04-01
In this work we propose a CUDA implementation for the simulation of landslide-generated tsunamis using a two-layer Savage-Hutter type model and adaptive mesh refinement (AMR). The AMR method consists of dynamically increasing the spatial resolution of the regions of interest of the domain while keeping the rest of the domain at low resolution, thus obtaining better runtimes and similar results compared to increasing the spatial resolution of the entire domain. Our AMR implementation uses a patch-based approach, it supports up to three levels, power-of-two ratios of refinement, different refinement criteria and also several user parameters to control the refinement and clustering behaviour. A strategy based on the variation of the cell values during the simulation is used to interpolate and propagate the values of the fine cells. Several numerical experiments using artificial and realistic scenarios are presented.
Parallel Adaptive Mesh Refinement
Diachin, L; Hornung, R; Plassmann, P; WIssink, A
2005-03-04
As large-scale, parallel computers have become more widely available and numerical models and algorithms have advanced, the range of physical phenomena that can be simulated has expanded dramatically. Many important science and engineering problems exhibit solutions with localized behavior where highly-detailed salient features or large gradients appear in certain regions which are separated by much larger regions where the solution is smooth. Examples include chemically-reacting flows with radiative heat transfer, high Reynolds number flows interacting with solid objects, and combustion problems where the flame front is essentially a two-dimensional sheet occupying a small part of a three-dimensional domain. Modeling such problems numerically requires approximating the governing partial differential equations on a discrete domain, or grid. Grid spacing is an important factor in determining the accuracy and cost of a computation. A fine grid may be needed to resolve key local features while a much coarser grid may suffice elsewhere. Employing a fine grid everywhere may be inefficient at best and, at worst, may make an adequately resolved simulation impractical. Moreover, the location and resolution of fine grid required for an accurate solution is a dynamic property of a problem's transient features and may not be known a priori. Adaptive mesh refinement (AMR) is a technique that can be used with both structured and unstructured meshes to adjust local grid spacing dynamically to capture solution features with an appropriate degree of resolution. Thus, computational resources can be focused where and when they are needed most to efficiently achieve an accurate solution without incurring the cost of a globally-fine grid. Figure 1.1 shows two example computations using AMR; on the left is a structured mesh calculation of a impulsively-sheared contact surface and on the right is the fuselage and volume discretization of an RAH-66 Comanche helicopter [35]. Note the
Parallel Adaptive Mesh Refinement Library
NASA Technical Reports Server (NTRS)
Mac-Neice, Peter; Olson, Kevin
2005-01-01
Parallel Adaptive Mesh Refinement Library (PARAMESH) is a package of Fortran 90 subroutines designed to provide a computer programmer with an easy route to extension of (1) a previously written serial code that uses a logically Cartesian structured mesh into (2) a parallel code with adaptive mesh refinement (AMR). Alternatively, in its simplest use, and with minimal effort, PARAMESH can operate as a domain-decomposition tool for users who want to parallelize their serial codes but who do not wish to utilize adaptivity. The package builds a hierarchy of sub-grids to cover the computational domain of a given application program, with spatial resolution varying to satisfy the demands of the application. The sub-grid blocks form the nodes of a tree data structure (a quad-tree in two or an oct-tree in three dimensions). Each grid block has a logically Cartesian mesh. The package supports one-, two- and three-dimensional models.
Adaptive and Unstructured Mesh Cleaving
Bronson, Jonathan R.; Sastry, Shankar P.; Levine, Joshua A.; Whitaker, Ross T.
2015-01-01
We propose a new strategy for boundary conforming meshing that decouples the problem of building tetrahedra of proper size and shape from the problem of conforming to complex, non-manifold boundaries. This approach is motivated by the observation that while several methods exist for adaptive tetrahedral meshing, they typically have difficulty at geometric boundaries. The proposed strategy avoids this conflict by extracting the boundary conforming constraint into a secondary step. We first build a background mesh having a desired set of tetrahedral properties, and then use a generalized stenciling method to divide, or “cleave”, these elements to get a set of conforming tetrahedra, while limiting the impacts cleaving has on element quality. In developing this new framework, we make several technical contributions including a new method for building graded tetrahedral meshes as well as a generalization of the isosurface stuffing and lattice cleaving algorithms to unstructured background meshes. PMID:26137171
Adaptive Mesh Refinement in CTH
Crawford, David
1999-05-04
This paper reports progress on implementing a new capability of adaptive mesh refinement into the Eulerian multimaterial shock- physics code CTH. The adaptivity is block-based with refinement and unrefinement occurring in an isotropic 2:1 manner. The code is designed to run on serial, multiprocessor and massive parallel platforms. An approximate factor of three in memory and performance improvements over comparable resolution non-adaptive calculations has-been demonstrated for a number of problems.
Adaptive Mesh Refinement for Microelectronic Device Design
NASA Technical Reports Server (NTRS)
Cwik, Tom; Lou, John; Norton, Charles
1999-01-01
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
Issues in adaptive mesh refinement
Dai, William Wenlong
2009-01-01
In this paper, we present an approach for a patch-based adaptive mesh refinement (AMR) for multi-physics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, and management of patches. Among the special features of this patch-based AMR are symmetry preserving, efficiency of refinement, special implementation offlux correction, and patch management in parallel computing environments. Here, higher efficiency of refinement means less unnecessarily refined cells for a given set of cells to be refined. To demonstrate the capability of the AMR framework, hydrodynamics simulations with many levels of refinement are shown in both two- and three-dimensions.
Nanowire mesh solar fuels generator
Yang, Peidong; Chan, Candace; Sun, Jianwei; Liu, Bin
2016-05-24
This disclosure provides systems, methods, and apparatus related to a nanowire mesh solar fuels generator. In one aspect, a nanowire mesh solar fuels generator includes (1) a photoanode configured to perform water oxidation and (2) a photocathode configured to perform water reduction. The photocathode is in electrical contact with the photoanode. The photoanode may include a high surface area network of photoanode nanowires. The photocathode may include a high surface area network of photocathode nanowires. In some embodiments, the nanowire mesh solar fuels generator may include an ion conductive polymer infiltrating the photoanode and the photocathode in the region where the photocathode is in electrical contact with the photoanode.
Adaptive Meshing Techniques for Viscous Flow Calculations on Mixed Element Unstructured Meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1997-01-01
An adaptive refinement strategy based on hierarchical element subdivision is formulated and implemented for meshes containing arbitrary mixtures of tetrahendra, hexahendra, prisms and pyramids. Special attention is given to keeping memory overheads as low as possible. This procedure is coupled with an algebraic multigrid flow solver which operates on mixed-element meshes. Inviscid flows as well as viscous flows are computed an adaptively refined tetrahedral, hexahedral, and hybrid meshes. The efficiency of the method is demonstrated by generating an adapted hexahedral mesh containing 3 million vertices on a relatively inexpensive workstation.
GRChombo: Numerical relativity with adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Clough, Katy; Figueras, Pau; Finkel, Hal; Kunesch, Markus; Lim, Eugene A.; Tunyasuvunakool, Saran
2015-12-01
In this work, we introduce {\\mathtt{GRChombo}}: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial ‘many-boxes-in-many-boxes’ mesh hierarchies and massive parallelism through the message passing interface. {\\mathtt{GRChombo}} evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3 + 1 setting, while also significantly simplifying the process of setting up the mesh for these problems. We show that {\\mathtt{GRChombo}} can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.
Adaptive mesh refinement in titanium
Colella, Phillip; Wen, Tong
2005-01-21
In this paper, we evaluate Titanium's usability as a high-level parallel programming language through a case study, where we implement a subset of Chombo's functionality in Titanium. Chombo is a software package applying the Adaptive Mesh Refinement methodology to numerical Partial Differential Equations at the production level. In Chombo, the library approach is used to parallel programming (C++ and Fortran, with MPI), whereas Titanium is a Java dialect designed for high-performance scientific computing. The performance of our implementation is studied and compared with that of Chombo in solving Poisson's equation based on two grid configurations from a real application. Also provided are the counts of lines of code from both sides.
Adaptive Hybrid Mesh Refinement for Multiphysics Applications
Khamayseh, Ahmed K; de Almeida, Valmor F
2007-01-01
The accuracy and convergence of computational solutions of mesh-based methods is strongly dependent on the quality of the mesh used. We have developed methods for optimizing meshes that are comprised of elements of arbitrary polygonal and polyhedral type. We present in this research the development of r-h hybrid adaptive meshing technology tailored to application areas relevant to multi-physics modeling and simulation. Solution-based adaptation methods are used to reposition mesh nodes (r-adaptation) or to refine the mesh cells (h-adaptation) to minimize solution error. The numerical methods perform either the r-adaptive mesh optimization or the h-adaptive mesh refinement method on the initial isotropic or anisotropic meshes to maximize the equidistribution of a weighted geometric and/or solution function. We have successfully introduced r-h adaptivity to a least-squares method with spherical harmonics basis functions for the solution of the spherical shallow atmosphere model used in climate forecasting. In addition, application of this technology also covers a wide range of disciplines in computational sciences, most notably, time-dependent multi-physics, multi-scale modeling and simulation.
Self-Organizing Mesh Generation
1991-11-01
A set of five programs which make up a self organizing mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily shaped two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchal input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program,more » RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight node elements (with mid side nodes) may be obtained with RENUM8. QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers, An overall plot showing the position of the selected plot areas is produced.« less
Auto-adaptive finite element meshes
NASA Technical Reports Server (NTRS)
Richter, Roland; Leyland, Penelope
1995-01-01
Accurate capturing of discontinuities within compressible flow computations is achieved by coupling a suitable solver with an automatic adaptive mesh algorithm for unstructured triangular meshes. The mesh adaptation procedures developed rely on non-hierarchical dynamical local refinement/derefinement techniques, which hence enable structural optimization as well as geometrical optimization. The methods described are applied for a number of the ICASE test cases are particularly interesting for unsteady flow simulations.
Procedure for Adapting Direct Simulation Monte Carlo Meshes
NASA Technical Reports Server (NTRS)
Woronowicz, Michael S.; Wilmoth, Richard G.; Carlson, Ann B.; Rault, Didier F. G.
1992-01-01
A technique is presented for adapting computational meshes used in the G2 version of the direct simulation Monte Carlo method. The physical ideas underlying the technique are discussed, and adaptation formulas are developed for use on solutions generated from an initial mesh. The effect of statistical scatter on adaptation is addressed, and results demonstrate the ability of this technique to achieve more accurate results without increasing necessary computational resources.
Efficient triangular adaptive meshes for tsunami simulations
NASA Astrophysics Data System (ADS)
Behrens, J.
2012-04-01
With improving technology and increased sensor density for accurate determination of tsunamogenic earthquake source parameters and consecutively uplift distribution, real-time simulations of even near-field tsunami hazard appears feasible in the near future. In order to support such efforts a new generation of tsunami models is currently under development. These models comprise adaptively refined meshes, in order to save computational resources (in areas of low wave activity) and still represent the inherently multi-scale behavior of a tsunami approaching coastal waters. So far, these methods have been based on oct-tree quadrilateral refinement. The method introduced here is based on binary tree refinement on triangular grids. By utilizing the structure stemming from the refinement strategy, a very efficient method can be achieved, with a triangular mesh, able to accurately represent complex boundaries.
Curved mesh generation and mesh refinement using Lagrangian solid mechanics
Persson, P.-O.; Peraire, J.
2008-12-31
We propose a method for generating well-shaped curved unstructured meshes using a nonlinear elasticity analogy. The geometry of the domain to be meshed is represented as an elastic solid. The undeformed geometry is the initial mesh of linear triangular or tetrahedral elements. The external loading results from prescribing a boundary displacement to be that of the curved geometry, and the final configuration is determined by solving for the equilibrium configuration. The deformations are represented using piecewise polynomials within each element of the original mesh. When the mesh is sufficiently fine to resolve the solid deformation, this method guarantees non-intersecting elements even for highly distorted or anisotropic initial meshes. We describe the method and the solution procedures, and we show a number of examples of two and three dimensional simplex meshes with curved boundaries. We also demonstrate how to use the technique for local refinement of non-curved meshes in the presence of curved boundaries.
Documentation for MeshKit - Reactor Geometry (&mesh) Generator
Jain, Rajeev; Mahadevan, Vijay
2015-09-30
This report gives documentation for using MeshKit’s Reactor Geometry (and mesh) Generator (RGG) GUI and also briefly documents other algorithms and tools available in MeshKit. RGG is a program designed to aid in modeling and meshing of complex/large hexagonal and rectilinear reactor cores. RGG uses Argonne’s SIGMA interfaces, Qt and VTK to produce an intuitive user interface. By integrating a 3D view of the reactor with the meshing tools and combining them into one user interface, RGG streamlines the task of preparing a simulation mesh and enables real-time feedback that reduces accidental scripting mistakes that could waste hours of meshing. RGG interfaces with MeshKit tools to consolidate the meshing process, meaning that going from model to mesh is as easy as a button click. This report is designed to explain RGG v 2.0 interface and provide users with the knowledge and skills to pilot RGG successfully. Brief documentation of MeshKit source code, tools and other algorithms available are also presented for developers to extend and add new algorithms to MeshKit. RGG tools work in serial and parallel and have been used to model complex reactor core models consisting of conical pins, load pads, several thousands of axially varying material properties of instrumentation pins and other interstices meshes.
Adaptive-mesh algorithms for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Roe, Philip L.; Quirk, James
1993-01-01
The basic goal of adaptive-mesh algorithms is to distribute computational resources wisely by increasing the resolution of 'important' regions of the flow and decreasing the resolution of regions that are less important. While this goal is one that is worthwhile, implementing schemes that have this degree of sophistication remains more of an art than a science. In this paper, the basic pieces of adaptive-mesh algorithms are described and some of the possible ways to implement them are discussed and compared. These basic pieces are the data structure to be used, the generation of an initial mesh, the criterion to be used to adapt the mesh to the solution, and the flow-solver algorithm on the resulting mesh. Each of these is discussed, with particular emphasis on methods suitable for the computation of compressible flows.
An Efficient Dynamically Adaptive Mesh for Potentially Singular Solutions
NASA Astrophysics Data System (ADS)
Ceniceros, Hector D.; Hou, Thomas Y.
2001-09-01
We develop an efficient dynamically adaptive mesh generator for time-dependent problems in two or more dimensions. The mesh generator is motivated by the variational approach and is based on solving a new set of nonlinear elliptic PDEs for the mesh map. When coupled to a physical problem, the mesh map evolves with the underlying solution and maintains high adaptivity as the solution develops complicated structures and even singular behavior. The overall mesh strategy is simple to implement, avoids interpolation, and can be easily incorporated into a broad range of applications. The efficacy of the mesh is first demonstrated by two examples of blowing-up solutions to the 2-D semilinear heat equation. These examples show that the mesh can follow with high adaptivity a finite-time singularity process. The focus of applications presented here is however the baroclinic generation of vorticity in a strongly layered 2-D Boussinesq fluid, a challenging problem. The moving mesh follows effectively the flow resolving both its global features and the almost singular shear layers developed dynamically. The numerical results show the fast collapse to small scales and an exponential vorticity growth.
Turbulent flow calculations using unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
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.
Hybrid Surface Mesh Adaptation for Climate Modeling
Ahmed Khamayseh; Valmor de Almeida; Glen Hansen
2008-10-01
Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called “mesh motion” (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.
Hybrid Surface Mesh Adaptation for Climate Modeling
Khamayseh, Ahmed K; de Almeida, Valmor F; Hansen, Glen
2008-01-01
Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications, such as climate modeling. Typically, spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest. A second, less-popular method of spatial adaptivity is called "mesh motion" (r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales. This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function, the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is produced by element subdivision alone. Further, in an attempt to support the requirements of a very general class of climate simulation applications, the proposed method is designed to accommodate unstructured, polygonal mesh topologies in addition to the most popular mesh types.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
Koniges, A.; Eder, D.; Masters, N.; Fisher, A.; Anderson, R.; Gunney, B.; Wang, P.; Benson, D.; Dixit, P.
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being applied to slurry flow (landslides).
Optimal fully adaptive wormhole routing for meshes
Schwiebert, L.; Jayasimha, D.N.
1993-12-31
A deadlock-free fully adaptive routing algorithm for 2D meshes which is optimal in the number of virtual channels required and in the number of restrictions placed on the use of these virtual channels is presented. The routing algorithm imposes less than half as many routing restrictions as any previous fully adaptive routing algorithm. It is also proved that, ignoring symmetry, this routing algorithm is the only fully adaptive routing algorithm that achieves both of these goals. The implementation of the routing algorithm requires relatively simple router control logic. The new algorithm is extended, in a straightforward manner to arbitrary dimension meshes. It needs only 4n-2 virtual channels, the minimum number for an n-dimensional mesh. All previous algorithms require an exponential number of virtual channels in the dimension of the mesh.
Hybrid mesh generation using advancing reduction technique
Technology Transfer Automated Retrieval System (TEKTRAN)
This study presents an extension of the application of the advancing reduction technique to the hybrid mesh generation. The proposed algorithm is based on a pre-generated rectangle mesh (RM) with a certain orientation. The intersection points between the two sets of perpendicular mesh lines in RM an...
Grid adaptation using chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1994-01-01
The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.
Grid adaptation using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
Grid adaption using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
Tomographic mesh generation for OSEM reconstruction of SPECT images
NASA Astrophysics Data System (ADS)
Lu, Yao; Yu, Bo; Vogelsang, Levon; Krol, Andrzej; Xu, Yuesheng; Hu, Xiaofei; Feiglin, David
2009-02-01
To improve quality of OSEM SPECT reconstruction in the mesh domain, we implemented an adaptive mesh generation method that produces tomographic mesh consisting of triangular elements with size and density commensurate with geometric detail of the objects. Node density and element size change smoothly as a function of distance from the edges and edge curvature without creation of 'bad' elements. Tomographic performance of mesh-based OSEM reconstruction is controlled by the tomographic mesh structure, i.e. node density distribution, which in turn is ruled by the number of key points on the boundaries. A greedy algorithm is used to influence the distribution of nodes on the boundaries. The relationship between tomographic mesh properties and OSEM reconstruction quality has been investigated. We conclude that by selecting adequate number of key points, one can produce a tomographic mesh with lowest number of nodes that is sufficient to provide desired quality of reconstructed images, appropriate for the imaging system properties.
Method of generating a surface mesh
Shepherd, Jason F.; Benzley, Steven; Grover, Benjamin T.
2008-03-04
A method and machine-readable medium provide a technique to generate and modify a quadrilateral finite element surface mesh using dual creation and modification. After generating a dual of a surface (mesh), a predetermined algorithm may be followed to generate and modify a surface mesh of quadrilateral elements. The predetermined algorithm may include the steps of generating two-dimensional cell regions in dual space, determining existing nodes in primal space, generating new nodes in the dual space, and connecting nodes to form the quadrilateral elements (faces) for the generated and modifiable surface mesh.
Adaptive mesh refinement for storm surge
NASA Astrophysics Data System (ADS)
Mandli, Kyle T.; Dawson, Clint N.
2014-03-01
An approach to utilizing adaptive mesh refinement algorithms for storm surge modeling is proposed. Currently numerical models exist that can resolve the details of coastal regions but are often too costly to be run in an ensemble forecasting framework without significant computing resources. The application of adaptive mesh refinement algorithms substantially lowers the computational cost of a storm surge model run while retaining much of the desired coastal resolution. The approach presented is implemented in the GEOCLAW framework and compared to ADCIRC for Hurricane Ike along with observed tide gauge data and the computational cost of each model run.
Arbitrary Lagrangian Eulerian Adaptive Mesh Refinement
2009-09-29
This is a simulation code involving an ALE (arbitrary Lagrangian-Eulerian) hydrocode with AMR (adaptive mesh refinement) and pluggable physics packages for material strength, heat conduction, radiation diffusion, and laser ray tracing developed a LLNL, UCSD, and Berkeley Lab. The code is an extension of the open source SAMRAI (Structured Adaptive Mesh Refinement Application Interface) code/library. The code can be used in laser facilities such as the National Ignition Facility. The code is alsi being appliedmore » to slurry flow (landslides).« less
Variational Mesh Adaptation: Isotropy and Equidistribution
NASA Astrophysics Data System (ADS)
Huang, Weizhang
2001-12-01
We present a new approach for developing more robust and error-oriented mesh adaptation methods. Specifically, assuming that a regular (in cell shape) and uniform (in cell size) computational mesh is used (as is commonly done in computation), we develop a criterion for mesh adaptation based on an error function whose definition is motivated by the analysis of function variation and local error behavior for linear interpolation. The criterion is then decomposed into two aspects, the isotropy (or conformity) and uniformity (or equidistribution) requirements, each of which can be easier to deal with. The functionals that satisfy these conditions approximately are constructed using discrete and continuous inequalities. A new functional is finally formulated by combining the functionals corresponding to the isotropy and uniformity requirements. The features of the functional are analyzed and demonstrated by numerical results. In particular, unlike the existing mesh adaptation functionals, the new functional has clear geometric meanings of minimization. A mesh that has the desired properties of isotropy and equidistribution can be obtained by properly choosing the values of two parameters. The analysis presented in this article also provides a better understanding of the increasingly popular method of harmonic mapping in two dimensions.
SHARP/PRONGHORN Interoperability: Mesh Generation
Avery Bingham; Javier Ortensi
2012-09-01
Progress toward collaboration between the SHARP and MOOSE computational frameworks has been demonstrated through sharing of mesh generation and ensuring mesh compatibility of both tools with MeshKit. MeshKit was used to build a three-dimensional, full-core very high temperature reactor (VHTR) reactor geometry with 120-degree symmetry, which was used to solve a neutron diffusion critical eigenvalue problem in PRONGHORN. PRONGHORN is an application of MOOSE that is capable of solving coupled neutron diffusion, heat conduction, and homogenized flow problems. The results were compared to a solution found on a 120-degree, reflected, three-dimensional VHTR mesh geometry generated by PRONGHORN. The ability to exchange compatible mesh geometries between the two codes is instrumental for future collaboration and interoperability. The results were found to be in good agreement between the two meshes, thus demonstrating the compatibility of the SHARP and MOOSE frameworks. This outcome makes future collaboration possible.
Approaches to the automatic generation and control of finite element meshes
NASA Technical Reports Server (NTRS)
Shephard, Mark S.
1987-01-01
The algorithmic approaches being taken to the development of finite element mesh generators capable of automatically discretizing general domains without the need for user intervention are discussed. It is demonstrated that because of the modeling demands placed on a automatic mesh generator, all the approaches taken to date produce unstructured meshes. Consideration is also given to both a priori and a posteriori mesh control devices for automatic mesh generators as well as their integration with geometric modeling and adaptive analysis procedures.
Parallel object-oriented adaptive mesh refinement
Balsara, D.; Quinlan, D.J.
1997-04-01
In this paper we study adaptive mesh refinement (AMR) for elliptic and hyperbolic systems. We use the Asynchronous Fast Adaptive Composite Grid Method (AFACX), a parallel algorithm based upon the of Fast Adaptive Composite Grid Method (FAC) as a test case of an adaptive elliptic solver. For our hyperbolic system example we use TVD and ENO schemes for solving the Euler and MHD equations. We use the structured grid load balancer MLB as a tool for obtaining a load balanced distribution in a parallel environment. Parallel adaptive mesh refinement poses difficulties in expressing both the basic single grid solver, whether elliptic or hyperbolic, in a fashion that parallelizes seamlessly. It also requires that these basic solvers work together within the adaptive mesh refinement algorithm which uses the single grid solvers as one part of its adaptive solution process. We show that use of AMR++, an object-oriented library within the OVERTURE Framework, simplifies the development of AMR applications. Parallel support is provided and abstracted through the use of the P++ parallel array class.
Variational method for adaptive grid generation
Brackbill, J.U.
1983-01-01
A variational method for generating adaptive meshes is described. Functionals measuring smoothness, skewness, orientation, and the Jacobian are minimized to generate a mapping from a rectilinear domain in natural coordinate to an arbitrary domain in physical coordinates. From the mapping, a mesh is easily constructed. In using the method to adaptively zone computational problems, as few as one third the number of mesh points are required in each coordinate direction compared with a uniformly zoned mesh.
Multigrid solution strategies for adaptive meshing problems
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1995-01-01
This paper discusses the issues which arise when combining multigrid strategies with adaptive meshing techniques for solving steady-state problems on unstructured meshes. A basic strategy is described, and demonstrated by solving several inviscid and viscous flow cases. Potential inefficiencies in this basic strategy are exposed, and various alternate approaches are discussed, some of which are demonstrated with an example. Although each particular approach exhibits certain advantages, all methods have particular drawbacks, and the formulation of a completely optimal strategy is considered to be an open problem.
Anisotropic mesh adaptation on Lagrangian Coherent Structures
NASA Astrophysics Data System (ADS)
Miron, Philippe; Vétel, Jérôme; Garon, André; Delfour, Michel; Hassan, Mouhammad El
2012-08-01
The finite-time Lyapunov exponent (FTLE) is extensively used as a criterion to reveal fluid flow structures, including unsteady separation/attachment surfaces and vortices, in laminar and turbulent flows. However, for large and complex problems, flow structure identification demands computational methodologies that are more accurate and effective. With this objective in mind, we propose a new set of ordinary differential equations to compute the flow map, along with its first (gradient) and second order (Hessian) spatial derivatives. We show empirically that the gradient of the flow map computed in this way improves the pointwise accuracy of the FTLE field. Furthermore, the Hessian allows for simple interpolation error estimation of the flow map, and the construction of a continuous optimal and multiscale Lp metric. The Lagrangian particles, or nodes, are then iteratively adapted on the flow structures revealed by this metric. Typically, the L1 norm provides meshes best suited to capturing small scale structures, while the L∞ norm provides meshes optimized to capture large scale structures. This means that the mesh density near large scale structures will be greater with the L∞ norm than with the L1 norm for the same mesh complexity, which is why we chose this technique for this paper. We use it to optimize the mesh in the vicinity of LCS. It is found that Lagrangian Coherent Structures are best revealed with the minimum number of vertices with the L∞ metric.
Details of tetrahedral anisotropic mesh adaptation
NASA Astrophysics Data System (ADS)
Jensen, Kristian Ejlebjerg; Gorman, Gerard
2016-04-01
We have implemented tetrahedral anisotropic mesh adaptation using the local operations of coarsening, swapping, refinement and smoothing in MATLAB without the use of any for- N loops, i.e. the script is fully vectorised. In the process of doing so, we have made three observations related to details of the implementation: 1. restricting refinement to a single edge split per element not only simplifies the code, it also improves mesh quality, 2. face to edge swapping is unnecessary, and 3. optimising for the Vassilevski functional tends to give a little higher value for the mean condition number functional than optimising for the condition number functional directly. These observations have been made for a uniform and a radial shock metric field, both starting from a structured mesh in a cube. Finally, we compare two coarsening techniques and demonstrate the importance of applying smoothing in the mesh adaptation loop. The results pertain to a unit cube geometry, but we also show the effect of corners and edges by applying the implementation in a spherical geometry.
Electrostatic PIC with adaptive Cartesian mesh
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert
2016-05-01
We describe an initial implementation of an electrostatic Particle-in-Cell (ES-PIC) module with adaptive Cartesian mesh in our Unified Flow Solver framework. Challenges of PIC method with cell-based adaptive mesh refinement (AMR) are related to a decrease of the particle-per-cell number in the refined cells with a corresponding increase of the numerical noise. The developed ES-PIC solver is validated for capacitively coupled plasma, its AMR capabilities are demonstrated for simulations of streamer development during high-pressure gas breakdown. It is shown that cell-based AMR provides a convenient particle management algorithm for exponential multiplications of electrons and ions in the ionization events.
Adaptive anisotropic meshing for steady convection-dominated problems
Nguyen, Hoa; Gunzburger, Max; Ju, Lili; Burkardt, John
2009-01-01
Obtaining accurate solutions for convection–diffusion equations is challenging due to the presence of layers when convection dominates the diffusion. To solve this problem, we design an adaptive meshing algorithm which optimizes the alignment of anisotropic meshes with the numerical solution. Three main ingredients are used. First, the streamline upwind Petrov–Galerkin method is used to produce a stabilized solution. Second, an adapted metric tensor is computed from the approximate solution. Third, optimized anisotropic meshes are generated from the computed metric tensor by an anisotropic centroidal Voronoi tessellation algorithm. Our algorithm is tested on a variety of two-dimensional examples and the results shows that the algorithm is robust in detecting layers and efficient in avoiding non-physical oscillations in the numerical approximation.
Kinetic solvers with adaptive mesh in phase space.
Arslanbekov, Robert R; Kolobov, Vladimir I; Frolova, Anna A
2013-12-01
An adaptive mesh in phase space (AMPS) methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method. A Cartesian mesh for both configuration (r) and velocity (v) spaces is produced using a "tree of trees" (ToT) data structure. The r mesh is automatically generated around embedded boundaries, and is dynamically adapted to local solution properties. The v mesh is created on-the-fly in each r cell. Mappings between neighboring v-space trees is implemented for the advection operator in r space. We have developed algorithms for solving the full Boltzmann and linear Boltzmann equations with AMPS. Several recent innovations were used to calculate the discrete Boltzmann collision integral with dynamically adaptive v mesh: the importance sampling, multipoint projection, and variance reduction methods. We have developed an efficient algorithm for calculating the linear Boltzmann collision integral for elastic and inelastic collisions of hot light particles in a Lorentz gas. Our AMPS technique has been demonstrated for simulations of hypersonic rarefied gas flows, ion and electron kinetics in weakly ionized plasma, radiation and light-particle transport through thin films, and electron streaming in semiconductors. We have shown that AMPS allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems.
Surface Generation and Cartesian Mesh Support
NASA Technical Reports Server (NTRS)
Haimes, Robert
2004-01-01
This document serves as the final report for the grant titled Surface Generation and Cartesian Mesh Support . This completed work was in algorithmic research into automatically generating surface triangulations from CAD geometries. NASA's OVERFLOW and Cart3D simulation packages use surface triangulations as an underlying geometry description and the ability to automatically generate these from CAD files (without translation) substantially reduces both the wall-clock time and expertise required to get geometry out of CAD and into mesh generation. This surface meshing was exercised greatly during the Shuttle investigation during the last year with success. The secondary efforts performed in this grant involve work on a visualization system cut-cell handling for Cartesian Meshes with embedded boundaries.
Efficiency considerations in triangular adaptive mesh refinement.
Behrens, Jörn; Bader, Michael
2009-11-28
Locally or adaptively refined meshes have been successfully applied to simulation applications involving multi-scale phenomena in the geosciences. In particular, for situations with complex geometries or domain boundaries, meshes with triangular or tetrahedral cells demonstrate their superior ability to accurately represent relevant realistic features. On the other hand, these methods require more complex data structures and are therefore less easily implemented, maintained and optimized. Acceptance in the Earth-system modelling community is still low. One of the major drawbacks is posed by indirect addressing due to unstructured or dynamically changing data structures and correspondingly lower efficiency of the related computations. In this paper, we will derive several strategies to circumvent the mentioned efficiency constraint. In particular, we will apply recent computational sciences methods in combination with results of classical mathematics (space-filling curves) in order to linearize the complex data and access structure.
Fully implicit adaptive mesh refinement MHD algorithm
NASA Astrophysics Data System (ADS)
Philip, Bobby
2005-10-01
In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former results in stiffness due to the presence of very fast waves. The latter requires one to resolve the localized features that the system develops. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. To our knowledge, a scalable, fully implicit AMR algorithm has not been accomplished before for MHD. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technologyootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite --FAC-- algorithms) for scalability. We will demonstrate that the concept is indeed feasible, featuring optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations will be presented on a variety of problems.
Feature recognition applications in mesh generation
Tautges, T.J.; Liu, S.S.; Lu, Y.; Kraftcheck, J.; Gadh, R.
1997-06-01
The use of feature recognition as part of an overall decomposition-based hexahedral meshing approach is described in this paper. The meshing approach consists of feature recognition, using a c-loop or hybrid c-loop method, and the use of cutting surfaces to decompose the solid model. These steps are part of an iterative process, which proceeds either until no more features can be recognized or until the model has been completely decomposed into meshable sub-volumes. This method can greatly reduce the time required to generate an all-hexahedral mesh, either through the use of more efficient meshing algorithms on more of the geometry or by reducing the amount of manual decomposition required to mesh a volume.
An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement.
Edgel, Jared; Benzley, Steven E.; Owen, Steven James
2010-08-01
Most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is often too coarse in some areas and over refined in other areas. Because this method generates 27 new hexes in place of a single hex, there is little control on mesh density. This paper presents an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement method. 2-refinement is based on dividing the hex to be refined into eight new hexes. This method allows a greater control on mesh density when compared to a 3-refinement procedure. This adaptive all-hexahedral meshing algorithm provides a mesh that is efficient for analysis by providing a high element density in specific locations and a reduced mesh density in other areas. In addition, this tool can be effectively used for inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, which have shown great promise in accommodating automatic all-hexahedral algorithms. This adaptive all-hexahedral grid-based meshing algorithm employs a 2-refinement insertion method. This allows greater control on mesh density when compared to 3-refinement methods. This algorithm uses a two layer transition zone to increase element quality and keeps transitions from lower to higher mesh densities smooth. Templates were introduced to allow both convex and concave refinement.
Curved Mesh Correction And Adaptation Tool to Improve COMPASS Electromagnetic Analyses
Luo, X.; Shephard, M.; Lee, L.Q.; Ng, C.; Ge, L.; /SLAC
2011-11-14
SLAC performs large-scale simulations for the next-generation accelerator design using higher-order finite elements. This method requires using valid curved meshes and adaptive mesh refinement in complex 3D curved domains to achieve its fast rate of convergence. ITAPS has developed a procedure to address those mesh requirements to enable petascale electromagnetic accelerator simulations by SLAC. The results demonstrate that those correct valid curvilinear meshes can not only make the simulation more reliable but also improve computational efficiency up to 30%. This paper presents a procedure to track moving adaptive mesh refinement in curved domains. The procedure is capable of generating suitable curvilinear meshes to enable large-scale accelerator simulations. The procedure can generate valid curved meshes with substantially fewer elements to improve the computational efficiency and reliability of the COMPASS electromagnetic analyses. Future work will focus on the scalable parallelization of all steps for petascale simulations.
Visualization of adaptive mesh refinement data
NASA Astrophysics Data System (ADS)
Weber, Gunther H.; Hagen, Hans; Hamann, Bernd; Joy, Kenneth I.; Ligocki, Terry J.; Ma, Kwan-Liu; Shalf, John M.
2001-05-01
The complexity of physical phenomena often varies substantially over space and time. There can be regions where a physical phenomenon/quantity varies very little over a large extent. At the same time, there can be small regions where the same quantity exhibits highly complex variations. Adaptive mesh refinement (AMR) is a technique used in computational fluid dynamics to simulate phenomena with drastically varying scales concerning the complexity of the simulated variables. Using multiple nested grids of different resolutions, AMR combines the topological simplicity of structured-rectilinear grids, permitting efficient computational and storage, with the possibility to adapt grid resolutions in regions of complex behavior. We present methods for direct volume rendering of AMR data. Our methods utilize AMR grids directly for efficiency of the visualization process. We apply a hardware-accelerated rendering method to AMR data supporting interactive manipulation of color-transfer functions and viewing parameters. We also present a cell-projection-based rendering technique for AMR data.
Optimal imaging with adaptive mesh refinement in electrical impedance tomography.
Molinari, Marc; Blott, Barry H; Cox, Simon J; Daniell, Geoffrey J
2002-02-01
In non-linear electrical impedance tomography the goodness of fit of the trial images is assessed by the well-established statistical chi2 criterion applied to the measured and predicted datasets. Further selection from the range of images that fit the data is effected by imposing an explicit constraint on the form of the image, such as the minimization of the image gradients. In particular, the logarithm of the image gradients is chosen so that conductive and resistive deviations are treated in the same way. In this paper we introduce the idea of adaptive mesh refinement to the 2D problem so that the local scale of the mesh is always matched to the scale of the image structures. This improves the reconstruction resolution so that the image constraint adopted dominates and is not perturbed by the mesh discretization. The avoidance of unnecessary mesh elements optimizes the speed of reconstruction without degrading the resulting images. Starting with a mesh scale length of the order of the electrode separation it is shown that, for data obtained at presently achievable signal-to-noise ratios of 60 to 80 dB, one or two refinement stages are sufficient to generate high quality images.
COSMOLOGICAL ADAPTIVE MESH REFINEMENT MAGNETOHYDRODYNAMICS WITH ENZO
Collins, David C.; Xu Hao; Norman, Michael L.; Li Hui; Li Shengtai
2010-02-01
In this work, we present EnzoMHD, the extension of the cosmological code Enzo to include the effects of magnetic fields through the ideal magnetohydrodynamics approximation. We use a higher order Godunov method for the computation of interface fluxes. We use two constrained transport methods to compute the electric field from those interface fluxes, which simultaneously advances the induction equation and maintains the divergence of the magnetic field. A second-order divergence-free reconstruction technique is used to interpolate the magnetic fields in the block-structured adaptive mesh refinement framework already extant in Enzo. This reconstruction also preserves the divergence of the magnetic field to machine precision. We use operator splitting to include gravity and cosmological expansion. We then present a series of cosmological and non-cosmological test problems to demonstrate the quality of solution resulting from this combination of solvers.
Visualization of Scalar Adaptive Mesh Refinement Data
VACET; Weber, Gunther; Weber, Gunther H.; Beckner, Vince E.; Childs, Hank; Ligocki, Terry J.; Miller, Mark C.; Van Straalen, Brian; Bethel, E. Wes
2007-12-06
Adaptive Mesh Refinement (AMR) is a highly effective computation method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations, which must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR grids as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR scalar data visualization research.
Visualization Tools for Adaptive Mesh Refinement Data
Weber, Gunther H.; Beckner, Vincent E.; Childs, Hank; Ligocki,Terry J.; Miller, Mark C.; Van Straalen, Brian; Bethel, E. Wes
2007-05-09
Adaptive Mesh Refinement (AMR) is a highly effective method for simulations that span a large range of spatiotemporal scales, such as astrophysical simulations that must accommodate ranges from interstellar to sub-planetary. Most mainstream visualization tools still lack support for AMR as a first class data type and AMR code teams use custom built applications for AMR visualization. The Department of Energy's (DOE's) Science Discovery through Advanced Computing (SciDAC) Visualization and Analytics Center for Enabling Technologies (VACET) is currently working on extending VisIt, which is an open source visualization tool that accommodates AMR as a first-class data type. These efforts will bridge the gap between general-purpose visualization applications and highly specialized AMR visual analysis applications. Here, we give an overview of the state of the art in AMR visualization research and tools and describe how VisIt currently handles AMR data.
Adaptive Mesh Refinement Simulations of Relativistic Binaries
NASA Astrophysics Data System (ADS)
Motl, Patrick M.; Anderson, M.; Lehner, L.; Olabarrieta, I.; Tohline, J. E.; Liebling, S. L.; Rahman, T.; Hirschman, E.; Neilsen, D.
2006-09-01
We present recent results from our efforts to evolve relativistic binaries composed of compact objects. We simultaneously solve the general relativistic hydrodynamics equations to evolve the material components of the binary and Einstein's equations to evolve the space-time. These two codes are coupled through an adaptive mesh refinement driver (had). One of the ultimate goals of this project is to address the merger of a neutron star and black hole and assess the possible observational signature of such systems as gamma ray bursts. This work has been supported in part by NSF grants AST 04-07070 and PHY 03-26311 and in part through NASA's ATP program grant NAG5-13430. The computations were performed primarily at NCSA through grant MCA98N043 and at LSU's Center for Computation & Technology.
Elliptic Solvers for Adaptive Mesh Refinement Grids
Quinlan, D.J.; Dendy, J.E., Jr.; Shapira, Y.
1999-06-03
We are developing multigrid methods that will efficiently solve elliptic problems with anisotropic and discontinuous coefficients on adaptive grids. The final product will be a library that provides for the simplified solution of such problems. This library will directly benefit the efforts of other Laboratory groups. The focus of this work is research on serial and parallel elliptic algorithms and the inclusion of our black-box multigrid techniques into this new setting. The approach applies the Los Alamos object-oriented class libraries that greatly simplify the development of serial and parallel adaptive mesh refinement applications. In the final year of this LDRD, we focused on putting the software together; in particular we completed the final AMR++ library, we wrote tutorials and manuals, and we built example applications. We implemented the Fast Adaptive Composite Grid method as the principal elliptic solver. We presented results at the Overset Grid Conference and other more AMR specific conferences. We worked on optimization of serial and parallel performance and published several papers on the details of this work. Performance remains an important issue and is the subject of continuing research work.
AMR++: Object-Oriented Parallel Adaptive Mesh Refinement
Quinlan, D.; Philip, B.
2000-02-02
Adaptive mesh refinement (AMR) computations are complicated by their dynamic nature. The development of solvers for realistic applications is complicated by both the complexity of the AMR and the geometry of realistic problem domains. The additional complexity of distributed memory parallelism within such AMR applications most commonly exceeds the level of complexity that can be reasonable maintained with traditional approaches toward software development. This paper will present the details of our object-oriented work on the simplification of the use of adaptive mesh refinement on applications with complex geometries for both serial and distributed memory parallel computation. We will present an independent set of object-oriented abstractions (C++ libraries) well suited to the development of such seemingly intractable scientific computations. As an example of the use of this object-oriented approach we will present recent results of an application modeling fluid flow in the eye. Within this example, the geometry is too complicated for a single curvilinear coordinate grid and so a set of overlapping curvilinear coordinate grids' are used. Adaptive mesh refinement and the required grid generation work to support the refinement process is coupled together in the solution of essentially elliptic equations within this domain. This paper will focus on the management of complexity within development of the AMR++ library which forms a part of the Overture object-oriented framework for the solution of partial differential equations within scientific computing.
Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.
Adaptive mesh refinement techniques for electrical impedance tomography.
Molinari, M; Cox, S J; Blott, B H; Daniell, G J
2001-02-01
Adaptive mesh refinement techniques can be applied to increase the efficiency of electrical impedance tomography reconstruction algorithms by reducing computational and storage cost as well as providing problem-dependent solution structures. A self-adaptive refinement algorithm based on an a posteriori error estimate has been developed and its results are shown in comparison with uniform mesh refinement for a simple head model.
A parallel adaptive mesh refinement algorithm
NASA Technical Reports Server (NTRS)
Quirk, James J.; Hanebutte, Ulf R.
1993-01-01
Over recent years, Adaptive Mesh Refinement (AMR) algorithms which dynamically match the local resolution of the computational grid to the numerical solution being sought have emerged as powerful tools for solving problems that contain disparate length and time scales. In particular, several workers have demonstrated the effectiveness of employing an adaptive, block-structured hierarchical grid system for simulations of complex shock wave phenomena. Unfortunately, from the parallel algorithm developer's viewpoint, this class of scheme is quite involved; these schemes cannot be distilled down to a small kernel upon which various parallelizing strategies may be tested. However, because of their block-structured nature such schemes are inherently parallel, so all is not lost. In this paper we describe the method by which Quirk's AMR algorithm has been parallelized. This method is built upon just a few simple message passing routines and so it may be implemented across a broad class of MIMD machines. Moreover, the method of parallelization is such that the original serial code is left virtually intact, and so we are left with just a single product to support. The importance of this fact should not be underestimated given the size and complexity of the original algorithm.
Optimizing triangular mesh generation from range images
NASA Astrophysics Data System (ADS)
Lu, Tianyu; Yun, David Y.
2000-03-01
An algorithm for the automatic reconstruction of triangular mesh surface model form range images is presented. The optimal piecewise linear surface approximation problem is defined as: given a set S of points uniformly sampled from a vibrate function f(x,y) on a rectangular grid of dimension W X H, find a minimum triangular mesh approximating the surface with vertices anchored at a subset S' of S, such that the deviation at any sample point is within a given bound of (epsilon) > 0. The algorithm deploys a multi- agent resource planning approach to achieve adaptive, accurate and concise piecewise linear approximation using the L-(infinity) norm. The resulting manifold triangular mesh can be directly used as 3D rendering model for visualization with controllable and guaranteed quality. Due to this dual optimality, the algorithm achieves both storage efficiency and visual quality. The error control scheme further facilitates the construction of models in multiple levels of details, which is desirable in animation and virtual reality moving scenes. Experiments with various benchmark range images form smooth functional surfaces to satellite terrain images yield succinct, accurate and visually pleasant triangular meshes. Furthermore, the independence and multiplicity of agents suggest a natural parallelism for triangulation computation, which provides a promising solution for the real-time exploration of large data sets.
Software for Automated Generation of Cartesian Meshes
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J.; Melton, John E.; Berger, Marshal J.
2006-01-01
Cart3D is a collection of computer programs for generating Cartesian meshes [for computational fluid dynamics (CFD) and other applications] in volumes bounded by solid objects. Aspects of Cart3D at earlier stages of development were reported in "Robust and Efficient Generation of Cartesian Meshes for CFD" (ARC-14275), NASA Tech Briefs, Vol. 23, No. 8 (August 1999), page 30. The geometric input to Cart3D comprises surface triangulations like those commonly generated by computer-aided-design programs. Complexly shaped objects can be represented as assemblies of simpler ones. Cart3D deletes all portions of such an assembled object that are not on the exterior surface. Intersections between components are preserved in the resulting triangulation. A tie-breaking routine unambiguously resolves geometric degeneracies. Then taking the intersected surface triangulation as input, the volume mesh is generated through division of cells of an initially coarse hexahedral grid. Cells are subdivided to refine the grid in regions of increased surface curvature and/or increased flow gradients. Cells that become split into multiple unconnected regions by thin pieces of surface are identified.
3D Finite Element Trajectory Code with Adaptive Meshing
NASA Astrophysics Data System (ADS)
Ives, Lawrence; Bui, Thuc; Vogler, William; Bauer, Andy; Shephard, Mark; Beal, Mark; Tran, Hien
2004-11-01
Beam Optics Analysis, a new, 3D charged particle program is available and in use for the design of complex, 3D electron guns and charged particle devices. The code reads files directly from most CAD and solid modeling programs, includes an intuitive Graphical User Interface (GUI), and a robust mesh generator that is fully automatic. Complex problems can be set up, and analysis initiated in minutes. The program includes a user-friendly post processor for displaying field and trajectory data using 3D plots and images. The electrostatic solver is based on the standard nodal finite element method. The magnetostatic field solver is based on the vector finite element method and is also called during the trajectory simulation process to solve for self magnetic fields. The user imports the geometry from essentially any commercial CAD program and uses the GUI to assign parameters (voltages, currents, dielectric constant) and designate emitters (including work function, emitter temperature, and number of trajectories). The the mesh is generated automatically and analysis is performed, including mesh adaptation to improve accuracy and optimize computational resources. This presentation will provide information on the basic structure of the code, its operation, and it's capabilities.
3-D Mesh Generation Nonlinear Systems
Christon, M. A.; Dovey, D.; Stillman, D. W.; Hallquist, J. O.; Rainsberger, R. B
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surface equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.
Anisotropic Mesh Adaptivity for Turbulent Flows with Boundary Layers
NASA Astrophysics Data System (ADS)
Chitale, Kedar C.
Turbulent flows are found everywhere in nature and are studied, analyzed and simulated using various experimental and numerical tools. For computational analysis, a variety of turbulence models are available and the accuracy of these models in capturing the phenomenon depends largely on the mesh spacings, especially near the walls, in the boundary layer region. Special semi-structured meshes called "mesh boundary layers" are widely used in the CFD community in simulations of turbulent flows, because of their graded and orthogonal layered structure. They provide an efficient way to achieve very fine and highly anisotropic mesh spacings without introducing poorly shaped elements. Since usually the required mesh spacings to accurately resolve the flow are not known a priori to the simulations, an adaptive approach based on a posteriori error indicators is used to achieve an appropriate mesh. In this study, we apply the adaptive meshing techniques to turbulent flows with a focus on boundary layers. We construct a framework to calculate the critical wall normal mesh spacings inside the boundary layers based on the flow physics and the knowledge of the turbulence model. This approach is combined with numerical error indicators to adapt the entire flow region. We illustrate the effectiveness of this hybrid approach by applying it to three aerodynamic flows and studying their superior performance in capturing the flow structures in detail. We also demonstrate the capabilities of the current developments in parallel boundary layer mesh adaptation by applying them to two internal flow problems. We also study the application of adaptive boundary layer meshes to complex geometries like multi element wings. We highlight the advantage of using such techniques for superior wake and tip region resolution by showcasing flow results. We also outline the future direction for the adaptive meshing techniques to be useful to the large scale flow computations.
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2011-01-01
Mesh deformation methods are a versatile strategy for solving partial differential equations (PDEs) with a vast variety of practical applications. However, these methods break down for elliptic PDEs with discontinuous coefficients, namely, elliptic interface problems. For this class of problems, the additional interface jump conditions are required to maintain the well-posedness of the governing equation. Consequently, in order to achieve high accuracy and high order convergence, additional numerical algorithms are required to enforce the interface jump conditions in solving elliptic interface problems. The present work introduces an interface technique based adaptively deformed mesh strategy for resolving elliptic interface problems. We take the advantages of the high accuracy, flexibility and robustness of the matched interface and boundary (MIB) method to construct an adaptively deformed mesh based interface method for elliptic equations with discontinuous coefficients. The proposed method generates deformed meshes in the physical domain and solves the transformed governed equations in the computational domain, which maintains regular Cartesian meshes. The mesh deformation is realized by a mesh transformation PDE, which controls the mesh redistribution by a source term. The source term consists of a monitor function, which builds in mesh contraction rules. Both interface geometry based deformed meshes and solution gradient based deformed meshes are constructed to reduce the L∞ and L2 errors in solving elliptic interface problems. The proposed adaptively deformed mesh based interface method is extensively validated by many numerical experiments. Numerical results indicate that the adaptively deformed mesh based interface method outperforms the original MIB method for dealing with elliptic interface problems. PMID:22586356
Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis
NASA Astrophysics Data System (ADS)
Yue, Zhihua
2005-11-01
The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems
Adaptive mesh refinement for stochastic reaction-diffusion processes
Bayati, Basil; Chatelain, Philippe; Koumoutsakos, Petros
2011-01-01
We present an algorithm for adaptive mesh refinement applied to mesoscopic stochastic simulations of spatially evolving reaction-diffusion processes. The transition rates for the diffusion process are derived on adaptive, locally refined structured meshes. Convergence of the diffusion process is presented and the fluctuations of the stochastic process are verified. Furthermore, a refinement criterion is proposed for the evolution of the adaptive mesh. The method is validated in simulations of reaction-diffusion processes as described by the Fisher-Kolmogorov and Gray-Scott equations.
Numerical modeling of seismic waves using frequency-adaptive meshes
NASA Astrophysics Data System (ADS)
Hu, Jinyin; Jia, Xiaofeng
2016-08-01
An improved modeling algorithm using frequency-adaptive meshes is applied to meet the computational requirements of all seismic frequency components. It automatically adopts coarse meshes for low-frequency computations and fine meshes for high-frequency computations. The grid intervals are adaptively calculated based on a smooth inversely proportional function of grid size with respect to the frequency. In regular grid-based methods, the uniform mesh or non-uniform mesh is used for frequency-domain wave propagators and it is fixed for all frequencies. A too coarse mesh results in inaccurate high-frequency wavefields and unacceptable numerical dispersion; on the other hand, an overly fine mesh may cause storage and computational overburdens as well as invalid propagation angles of low-frequency wavefields. Experiments on the Padé generalized screen propagator indicate that the Adaptive mesh effectively solves these drawbacks of regular fixed-mesh methods, thus accurately computing the wavefield and its propagation angle in a wide frequency band. Several synthetic examples also demonstrate its feasibility for seismic modeling and migration.
Vertical-Axis Wind Turbine Mesh Generator
2014-01-24
VAWTGen is a mesh generator for creating a finite element beam mesh of arbitrary vertical-axis wind turbines (VAWT). The software accepts input files specifying tower and blade structural and aerodynamic descriptions and constructs a VAWT using a minimal set of inputs. VAWTs with an arbitrary number of blades can be constructed with or without a central tower. Strut connections between the tower and blades can be specified in an arbitrary manner. The software also facilitates specifying arbitrary joints between structural components and concentrated structural tenns (mass and stiffness). The output files which describe the VAWT configuration are intended to be used with the Offshore Wind ENergy Simulation (OWENS) Toolkit software for structural dynamics analysis of VAWTs. Furthermore, VAWTGen is useful for visualizing output from the OWENS analysis software.
Vertical-Axis Wind Turbine Mesh Generator
2014-01-24
VAWTGen is a mesh generator for creating a finite element beam mesh of arbitrary vertical-axis wind turbines (VAWT). The software accepts input files specifying tower and blade structural and aerodynamic descriptions and constructs a VAWT using a minimal set of inputs. VAWTs with an arbitrary number of blades can be constructed with or without a central tower. Strut connections between the tower and blades can be specified in an arbitrary manner. The software also facilitatesmore » specifying arbitrary joints between structural components and concentrated structural tenns (mass and stiffness). The output files which describe the VAWT configuration are intended to be used with the Offshore Wind ENergy Simulation (OWENS) Toolkit software for structural dynamics analysis of VAWTs. Furthermore, VAWTGen is useful for visualizing output from the OWENS analysis software.« less
Serial and parallel dynamic adaptation of general hybrid meshes
NASA Astrophysics Data System (ADS)
Kavouklis, Christos
The Navier-Stokes equations are a standard mathematical representation of viscous fluid flow. Their numerical solution in three dimensions remains a computationally intensive and challenging task, despite recent advances in computer speed and memory. A strategy to increase accuracy of Navier-Stokes simulations, while maintaining computing resources to a minimum, is local refinement of the associated computational mesh in regions of large solution gradients and coarsening in regions where the solution does not vary appreciably. In this work we consider adaptation of general hybrid meshes for Computational Fluid Dynamics (CFD) applications. Hybrid meshes are composed of four types of elements; hexahedra, prisms, pyramids and tetrahedra, and have been proven a promising technology in accurately resolving fluid flow for complex geometries. The first part of this dissertation is concerned with the design and implementation of a serial scheme for the adaptation of general three dimensional hybrid meshes. We have defined 29 refinement types, for all four kinds of elements. The core of the present adaptation scheme is an iterative algorithm that flags mesh edges for refinement, so that the adapted mesh is conformal. Of primary importance is considered the design of a suitable dynamic data structure that facilitates refinement and coarsening operations and furthermore minimizes memory requirements. A special dynamic list is defined for mesh elements, in contrast with the usual tree structures. It contains only elements of the current adaptation step and minimal information that is utilized to reconstruct parent elements when the mesh is coarsened. In the second part of this work, a new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid meshes is presented. Partitioning of a hybrid mesh reduces to partitioning of the corresponding dual graph. Communication among processors is based on the faces of the interpartition boundary. The distributed
Automatic Mesh Generation of Hybrid Mesh on Valves in Multiple Positions in Feedline Systems
NASA Technical Reports Server (NTRS)
Ross, Douglass H.; Ito, Yasushi; Dorothy, Fredric W.; Shih, Alan M.; Peugeot, John
2010-01-01
Fluid flow simulations through a valve often require evaluation of the valve in multiple opening positions. A mesh has to be generated for the valve for each position and compounding. The problem is the fact that the valve is typically part of a larger feedline system. In this paper, we propose to develop a system to create meshes for feedline systems with parametrically controlled valve openings. Herein we outline two approaches to generate the meshes for a valve in a feedline system at multiple positions. There are two issues that must be addressed. The first is the creation of the mesh on the valve for multiple positions. The second is the generation of the mesh for the total feedline system including the valve. For generation of the mesh on the valve, we will describe the use of topology matching and mesh generation parameter transfer. For generation of the total feedline system, we will describe two solutions that we have implemented. In both cases the valve is treated as a component in the feedline system. In the first method the geometry of the valve in the feedline system is replaced with a valve at a different opening position. Geometry is created to connect the valve to the feedline system. Then topology for the valve is created and the portion of the topology for the valve is topology matched to the standard valve in a different position. The mesh generation parameters are transferred and then the volume mesh for the whole feedline system is generated. The second method enables the user to generate the volume mesh on the valve in multiple open positions external to the feedline system, to insert it into the volume mesh of the feedline system, and to reduce the amount of computer time required for mesh generation because only two small volume meshes connecting the valve to the feedline mesh need to be updated.
Automated subject-specific, hexahedral mesh generation via image registration
Ji, Songbai; Ford, James C.; Greenwald, Richard M.; Beckwith, Jonathan G.; Paulsen, Keith D.; Flashman, Laura A.; McAllister, Thomas W.
2011-01-01
Generating subject-specific, all-hexahedral meshes for finite element analysis continues to be of significant interest in biomechanical research communities. To date, most automated methods “morph” an existing atlas mesh to match with a subject anatomy, which usually result in degradation in mesh quality because of mesh distortion. We present an automated meshing technique that produces satisfactory mesh quality and accuracy without mesh repair. An atlas mesh is first developed using a script. A subject-specific mesh is generated with the same script after transforming the geometry into the atlas space following rigid image registration, and is transformed back into the subject space. By meshing the brain in 11 subjects, we demonstrate that the technique’s performance is satisfactory in terms of both mesh quality (99.5% of elements had a scaled Jacobian >0.6 while <0.01% were between 0 and 0.2) and accuracy (average distance between mesh boundary and geometrical surface was 0.07 mm while <1% greater than 0.5mm). The combined computational cost for image registration and meshing was <4 min. Our results suggest that the technique is effective for generating subject-specific, all-hexahedral meshes and that it may be useful for meshing a variety of anatomical structures across different biomechanical research fields. PMID:21731153
PARAMESH: A Parallel Adaptive Mesh Refinement Community Toolkit
NASA Technical Reports Server (NTRS)
MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; deFainchtein, Rosalinda; Packer, Charles
1999-01-01
In this paper, we describe a community toolkit which is designed to provide parallel support with adaptive mesh capability for a large and important class of computational models, those using structured, logically cartesian meshes. The package of Fortran 90 subroutines, called PARAMESH, is designed to provide an application developer with an easy route to extend an existing serial code which uses a logically cartesian structured mesh into a parallel code with adaptive mesh refinement. Alternatively, in its simplest use, and with minimal effort, it can operate as a domain decomposition tool for users who want to parallelize their serial codes, but who do not wish to use adaptivity. The package can provide them with an incremental evolutionary path for their code, converting it first to uniformly refined parallel code, and then later if they so desire, adding adaptivity.
3D Compressible Melt Transport with Mesh Adaptivity
NASA Astrophysics Data System (ADS)
Dannberg, J.; Heister, T.
2015-12-01
Melt generation and migration have been the subject of numerous investigations. However, their typical time and length scales are vastly different from mantle convection, and the material properties are highly spatially variable and make the problem strongly non-linear. These challenges make it difficult to study these processes in a unified framework and in three dimensions. We present our extension of the mantle convection code ASPECT that allows for solving additional equations describing the behavior of melt percolating through and interacting with a viscously deforming host rock. One particular advantage is ASPECT's adaptive mesh refinement, as the resolution can be increased in areas where melt is present and viscosity gradients are steep, whereas a lower resolution is sufficient in regions without melt. Our approach includes both melt migration and melt generation, allowing for different melting parametrizations. In contrast to previous formulations, we consider the individual compressibilities of the solid and fluid phases in addition to compaction flow. This ensures self-consistency when linking melt generation to processes in the deeper mantle, where the compressibility of the solid phase becomes more important. We evaluate the functionality and potential of this method using a series of benchmarks and applications, including solitary waves, magmatic shear bands and melt generation and transport in a rising mantle plume. We compare results of the compressible and incompressible formulation and find melt volume differences of up to 15%. Moreover, we demonstrate that adaptive mesh refinement has the potential to reduce the runtime of a computation by more than one order of magnitude. Our model of magma dynamics provides a framework for investigating links between the deep mantle and melt generation and migration. This approach could prove particularly useful applied to modeling the generation of komatiites or other melts originating in greater depths.
CUBIT mesh generation environment. Volume 1: Users manual
Blacker, T.D.; Bohnhoff, W.J.; Edwards, T.L.
1994-05-01
The CUBIT mesh generation environment is a two- and three-dimensional finite element mesh generation tool which is being developed to pursue the goal of robust and unattended mesh generation--effectively automating the generation of quadrilateral and hexahedral elements. It is a solid-modeler based preprocessor that meshes volume and surface solid models for finite element analysis. A combination of techniques including paving, mapping, sweeping, and various other algorithms being developed are available for discretizing the geometry into a finite element mesh. CUBIT also features boundary layer meshing specifically designed for fluid flow problems. Boundary conditions can be applied to the mesh through the geometry and appropriate files for analysis generated. CUBIT is specifically designed to reduce the time required to create all-quadrilateral and all-hexahedral meshes. This manual is designed to serve as a reference and guide to creating finite element models in the CUBIT environment.
Parallel adaptive mesh refinement for electronic structure calculations
Kohn, S.; Weare, J.; Ong, E.; Baden, S.
1996-12-01
We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradients with multigrid preconditioning. We have parallelized our solver using an object-oriented adaptive mesh refinement framework.
Cubit Mesh Generation Toolkit V11.1
2009-03-25
CUBIT prepares models to be used in computer-based simulation of real-world events. CUBIT is a full-featured software toolkit for robust generation of two- and three-dimensional finite element meshes (grids) and geometry preparation. Its main goal is to reduce the time to generate meshes, particularly large hex meshes of complicated, interlocking assemblies.
The 3-D unstructured mesh generation using local transformations
NASA Technical Reports Server (NTRS)
Barth, Timothy J.
1993-01-01
The topics are presented in viewgraph form and include the following: 3D combinatorial edge swapping; 3D incremental triangulation via local transformations; a new approach to multigrid for unstructured meshes; surface mesh generation using local transforms; volume triangulations; viscous mesh generation; and future directions.
Adaptive Mesh Enrichment for the Poisson-Boltzmann Equation
NASA Astrophysics Data System (ADS)
Dyshlovenko, Pavel
2001-09-01
An adaptive mesh enrichment procedure for a finite-element solution of the two-dimensional Poisson-Boltzmann equation is described. The mesh adaptation is performed by subdividing the cells using information obtained in the previous step of the solution and next rearranging the mesh to be a Delaunay triangulation. The procedure allows the gradual improvement of the quality of the solution and adjustment of the geometry of the problem. The performance of the proposed approach is illustrated by applying it to the problem of two identical colloidal particles in a symmetric electrolyte.
Update on Development of Mesh Generation Algorithms in MeshKit
Jain, Rajeev; Vanderzee, Evan; Mahadevan, Vijay
2015-09-30
MeshKit uses a graph-based design for coding all its meshing algorithms, which includes the Reactor Geometry (and mesh) Generation (RGG) algorithms. This report highlights the developmental updates of all the algorithms, results and future work. Parallel versions of algorithms, documentation and performance results are reported. RGG GUI design was updated to incorporate new features requested by the users; boundary layer generation and parallel RGG support were added to the GUI. Key contributions to the release, upgrade and maintenance of other SIGMA1 libraries (CGM and MOAB) were made. Several fundamental meshing algorithms for creating a robust parallel meshing pipeline in MeshKit are under development. Results and current status of automated, open-source and high quality nuclear reactor assembly mesh generation algorithms such as trimesher, quadmesher, interval matching and multi-sweeper are reported.
Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes
Parsons, I D; Solberg, J M
2006-02-03
This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.
3D Compressible Melt Transport with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Dannberg, Juliane; Heister, Timo
2015-04-01
Melt generation and migration have been the subject of numerous investigations, but their typical time and length-scales are vastly different from mantle convection, which makes it difficult to study these processes in a unified framework. The equations that describe coupled Stokes-Darcy flow have been derived a long time ago and they have been successfully implemented and applied in numerical models (Keller et al., 2013). However, modelling magma dynamics poses the challenge of highly non-linear and spatially variable material properties, in particular the viscosity. Applying adaptive mesh refinement to this type of problems is particularly advantageous, as the resolution can be increased in mesh cells where melt is present and viscosity gradients are high, whereas a lower resolution is sufficient in regions without melt. In addition, previous models neglect the compressibility of both the solid and the fluid phase. However, experiments have shown that the melt density change from the depth of melt generation to the surface leads to a volume increase of up to 20%. Considering these volume changes in both phases also ensures self-consistency of models that strive to link melt generation to processes in the deeper mantle, where the compressibility of the solid phase becomes more important. We describe our extension of the finite-element mantle convection code ASPECT (Kronbichler et al., 2012) that allows for solving additional equations describing the behaviour of silicate melt percolating through and interacting with a viscously deforming host rock. We use the original compressible formulation of the McKenzie equations, augmented by an equation for the conservation of energy. This approach includes both melt migration and melt generation with the accompanying latent heat effects. We evaluate the functionality and potential of this method using a series of simple model setups and benchmarks, comparing results of the compressible and incompressible formulation and
Importance of dynamic mesh adaptivity for simulation of viscous fingering in porous media
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Jackson, M.; Pain, C.; Gorman, G.
2014-12-01
Viscous fingering is a major concern in many natural and engineered processes such as water flooding of heavy-oil reservoirs. Common reservoir simulators employ low-order finite volume/difference methods on structured grids to resolve this phenomenon. However, their approach suffers from a significant numerical dispersion error along the fingering patterns due to insufficient mesh resolution and smears out some important features of the flow. We propose use of an unstructured control volume finite element method for simulation of viscous fingering in porous media. Our approach is equipped with anisotropic mesh adaptivity where the mesh resolution is optimized based on the evolving features of flow. The adaptive algorithm uses a metric tensor field based on solution error estimates to locally control the size and shape of elements in the metric. We resolve the viscous fingering patterns accurately and reduce the numerical dispersion error significantly. The mesh optimization, generates an unstructured coarse mesh in other regions of the computational domain which significantly decreases the computational cost. The effect of grid resolution on the resolved fingers is thoroughly investigated. We analyze the computational cost of mesh adaptivty on unstructured mesh and compare it with common finite volume methods. The results of this study suggests that mesh adaptivity is an efficient and accurate approach for resolving complex behaviors and instabilities of flow in porous media such as viscous fingering.
3-D Mesh Generation Nonlinear Systems
1994-04-07
INGRID is a general-purpose, three-dimensional mesh generator developed for use with finite element, nonlinear, structural dynamics codes. INGRID generates the large and complex input data files for DYNA3D, NIKE3D, FACET, and TOPAZ3D. One of the greatest advantages of INGRID is that virtually any shape can be described without resorting to wedge elements, tetrahedrons, triangular elements or highly distorted quadrilateral or hexahedral elements. Other capabilities available are in the areas of geometry and graphics. Exact surfacemore » equations and surface intersections considerably improve the ability to deal with accurate models, and a hidden line graphics algorithm is included which is efficient on the most complicated meshes. The primary new capability is associated with the boundary conditions, loads, and material properties required by nonlinear mechanics programs. Commands have been designed for each case to minimize user effort. This is particularly important since special processing is almost always required for each load or boundary condition.« less
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
Peron, Stephanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes
NASA Technical Reports Server (NTRS)
Oliker, Leonid
1998-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at
Removal of line artifacts on mesh boundary in computer generated hologram by mesh phase matching.
Park, Jae-Hyeung; Yeom, Han-Ju; Kim, Hee-Jae; Zhang, HuiJun; Li, BoNi; Ji, Yeong-Min; Kim, Sang-Hoo
2015-03-23
Mesh-based computer generated hologram enables realistic and efficient representation of three-dimensional scene. However, the dark line artifacts on the boundary between neighboring meshes are frequently observed, degrading the quality of the reconstruction. In this paper, we propose a simple technique to remove the dark line artifacts by matching the phase on the boundary of neighboring meshes. The feasibility of the proposed method is confirmed by the numerical and optical reconstruction of the generated hologram.
Adaptive meshing technique applied to an orthopaedic finite element contact problem.
Roarty, Colleen M; Grosland, Nicole M
2004-01-01
Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants. Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely applied in the analysis and design of hip and knee implants, with additional joints (ankle, shoulder, wrist) attracting increased attention. The objective of this investigation was to develop a simplified adaptive meshing scheme to facilitate the finite element analysis of a dual-curvature total wrist implant. Using currently available software, the analyst has great flexibility in mesh generation, but must prescribe element sizes and refinement schemes throughout the domain of interest. Unfortunately, it is often difficult to predict in advance a mesh spacing that will give acceptable results. Adaptive finite-element mesh capabilities operate to continuously refine the mesh to improve accuracy where it is required, with minimal intervention by the analyst. Such mesh adaptation generally means that in certain areas of the analysis domain, the size of the elements is decreased (or increased) and/or the order of the elements may be increased (or decreased). In concept, mesh adaptation is very appealing. Although there have been several previous applications of adaptive meshing for in-house FE codes, we have coupled an adaptive mesh formulation with the pre-existing commercial programs PATRAN (MacNeal-Schwendler Corp., USA) and ABAQUS (Hibbit Karlson and Sorensen, Pawtucket, RI). In doing so, we have retained several attributes of the commercial software, which are very attractive for orthopaedic implant applications.
Adaptive upscaling with the dual mesh method
Guerillot, D.; Verdiere, S.
1997-08-01
The objective of this paper is to demonstrate that upscaling should be calculated during the flow simulation instead of trying to enhance the a priori upscaling methods. Hence, counter-examples are given to motivate our approach, the so-called Dual Mesh Method. The main steps of this numerical algorithm are recalled. Applications illustrate the necessity to consider different average relative permeability values depending on the direction in space. Moreover, these values could be different for the same average saturation. This proves that an a priori upscaling cannot be the answer even in homogeneous cases because of the {open_quotes}dynamical heterogeneity{close_quotes} created by the saturation profile. Other examples show the efficiency of the Dual Mesh Method applied to heterogeneous medium and to an actual field case in South America.
Structured Adaptive Mesh Refinement Application Infrastructure
2010-07-15
SAMRAI is an object-oriented support library for structured adaptice mesh refinement (SAMR) simulation of computational science problems, modeled by systems of partial differential equations (PDEs). SAMRAI is developed and maintained in the Center for Applied Scientific Computing (CASC) under ASCI ITS and PSE support. SAMRAI is used in a variety of application research efforts at LLNL and in academia. These applications are developed in collaboration with SAMRAI development team members.
Parallel tetrahedral mesh adaptation with dynamic load balancing
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
2000-06-28
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D-TAG, using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However, performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region, creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D-TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
1999-01-01
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D_TAG. using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However. performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region., creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D_TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Parallel adaptation of general three-dimensional hybrid meshes
Kavouklis, Christos Kallinderis, Yannis
2010-05-01
A new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid grids has been developed. The meshes considered in this work are composed of four kinds of elements; tetrahedra, prisms, hexahedra and pyramids, which poses a challenge to parallel mesh adaptation. Additional complexity imposed by the presence of multiple types of elements affects especially data migration, updates of local data structures and interpartition data structures. Efficient partition of hybrid meshes has been accomplished by transforming them to suitable graphs and using serial graph partitioning algorithms. Communication among processors is based on the faces of the interpartition boundary and the termination detection algorithm of Dijkstra is employed to ensure proper flagging of edges for refinement. An inexpensive dynamic load balancing strategy is introduced to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced which yields savings in computation time and relatively simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) data migration and dynamic updates of the local data structures, (ii) determination of the resulting interpartition boundary and (iii) identification of the communication pattern of processors. Several representative applications are included to evaluate the method.
Ibrahim, Ahmad M; Wilson, P.; Sawan, M.; Mosher, Scott W; Peplow, Douglas E.; Grove, Robert E
2013-01-01
Three mesh adaptivity algorithms were developed to facilitate and expedite the use of the CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques in accurate full-scale neutronics simulations of fusion energy systems with immense sizes and complicated geometries. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility and resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation. Additionally, because of the significant increase in the efficiency of FW-CADIS simulations, the three algorithms enabled this difficult calculation to be accurately solved on a regular computer cluster, eliminating the need for a world-class super computer.
Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme
NASA Astrophysics Data System (ADS)
Yabe, Takashi; Mizoe, Hiroki; Takizawa, Kenji; Moriki, Hiroshi; Im, Hyo-Nam; Ogata, Youichi
2004-02-01
A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.
A structured multi-block solution-adaptive mesh algorithm with mesh quality assessment
NASA Technical Reports Server (NTRS)
Ingram, Clint L.; Laflin, Kelly R.; Mcrae, D. Scott
1995-01-01
The dynamic solution adaptive grid algorithm, DSAGA3D, is extended to automatically adapt 2-D structured multi-block grids, including adaption of the block boundaries. The extension is general, requiring only input data concerning block structure, connectivity, and boundary conditions. Imbedded grid singular points are permitted, but must be prevented from moving in space. Solutions for workshop cases 1 and 2 are obtained on multi-block grids and illustrate both increased resolution of and alignment with the solution. A mesh quality assessment criteria is proposed to determine how well a given mesh resolves and aligns with the solution obtained upon it. The criteria is used to evaluate the grid quality for solutions of workshop case 6 obtained on both static and dynamically adapted grids. The results indicate that this criteria shows promise as a means of evaluating resolution.
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-09
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
NASA Astrophysics Data System (ADS)
Kolobov, Vladimir; Arslanbekov, Robert; Frolova, Anna
2014-12-01
The paper describes an Adaptive Mesh in Phase Space (AMPS) technique for solving kinetic equations with deterministic mesh-based methods. The AMPS technique allows automatic generation of adaptive Cartesian mesh in both physical and velocity spaces using a Tree-of-Trees data structure. We illustrate advantages of AMPS for simulations of rarefied gas dynamics and electron kinetics on low temperature plasmas. In particular, we consider formation of the velocity distribution functions in hypersonic flows, particle kinetics near oscillating boundaries, and electron kinetics in a radio-frequency sheath. AMPS provide substantial savings in computational cost and increased efficiency of the mesh-based kinetic solvers.
Developments and trends in three-dimensional mesh generation
NASA Technical Reports Server (NTRS)
Baker, Timothy J.
1989-01-01
An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. Recent progress is reviewed and the central themes are emphasized which form a solid foundation for future developments in mesh generation.
Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Philip, Bobby; Chacón, Luis; Pernice, Michael
2008-10-01
An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.
Adaptive mesh refinement for shocks and material interfaces
Dai, William Wenlong
2010-01-01
There are three kinds of adaptive mesh refinement (AMR) in structured meshes. Block-based AMR sometimes over refines meshes. Cell-based AMR treats cells cell by cell and thus loses the advantage of the nature of structured meshes. Patch-based AMR is intended to combine advantages of block- and cell-based AMR, i.e., the nature of structured meshes and sharp regions of refinement. But, patch-based AMR has its own difficulties. For example, patch-based AMR typically cannot preserve symmetries of physics problems. In this paper, we will present an approach for a patch-based AMR for hydrodynamics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, management of patches, and load balance. The special features of this patch-based AMR include symmetry preserving, efficiency of refinement across shock fronts and material interfaces, special implementation of flux correction, and patch management in parallel computing environments. To demonstrate the capability of the AMR framework, we will show both two- and three-dimensional hydrodynamics simulations with many levels of refinement.
Adaptive unstructured meshing for thermal stress analysis of built-up structures
NASA Technical Reports Server (NTRS)
Dechaumphai, Pramote
1992-01-01
An adaptive unstructured meshing technique for mechanical and thermal stress analysis of built-up structures has been developed. A triangular membrane finite element and a new plate bending element are evaluated on a panel with a circular cutout and a frame stiffened panel. The adaptive unstructured meshing technique, without a priori knowledge of the solution to the problem, generates clustered elements only where needed. An improved solution accuracy is obtained at a reduced problem size and analysis computational time as compared to the results produced by the standard finite element procedure.
An adaptive level set segmentation on a triangulated mesh.
Xu, Meihe; Thompson, Paul M; Toga, Arthur W
2004-02-01
Level set methods offer highly robust and accurate methods for detecting interfaces of complex structures. Efficient techniques are required to transform an interface to a globally defined level set function. In this paper, a novel level set method based on an adaptive triangular mesh is proposed for segmentation of medical images. Special attention is paid to an adaptive mesh refinement and redistancing technique for level set propagation, in order to achieve higher resolution at the interface with minimum expense. First, a narrow band around the interface is built in an upwind fashion. An active square technique is used to determine the shortest distance correspondence (SDC) for each grid vertex. Simultaneously, we also give an efficient approach for signing the distance field. Then, an adaptive improvement algorithm is proposed, which essentially combines two basic techniques: a long-edge-based vertex insertion strategy, and a local improvement. These guarantee that the refined triangulation is related to features along the front and has elements with appropriate size and shape, which fit the front well. We propose a short-edge elimination scheme to coarsen the refined triangular mesh, in order to reduce the extra storage. Finally, we reformulate the general evolution equation by updating 1) the velocities and 2) the gradient of level sets on the triangulated mesh. We give an approach for tracing contours from the level set on the triangulated mesh. Given a two-dimensional image with N grids along a side, the proposed algorithms run in O(kN) time at each iteration. Quantitative analysis shows that our algorithm is of first order accuracy; and when the interface-fitted property is involved in the mesh refinement, both the convergence speed and numerical accuracy are greatly improved. We also analyze the effect of redistancing frequency upon convergence speed and accuracy. Numerical examples include the extraction of inner and outer surfaces of the cerebral cortex
Numerical simulation of immiscible viscous fingering using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Adam, A.; Salinas, P.; Percival, J. R.; Pavlidis, D.; Pain, C.; Muggeridge, A. H.; Jackson, M.
2015-12-01
Displacement of one fluid by another in porous media occurs in various settings including hydrocarbon recovery, CO2 storage and water purification. When the invading fluid is of lower viscosity than the resident fluid, the displacement front is subject to a Saffman-Taylor instability and is unstable to transverse perturbations. These instabilities can grow, leading to fingering of the invading fluid. Numerical simulation of viscous fingering is challenging. The physics is controlled by a complex interplay of viscous and diffusive forces and it is necessary to ensure physical diffusion dominates numerical diffusion to obtain converged solutions. This typically requires the use of high mesh resolution and high order numerical methods. This is computationally expensive. We demonstrate here the use of a novel control volume - finite element (CVFE) method along with dynamic unstructured mesh adaptivity to simulate viscous fingering with higher accuracy and lower computational cost than conventional methods. Our CVFE method employs a discontinuous representation for both pressure and velocity, allowing the use of smaller control volumes (CVs). This yields higher resolution of the saturation field which is represented CV-wise. Moreover, dynamic mesh adaptivity allows high mesh resolution to be employed where it is required to resolve the fingers and lower resolution elsewhere. We use our results to re-examine the existing criteria that have been proposed to govern the onset of instability.Mesh adaptivity requires the mapping of data from one mesh to another. Conventional methods such as consistent interpolation do not readily generalise to discontinuous fields and are non-conservative. We further contribute a general framework for interpolation of CV fields by Galerkin projection. The method is conservative, higher order and yields improved results, particularly with higher order or discontinuous elements where existing approaches are often excessively diffusive.
Adaptive mesh refinement techniques for 3-D skin electrode modeling.
Sawicki, Bartosz; Okoniewski, Michal
2010-03-01
In this paper, we develop a 3-D adaptive mesh refinement technique. The algorithm is constructed with an electric impedance tomography forward problem and the finite-element method in mind, but is applicable to a much wider class of problems. We use the method to evaluate the distribution of currents injected into a model of a human body through skin contact electrodes. We demonstrate that the technique leads to a significantly improved solution, particularly near the electrodes. We discuss error estimation, efficiency, and quality of the refinement algorithm and methods that allow for preserving mesh attributes in the refinement process.
Adaptive mesh refinement for 1-dimensional gas dynamics
Hedstrom, G.; Rodrigue, G.; Berger, M.; Oliger, J.
1982-01-01
We consider the solution of the one-dimensional equation of gas-dynamics. Accurate numerical solutions are difficult to obtain on a given spatial mesh because of the existence of physical regions where components of the exact solution are either discontinuous or have large gradient changes. Numerical methods treat these phenomena in a variety of ways. In this paper, the method of adaptive mesh refinement is used. A thorough description of this method for general hyperbolic systems is given elsewhere and only properties of the method pertinent to the system are elaborated.
PLUM: Parallel Load Balancing for Adaptive Unstructured Meshes
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Saini, Subhash (Technical Monitor)
1998-01-01
Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. We present a novel method called PLUM to dynamically balance the processor workloads with a global view. This paper presents the implementation and integration of all major components within our dynamic load balancing strategy for adaptive grid calculations. Mesh adaption, repartitioning, processor assignment, and remapping are critical components of the framework that must be accomplished rapidly and efficiently so as not to cause a significant overhead to the numerical simulation. A data redistribution model is also presented that predicts the remapping cost on the SP2. This model is required to determine whether the gain from a balanced workload distribution offsets the cost of data movement. Results presented in this paper demonstrate that PLUM is an effective dynamic load balancing strategy which remains viable on a large number of processors.
QMESH,RENUM,QPLOT. Self-Organizing Mesh Generation
Jones, R.E.
1991-11-01
A set of five programs which make up a self organizing mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily shaped two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchal input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program, RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight node elements (with mid side nodes) may be obtained with RENUM8. QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers, An overall plot showing the position of the selected plot areas is produced.
Adaptive mesh strategies for the spectral element method
NASA Technical Reports Server (NTRS)
Mavriplis, Catherine
1992-01-01
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.
An arbitrary boundary triangle mesh generation method for multi-modality imaging
NASA Astrophysics Data System (ADS)
Zhang, Xuanxuan; Deng, Yong; Gong, Hui; Meng, Yuanzheng; Yang, Xiaoquan; Luo, Qingming
2011-11-01
Low-resolution and ill-posedness are the major challenges in diffuse optical tomography(DOT)/fluorescence molecular tomography(FMT). Recently, the multi-modality imaging technology that combines micro-computed tomography (micro-CT) with DOT/FMT is developed to improve resolution and ill-posedness. To take advantage of the fine priori anatomical maps obtained from micro-CT, we present an arbitrary boundary triangle mesh generation method for FMT/DOT/micro-CT multi-modality imaging. A planar straight line graph (PSLG) based on the image of micro-CT is obtained by an adaptive boundary sampling algorithm. The subregions of mesh are accurately matched with anatomical structures by a two-step solution, firstly, the triangles and nodes during mesh refinement are labeled respectively, and then a revising algorithm is used to modifying meshes of each subregion. The triangle meshes based on a regular model and a micro-CT image are generated respectively. The results show that the subregions of triangle meshes can match with anatomical structures accurately and triangle meshes have good quality. This provides an arbitrary boundaries triangle mesh generation method with the ability to incorporate the fine priori anatomical information into DOT/FMT reconstructions.
An arbitrary boundary triangle mesh generation method for multi-modality imaging
NASA Astrophysics Data System (ADS)
Zhang, Xuanxuan; Deng, Yong; Gong, Hui; Meng, Yuanzheng; Yang, Xiaoquan; Luo, Qingming
2012-03-01
Low-resolution and ill-posedness are the major challenges in diffuse optical tomography(DOT)/fluorescence molecular tomography(FMT). Recently, the multi-modality imaging technology that combines micro-computed tomography (micro-CT) with DOT/FMT is developed to improve resolution and ill-posedness. To take advantage of the fine priori anatomical maps obtained from micro-CT, we present an arbitrary boundary triangle mesh generation method for FMT/DOT/micro-CT multi-modality imaging. A planar straight line graph (PSLG) based on the image of micro-CT is obtained by an adaptive boundary sampling algorithm. The subregions of mesh are accurately matched with anatomical structures by a two-step solution, firstly, the triangles and nodes during mesh refinement are labeled respectively, and then a revising algorithm is used to modifying meshes of each subregion. The triangle meshes based on a regular model and a micro-CT image are generated respectively. The results show that the subregions of triangle meshes can match with anatomical structures accurately and triangle meshes have good quality. This provides an arbitrary boundaries triangle mesh generation method with the ability to incorporate the fine priori anatomical information into DOT/FMT reconstructions.
Parallel Block Structured Adaptive Mesh Refinement on Graphics Processing Units
Beckingsale, D. A.; Gaudin, W. P.; Hornung, R. D.; Gunney, B. T.; Gamblin, T.; Herdman, J. A.; Jarvis, S. A.
2014-11-17
Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87× faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
NASA Technical Reports Server (NTRS)
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Anisotropic norm-oriented mesh adaptation for a Poisson problem
NASA Astrophysics Data System (ADS)
Brèthes, Gautier; Dervieux, Alain
2016-10-01
We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.
A Diffusion Synthetic Acceleration Method for Block Adaptive Mesh Refinement.
Ward, R. C.; Baker, R. S.; Morel, J. E.
2005-01-01
A prototype two-dimensional Diffusion Synthetic Acceleration (DSA) method on a Block-based Adaptive Mesh Refinement (BAMR) transport mesh has been developed. The Block-Adaptive Mesh Refinement Diffusion Synthetic Acceleration (BAMR-DSA) method was tested in the PARallel TIme-Dependent SN (PARTISN) deterministic transport code. The BAMR-DSA equations are derived by differencing the DSA equation using a vertex-centered diffusion discretization that is diamond-like and may be characterized as 'partially' consistent. The derivation of a diffusion discretization that is fully consistent with diamond transport differencing on BAMR mesh does not appear to be possible. However, despite being partially consistent, the BAMR-DSA method is effective for many applications. The BAMR-DSA solver was implemented and tested in two dimensions for rectangular (XY) and cylindrical (RZ) geometries. Testing results confirm that a partially consistent BAMR-DSA method will introduce instabilities for extreme cases, e.g., scattering ratios approaching 1.0 with optically thick cells, but for most realistic problems the BAMR-DSA method provides effective acceleration. The initial use of a full matrix to store and LU-Decomposition to solve the BAMR-DSA equations has been extended to include Compressed Sparse Row (CSR) storage and a Conjugate Gradient (CG) solver. The CSR and CG methods provide significantly more efficient and faster storage and solution methods.
Configurational forces and variational mesh adaptation in solid dynamics
NASA Astrophysics Data System (ADS)
Zielonka, Matias G.
This thesis is concerned with the exploration and development of a variational finite element mesh adaption framework for non-linear solid dynamics and its conceptual links with the theory of dynamic configurational forces. The distinctive attribute of this methodology is that the underlying variational principle of the problem under study is used to supply both the discretized fields and the mesh on which the discretization is supported. To this end a mixed-multifield version of Hamilton's principle of stationary action and Lagrange-d'Alembert, principle is proposed, a fresh perspective on the theory of dynamic configurational forces is presented, and a unifying variational formulation that generalizes the framework to systems with general dissipative behavior is developed. A mixed finite element formulation with independent spatial interpolations for deformations and velocities and a mixed variational integrator with independent time interpolations for the resulting nodal parameters is constructed. This discretization is supported on a continuously deforming mesh that is not prescribed at the outset but computed as part of the solution. The resulting space-time discretization satisfies exact discrete configurational force balance and exhibits excellent long term global energy stability behavior. The robustness of the mesh adaption framework is assessed and demonstrated with a set of examples and convergence tests.
Projection of Discontinuous Galerkin Variable Distributions During Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Ballesteros, Carlos; Herrmann, Marcus
2012-11-01
Adaptive mesh refinement (AMR) methods decrease the computational expense of CFD simulations by increasing the density of solution cells only in areas of the computational domain that are of interest in that particular simulation. In particular, unstructured Cartesian AMR has several advantages over other AMR approaches, as it does not require the creation of numerous guard-cell blocks, neighboring cell lookups become straightforward, and the hexahedral nature of the mesh cells greatly simplifies the refinement and coarsening operations. The h-refinement from this AMR approach can be leveraged by making use of highly-accurate, but computationally costly methods, such as the Discontinuous Galerkin (DG) numerical method. DG methods are capable of high orders of accuracy while retaining stencil locality--a property critical to AMR using unstructured meshes. However, the use of DG methods with AMR requires the use of special flux and projection operators during refinement and coarsening operations in order to retain the high order of accuracy. The flux and projection operators needed for refinement and coarsening of unstructured Cartesian adaptive meshes using Legendre polynomial test functions will be discussed, and their performance will be shown using standard test cases.
Generation of multi-million element meshes for solid model-based geometries: The Dicer algorithm
Melander, D.J.; Benzley, S.E.; Tautges, T.J.
1997-06-01
The Dicer algorithm generates a fine mesh by refining each element in a coarse all-hexahedral mesh generated by any existing all-hexahedral mesh generation algorithm. The fine mesh is geometry-conforming. Using existing all-hexahedral meshing algorithms to define the initial coarse mesh simplifies the overall meshing process and allows dicing to take advantage of improvements in other meshing algorithms immediately. The Dicer algorithm will be used to generate large meshes in support of the ASCI program. The authors also plan to use dicing as the basis for parallel mesh generation. Dicing strikes a careful balance between the interactive mesh generation and multi-million element mesh generation processes for complex 3D geometries, providing an efficient means for producing meshes of varying refinement once the coarse mesh is obtained.
An adaptive mesh refinement algorithm for the discrete ordinates method
Jessee, J.P.; Fiveland, W.A.; Howell, L.H.; Colella, P.; Pember, R.B.
1996-03-01
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.
Hexahedral mesh generation via the dual arrangement of surfaces
Mitchell, S.A.; Tautges, T.J.
1997-12-31
Given a general three-dimensional geometry with a prescribed quadrilateral surface mesh, the authors consider the problem of constructing a hexahedral mesh of the geometry whose boundary is exactly the prescribed surface mesh. Due to the specialized topology of hexahedra, this problem is more difficult than the analogous one for tetrahedra. Folklore has maintained that a surface mesh must have a constrained structure in order for there to exist a compatible hexahedral mesh. However, they have proof that a surface mesh need only satisfy mild parity conditions, depending on the topology of the three-dimensional geometry, for there to exist a compatible hexahedral mesh. The proof is based on the realization that a hexahedral mesh is dual to an arrangement of surfaces, and the quadrilateral surface mesh is dual to the arrangement of curves bounding these surfaces. The proof is constructive and they are currently developing an algorithm called Whisker Weaving (WW) that mirrors the proof steps. Given the bounding curves, WW builds the topological structure of an arrangement of surfaces having those curves as its boundary. WW progresses in an advancing front manner. Certain local rules are applied to avoid structures that lead to poor mesh quality. Also, after the arrangement is constructed, additional surfaces are inserted to separate features, so e.g., no two hexahedra share more than one quadrilateral face. The algorithm has generated meshes for certain non-trivial problems, but is currently unreliable. The authors are exploring strategies for consistently selecting which portion of the surface arrangement to advance based on the existence proof. This should lead us to a robust algorithm for arbitrary geometries and surface meshes.
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
A fourth order accurate adaptive mesh refinement method forpoisson's equation
Barad, Michael; Colella, Phillip
2004-08-20
We present a block-structured adaptive mesh refinement (AMR) method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume AMR discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.
Visualizing Geophysical Flow Problems with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Sevre, E. O.; Yuen, D. A.; George, D. L.; Lee, S.
2011-12-01
Adaptive Mesh Refinement (AMR) is a technique used in software to decompose a computational domain based on the level of refinement necessary for spatial and temporal calculations. Comparing AMR runs to uniform grids allows for an unbounded gain in computational time. In this paper we will look at techniques for visualizing tsunami simulations that were run with AMR using the GeoClaw [Berger2011-1, Berger2011-2] software. Due to the computational efficiency of AMR we have decided to look into techniques for visualization of AMR data. By having good visualization tools for geoscientists more time can be spent interpreting results and analyzing data. Good visualization tools can be adapted easily to work with a variety of output formats, and the goal of this work is to provide a foundation for geoscientists to work with. In the past year GeoClaw has been used to model the 2011 Tohoku tsunami originating off the coast of Sendai Japan and delivering catastrophic damage to the Fukushima power plant. The aftermath of this single geologic event is still making headlines 4 months after the fact [Fackler2011]. GeoClaw utilizes the shallow water equations to model a variety of flows that range from tsunami to floods to landslides and debris flows [George2011]. With the advanced computations provided by AMR it is important for researchers to visualize and understand ways that are meaningful to both scientists and civilians affected by the potential outcomes of the computation. Special visualization techniques can be used to visualize and look at data generated with AMR. By incorporating these techniques into their software geoscientists will be able to harness powerful computational tools, such as GeoClaw, while also maintaining an informative view of their data.
Volume Decomposition and Feature Recognition for Hexahedral Mesh Generation
GADH,RAJIT; LU,YONG; TAUTGES,TIMOTHY J.
1999-09-27
Considerable progress has been made on automatic hexahedral mesh generation in recent years. Several automatic meshing algorithms have proven to be very reliable on certain classes of geometry. While it is always worth pursuing general algorithms viable on more general geometry, a combination of the well-established algorithms is ready to take on classes of complicated geometry. By partitioning the entire geometry into meshable pieces matched with appropriate meshing algorithm the original geometry becomes meshable and may achieve better mesh quality. Each meshable portion is recognized as a meshing feature. This paper, which is a part of the feature based meshing methodology, presents the work on shape recognition and volume decomposition to automatically decompose a CAD model into meshable volumes. There are four phases in this approach: (1) Feature Determination to extinct decomposition features, (2) Cutting Surfaces Generation to form the ''tailored'' cutting surfaces, (3) Body Decomposition to get the imprinted volumes; and (4) Meshing Algorithm Assignment to match volumes decomposed with appropriate meshing algorithms. The feature determination procedure is based on the CLoop feature recognition algorithm that is extended to be more general. Results are demonstrated over several parts with complicated topology and geometry.
Advances in Patch-Based Adaptive Mesh Refinement Scalability
Gunney, Brian T.N.; Anderson, Robert W.
2015-12-18
Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extension of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.
Advances in Patch-Based Adaptive Mesh Refinement Scalability
Gunney, Brian T.N.; Anderson, Robert W.
2015-12-18
Patch-based structured adaptive mesh refinement (SAMR) is widely used for high-resolution simu- lations. Combined with modern supercomputers, it could provide simulations of unprecedented size and resolution. A persistent challenge for this com- bination has been managing dynamically adaptive meshes on more and more MPI tasks. The dis- tributed mesh management scheme in SAMRAI has made some progress SAMR scalability, but early al- gorithms still had trouble scaling past the regime of 105 MPI tasks. This work provides two critical SAMR regridding algorithms, which are integrated into that scheme to ensure efficiency of the whole. The clustering algorithm is an extensionmore » of the tile- clustering approach, making it more flexible and efficient in both clustering and parallelism. The partitioner is a new algorithm designed to prevent the network congestion experienced by its prede- cessor. We evaluated performance using weak- and strong-scaling benchmarks designed to be difficult for dynamic adaptivity. Results show good scaling on up to 1.5M cores and 2M MPI tasks. Detailed timing diagnostics suggest scaling would continue well past that.« less
Adaptive radial basis function mesh deformation using data reduction
NASA Astrophysics Data System (ADS)
Gillebaart, T.; Blom, D. S.; van Zuijlen, A. H.; Bijl, H.
2016-09-01
Radial Basis Function (RBF) mesh deformation is one of the most robust mesh deformation methods available. Using the greedy (data reduction) method in combination with an explicit boundary correction, results in an efficient method as shown in literature. However, to ensure the method remains robust, two issues are addressed: 1) how to ensure that the set of control points remains an accurate representation of the geometry in time and 2) how to use/automate the explicit boundary correction, while ensuring a high mesh quality. In this paper, we propose an adaptive RBF mesh deformation method, which ensures the set of control points always represents the geometry/displacement up to a certain (user-specified) criteria, by keeping track of the boundary error throughout the simulation and re-selecting when needed. Opposed to the unit displacement and prescribed displacement selection methods, the adaptive method is more robust, user-independent and efficient, for the cases considered. Secondly, the analysis of a single high aspect ratio cell is used to formulate an equation for the correction radius needed, depending on the characteristics of the correction function used, maximum aspect ratio, minimum first cell height and boundary error. Based on the analysis two new radial basis correction functions are derived and proposed. This proposed automated procedure is verified while varying the correction function, Reynolds number (and thus first cell height and aspect ratio) and boundary error. Finally, the parallel efficiency is studied for the two adaptive methods, unit displacement and prescribed displacement for both the CPU as well as the memory formulation with a 2D oscillating and translating airfoil with oscillating flap, a 3D flexible locally deforming tube and deforming wind turbine blade. Generally, the memory formulation requires less work (due to the large amount of work required for evaluating RBF's), but the parallel efficiency reduces due to the limited
Block-structured adaptive mesh refinement - theory, implementation and application
Deiterding, Ralf
2011-01-01
Structured adaptive mesh refinement (SAMR) techniques can enable cutting-edge simulations of problems governed by conservation laws. Focusing on the strictly hyperbolic case, these notes explain all algorithmic and mathematical details of a technically relevant implementation tailored for distributed memory computers. An overview of the background of commonly used finite volume discretizations for gas dynamics is included and typical benchmarks to quantify accuracy and performance of the dynamically adaptive code are discussed. Large-scale simulations of shock-induced realistic combustion in non-Cartesian geometry and shock-driven fluid-structure interaction with fully coupled dynamic boundary motion demonstrate the applicability of the discussed techniques for complex scenarios.
Mesh adaptation technique for Fourier-domain fluorescence lifetime imaging
Soloviev, Vadim Y.
2006-11-15
A novel adaptive mesh technique in the Fourier domain is introduced for problems in fluorescence lifetime imaging. A dynamical adaptation of the three-dimensional scheme based on the finite volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. Light propagation in the medium is modeled by the telegraph equation, while the lifetime reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the method are demonstrated by image reconstruction of two spherical fluorescent objects embedded in a tissue phantom.
Automatic mesh adaptivity for CADIS and FW-CADIS neutronics modeling of difficult shielding problems
Ibrahim, A. M.; Peplow, D. E.; Mosher, S. W.; Wagner, J. C.; Evans, T. M.; Wilson, P. P.; Sawan, M. E.
2013-07-01
The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macro-material approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm de-couples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, obviating the need for a world-class super computer. (authors)
Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert E.
2015-06-30
The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as muchmore » geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.« less
Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed E.; Mosher, Scott W.; Peplow, Douglas E.; Wagner, John C.; Evans, Thomas M.; Grove, Robert E.
2015-06-30
The CADIS and FW-CADIS hybrid Monte Carlo/deterministic techniques dramatically increase the efficiency of neutronics modeling, but their use in the accurate design analysis of very large and geometrically complex nuclear systems has been limited by the large number of processors and memory requirements for their preliminary deterministic calculations and final Monte Carlo calculation. Three mesh adaptivity algorithms were developed to reduce the memory requirements of CADIS and FW-CADIS without sacrificing their efficiency improvement. First, a macromaterial approach enhances the fidelity of the deterministic models without changing the mesh. Second, a deterministic mesh refinement algorithm generates meshes that capture as much geometric detail as possible without exceeding a specified maximum number of mesh elements. Finally, a weight window coarsening algorithm decouples the weight window mesh and energy bins from the mesh and energy group structure of the deterministic calculations in order to remove the memory constraint of the weight window map from the deterministic mesh resolution. The three algorithms were used to enhance an FW-CADIS calculation of the prompt dose rate throughout the ITER experimental facility. Using these algorithms resulted in a 23.3% increase in the number of mesh tally elements in which the dose rates were calculated in a 10-day Monte Carlo calculation and, additionally, increased the efficiency of the Monte Carlo simulation by a factor of at least 3.4. The three algorithms enabled this difficult calculation to be accurately solved using an FW-CADIS simulation on a regular computer cluster, eliminating the need for a world-class super computer.
Fluidity: A New Adaptive, Unstructured Mesh Geodynamics Model
NASA Astrophysics Data System (ADS)
Davies, D. R.; Wilson, C. R.; Kramer, S. C.; Piggott, M. D.; Le Voci, G.; Collins, G. S.
2010-05-01
Fluidity is a sophisticated fluid dynamics package, which has been developed by the Applied Modelling and Computation Group (AMCG) at Imperial College London. It has many environmental applications, from nuclear reactor safety to simulations of ocean circulation. Fluidity has state-of-the-art features that place it at the forefront of computational fluid dynamics. The code: Dynamically optimizes the mesh, providing increased resolution in areas of dynamic importance, thus allowing for accurate simulations across a range of length scales, within a single model. Uses an unstructured mesh, which enables the representation of complex geometries. It also enhances mesh optimization using anisotropic elements, which are particularly useful for resolving one-dimensional flow features and material interfaces. Uses implicit solvers thus allowing for large time-steps with minimal loss of accuracy. PETSc provides some of these, though multigrid preconditioning methods have been developed in-house. Is optimized to run on parallel processors and has the ability to perform parallel mesh adaptivity - the subdomains used in parallel computing automatically adjust themselves to balance the computational load on each processor, as the mesh evolves. Has a novel interface-preserving advection scheme for maintaining sharp interfaces between multiple materials / components. Has an automated test-bed for verification of model developments. Such attributes provide an extremely powerful base on which to build a new geodynamical model. Incorporating into Fluidity the necessary physics and numerical technology for geodynamical flows is an ongoing task, though progress, to date, includes: Development and implementation of parallel, scalable solvers for Stokes flow, which can handle sharp, orders of magnitude variations in viscosity and, significantly, an anisotropic viscosity tensor. Modification of the multi-material interface-preserving scheme to allow for tracking of chemical
Passive intermodulation generation in wire mesh deployable reflector antennas
NASA Technical Reports Server (NTRS)
Turner, Gregory M.
1993-01-01
Deployable reflector antennas represent a proven technology with obvious benefits for mobile satellite applications. Harris Corporation has provided deployable reflector antennas for NASA's Tracking and Data Relay Satellite System (TDRSS). These antennas utilize a rigid, radial rib unfurlable reflector with a wire mesh surface. This type of mesh has been identified as a potential design risk for multichannel communications applications based on the potential for generation of Passive Intermodulation (PIM). These concerns are based on the existence of numerous, nonpermanent metal to metal contacts that are inherent to the mesh design. To address this issue, Harris has an ongoing IR&D program to characterize mesh PIM performance. This paper presents the results of the investigation into mesh PIM performance to date and provides background information on the design and performance of the Harris radial rib deployable reflector.
Passive intermodulation generation in wire mesh deployable reflector antennas
NASA Astrophysics Data System (ADS)
Turner, Gregory M.
Deployable reflector antennas represent a proven technology with obvious benefits for mobile satellite applications. Harris Corporation has provided deployable reflector antennas for NASA's Tracking and Data Relay Satellite System (TDRSS). These antennas utilize a rigid, radial rib unfurlable reflector with a wire mesh surface. This type of mesh has been identified as a potential design risk for multichannel communications applications based on the potential for generation of Passive Intermodulation (PIM). These concerns are based on the existence of numerous, nonpermanent metal to metal contacts that are inherent to the mesh design. To address this issue, Harris has an ongoing IR&D program to characterize mesh PIM performance. This paper presents the results of the investigation into mesh PIM performance to date and provides background information on the design and performance of the Harris radial rib deployable reflector.
N-Body Code with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Yahagi, Hideki; Yoshii, Yuzuru
2001-09-01
We have developed a simulation code with the techniques that enhance both spatial and time resolution of the particle-mesh (PM) method, for which the spatial resolution is restricted by the spacing of structured mesh. The adaptive-mesh refinement (AMR) technique subdivides the cells that satisfy the refinement criterion recursively. The hierarchical meshes are maintained by the special data structure and are modified in accordance with the change of particle distribution. In general, as the resolution of the simulation increases, its time step must be shortened and more computational time is required to complete the simulation. Since the AMR enhances the spatial resolution locally, we reduce the time step locally also, instead of shortening it globally. For this purpose, we used a technique of hierarchical time steps (HTS), which changes the time step, from particle to particle, depending on the size of the cell in which particles reside. Some test calculations show that our implementation of AMR and HTS is successful. We have performed cosmological simulation runs based on our code and found that many of halo objects have density profiles that are well fitted to the universal profile proposed in 1996 by Navarro, Frenk, & White over the entire range of their radius.
Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.
2001-12-01
Several physical systems, such as nonrelativistic and relativistic magnetohydrodynamics (MHD), radiation MHD, electromagnetics, and incompressible hydrodynamics, satisfy Stoke's law type equations for the divergence-free evolution of vector fields. In this paper we present a full-fledged scheme for the second-order accurate, divergence-free evolution of vector fields on an adaptive mesh refinement (AMR) hierarchy. We focus here on adaptive mesh MHD. However, the scheme has applicability to the other systems of equations mentioned above. The scheme is based on making a significant advance in the divergence-free reconstruction of vector fields. In that sense, it complements the earlier work of D. S. Balsara and D. S. Spicer (1999, J. Comput. Phys. 7, 270) where we discussed the divergence-free time-update of vector fields which satisfy Stoke's law type evolution equations. Our advance in divergence-free reconstruction of vector fields is such that it reduces to the total variation diminishing (TVD) property for one-dimensional evolution and yet goes beyond it in multiple dimensions. For that reason, it is extremely suitable for the construction of higher order Godunov schemes for MHD. Both the two-dimensional and three-dimensional reconstruction strategies are developed. A slight extension of the divergence-free reconstruction procedure yields a divergence-free prolongation strategy for prolonging magnetic fields on AMR hierarchies. Divergence-free restriction is also discussed. Because our work is based on an integral formulation, divergence-free restriction and prolongation can be carried out on AMR meshes with any integral refinement ratio, though we specialize the expressions for the most popular situation where the refinement ratio is two. Furthermore, we pay attention to the fact that in order to efficiently evolve the MHD equations on AMR hierarchies, the refined meshes must evolve in time with time steps that are a fraction of their parent mesh's time step
Elliptic Solvers with Adaptive Mesh Refinement on Complex Geometries
Phillip, B.
2000-07-24
Adaptive Mesh Refinement (AMR) is a numerical technique for locally tailoring the resolution computational grids. Multilevel algorithms for solving elliptic problems on adaptive grids include the Fast Adaptive Composite grid method (FAC) and its parallel variants (AFAC and AFACx). Theory that confirms the independence of the convergence rates of FAC and AFAC on the number of refinement levels exists under certain ellipticity and approximation property conditions. Similar theory needs to be developed for AFACx. The effectiveness of multigrid-based elliptic solvers such as FAC, AFAC, and AFACx on adaptively refined overlapping grids is not clearly understood. Finally, a non-trivial eye model problem will be solved by combining the power of using overlapping grids for complex moving geometries, AMR, and multilevel elliptic solvers.
Lazarov, R; Pasciak, J; Jones, J
2002-02-01
Construction, analysis and numerical testing of efficient solution techniques for solving elliptic PDEs that allow for parallel implementation have been the focus of the research. A number of discretization and solution methods for solving second order elliptic problems that include mortar and penalty approximations and domain decomposition methods for finite elements and finite volumes have been investigated and analyzed. Techniques for parallel domain decomposition algorithms in the framework of PETC and HYPRE have been studied and tested. Hierarchical parallel grid refinement and adaptive solution methods have been implemented and tested on various model problems. A parallel code implementing the mortar method with algebraically constructed multiplier spaces was developed.
Extraction and applications of skeletons in finite element mesh generation.
Quadros, William Roshan
2010-05-01
This paper focuses on the extraction of skeletons of CAD models and its applications in finite element (FE) mesh generation. The term 'skeleton of a CAD model' can be visualized as analogous to the 'skeleton of a human body'. The skeletal representations covered in this paper include medial axis transform (MAT), Voronoi diagram (VD), chordal axis transform (CAT), mid surface, digital skeletons, and disconnected skeletons. In the literature, the properties of a skeleton have been utilized in developing various algorithms for extracting skeletons. Three main approaches include: (1) the bisection method where the skeleton exists at equidistant from at least two points on boundary, (2) the grassfire propagation method in which the skeleton exists where the opposing fronts meet, and (3) the duality method where the skeleton is a dual of the object. In the last decade, the author has applied different skeletal representations in all-quad meshing, hex meshing, mid-surface meshing, mesh size function generation, defeaturing, and decomposition. A brief discussion on the related work from other researchers in the area of tri meshing, tet meshing, and anisotropic meshing is also included. This paper concludes by summarizing the strengths and weaknesses of the skeleton-based approaches in solving various geometry-centered problems in FE mesh generation. The skeletons have proved to be a great shape abstraction tool in analyzing the geometric complexity of CAD models as they are symmetric, simpler (reduced dimension), and provide local thickness information. However, skeletons generally require some cleanup, and stability and sensitivity of the skeletons should be controlled during extraction. Also, selecting a suitable application-specific skeleton and a computationally efficient method of extraction is critical.
Fully implicit adaptive mesh refinement algorithm for reduced MHD
NASA Astrophysics Data System (ADS)
Philip, Bobby; Pernice, Michael; Chacon, Luis
2006-10-01
In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)
Three dimensional mesh generation by triangulation of arbitrary point sets
NASA Technical Reports Server (NTRS)
Baker, Timothy J.
1987-01-01
A method for generating an unstructured mesh is described. The approach is quite general and joins an arbitrary set of points to produce a covering of three dimensional space by tetrahedra. After removing the tetrahedra that connect surface points, a mesh suitable for a finite element based flow solver is obtained. Details of the triangulation algorithm are provided together with an analysis of the algorithm efficiency and validity.
NASA Technical Reports Server (NTRS)
Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.
2014-01-01
Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.
AMRA: An Adaptive Mesh Refinement hydrodynamic code for astrophysics
NASA Astrophysics Data System (ADS)
Plewa, T.; Müller, E.
2001-08-01
Implementation details and test cases of a newly developed hydrodynamic code, amra, are presented. The numerical scheme exploits the adaptive mesh refinement technique coupled to modern high-resolution schemes which are suitable for relativistic and non-relativistic flows. Various physical processes are incorporated using the operator splitting approach, and include self-gravity, nuclear burning, physical viscosity, implicit and explicit schemes for conductive transport, simplified photoionization, and radiative losses from an optically thin plasma. Several aspects related to the accuracy and stability of the scheme are discussed in the context of hydrodynamic and astrophysical flows.
Computational relativistic astrophysics with adaptive mesh refinement: Testbeds
Evans, Edwin; Iyer, Sai; Tao Jian; Wolfmeyer, Randy; Zhang Huimin; Schnetter, Erik; Suen, Wai-Mo
2005-04-15
We have carried out numerical simulations of strongly gravitating systems based on the Einstein equations coupled to the relativistic hydrodynamic equations using adaptive mesh refinement (AMR) techniques. We show AMR simulations of NS binary inspiral and coalescence carried out on a workstation having an accuracy equivalent to that of a 1025{sup 3} regular unigrid simulation, which is, to the best of our knowledge, larger than all previous simulations of similar NS systems on supercomputers. We believe the capability opens new possibilities in general relativistic simulations.
FLY: a Tree Code for Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Becciani, U.; Antonuccio-Delogu, V.; Costa, A.; Ferro, D.
FLY is a public domain parallel treecode, which makes heavy use of the one-sided communication paradigm to handle the management of the tree structure. It implements the equations for cosmological evolution and can be run for different cosmological models. This paper shows an example of the integration of a tree N-body code with an adaptive mesh, following the PARAMESH scheme. This new implementation will allow the FLY output, and more generally any binary output, to be used with any hydrodynamics code that adopts the PARAMESH data structure, to study compressible flow problems.
Shape design sensitivities using fully automatic 3-D mesh generation
NASA Technical Reports Server (NTRS)
Botkin, M. E.
1990-01-01
Previous work in three dimensional shape optimization involved specifying design variables by associating parameters directly with mesh points. More recent work has shown the use of fully-automatic mesh generation based upon a parameterized geometric representation. Design variables have been associated with a mathematical model of the part rather than the discretized representation. The mesh generation procedure uses a nonuniform grid intersection technique to place nodal points directly on the surface geometry. Although there exists an associativity between the mesh and the geometrical/topological entities, there is no mathematical functional relationship. This poses a problem during certain steps in the optimization process in which geometry modification is required. For the large geometrical changes which occur at the beginning of each optimization step, a completely new mesh is created. However, for gradient calculations many small changes must be made and it would be too costly to regenerate the mesh for each design variable perturbation. For that reason, a local remeshing procedure has been implemented which operates only on the specific edges and faces associated with the design variable being perturbed. Two realistic design problems are presented which show the efficiency of this process and test the accuracy of the gradient computations.
Thermal-chemical Mantle Convection Models With Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Leng, W.; Zhong, S.
2008-12-01
In numerical modeling of mantle convection, resolution is often crucial for resolving small-scale features. New techniques, adaptive mesh refinement (AMR), allow local mesh refinement wherever high resolution is needed, while leaving other regions with relatively low resolution. Both computational efficiency for large- scale simulation and accuracy for small-scale features can thus be achieved with AMR. Based on the octree data structure [Tu et al. 2005], we implement the AMR techniques into the 2-D mantle convection models. For pure thermal convection models, benchmark tests show that our code can achieve high accuracy with relatively small number of elements both for isoviscous cases (i.e. 7492 AMR elements v.s. 65536 uniform elements) and for temperature-dependent viscosity cases (i.e. 14620 AMR elements v.s. 65536 uniform elements). We further implement tracer-method into the models for simulating thermal-chemical convection. By appropriately adding and removing tracers according to the refinement of the meshes, our code successfully reproduces the benchmark results in van Keken et al. [1997] with much fewer elements and tracers compared with uniform-mesh models (i.e. 7552 AMR elements v.s. 16384 uniform elements, and ~83000 tracers v.s. ~410000 tracers). The boundaries of the chemical piles in our AMR code can be easily refined to the scales of a few kilometers for the Earth's mantle and the tracers are concentrated near the chemical boundaries to precisely trace the evolvement of the boundaries. It is thus very suitable for our AMR code to study the thermal-chemical convection problems which need high resolution to resolve the evolvement of chemical boundaries, such as the entrainment problems [Sleep, 1988].
Wilson, B G; Sonnad, V
2011-02-14
Precise electronic structure calculations of ions in plasmas benefit from optimized numerical radial meshes. A new closed form expression for obtaining non-linear parameters for the efficient generation of analytic log-linear radial meshes is presented. In conjunction with the (very simple) algorithm for the rapid high precision evaluation of Lambert's W-function, the above identity allows the precise construction of generalized log-linear radial meshes adapted to various constraints.
Detecting Translation Errors in CAD Surfaces and Preparing Geometries for Mesh Generation
Petersson, N Anders; Chand, K K
2001-08-27
The authors have developed tools for the efficient preparation of CAD geometries for mesh generation. Geometries are read from IGES files and then maintained in a boundary-representation consisting of a patchwork of trimmed and untrimmed surfaces. Gross errors in the geometry can be identified and removed automatically while a user interface is provided for manipulating the geometry (such as correcting invalid trimming curves or removing unwanted details). Modifying the geometry by adding or deleting surfaces and/or sectioning it by arbitrary planes (e.g. symmetry planes) is also supported. These tools are used for robust and accurate geometry models for initial mesh generation and will be applied to in situ mesh generation requirements of moving and adaptive grid simulations.
Parallel Processing of Adaptive Meshes with Load Balancing
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Biegel, Bryan (Technical Monitor)
2001-01-01
Many scientific applications involve grids that lack a uniform underlying structure. These applications are often also dynamic in nature in that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of unstructured grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing interprocessor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view of system loads across processors. In this paper, we propose a novel and general-purpose load balancer that utilizes symmetric broadcast networks (SBN) as the underlying communication topology, and compare its performance with a successful global load balancing environment, called PLUM, specifically created to handle adaptive unstructured applications. Our experimental results on an IBM SP2 demonstrate that the SBN-based load balancer achieves lower redistribution costs than that under PLUM by overlapping processing and data migration.
Dynamic Load Balancing for Adaptive Meshes using Symmetric Broadcast Networks
NASA Technical Reports Server (NTRS)
Das, Sajal K.; Harvey, Daniel J.; Biswas, Rupak; Saini, Subhash (Technical Monitor)
1998-01-01
Many scientific applications involve grids that lack a uniform underlying structure. These applications are often dynamic in the sense that the grid structure significantly changes between successive phases of execution. In parallel computing environments, mesh adaptation of grids through selective refinement/coarsening has proven to be an effective approach. However, achieving load balance while minimizing inter-processor communication and redistribution costs is a difficult problem. Traditional dynamic load balancers are mostly inadequate because they lack a global view across processors. In this paper, we compare a novel load balancer that utilizes symmetric broadcast networks (SBN) to a successful global load balancing environment (PLUM) created to handle adaptive unstructured applications. Our experimental results on the IBM SP2 demonstrate that performance of the proposed SBN load balancer is comparable to results achieved under PLUM.
QMESH,RENUM,QPLOT. Self-Organizing Mesh Generation
Jones, R.E.; Schkade, A.F.
1991-11-01
A set of five programs which make up a self-organizing mesh generation package. QMESH generates meshes having quadrilateral elements on arbitrarily shaped two-dimensional (planar or axisymmetric) bodies. It is designed for use with two-dimensional finite element analysis applications. A flexible hierarchal input scheme is used to describe bodies to QMESH as collections of regions. A mesh for each region is developed independently, with the final assembly and bandwidth minimization performed by the independent program, RENUM or RENUM8. RENUM is applied when four-node elements are desired. Eight-node elements (with mid-size nodes) may be obtained with RENUM8. QPLOT and QPLOT8 are plot programs for meshes generated by the QMESH/RENUM and QMESH/RENUM8 program pairs, respectively. QPLOT and QPLOT8 automatically section the mesh into appropriately-sized sections for legible display of node and element numbers. An overall plot showing the position of the selected plot areas is produced.
D Octree Based Watertight Mesh Generation from Ubiquitous Data
NASA Astrophysics Data System (ADS)
Caraffa, L.; Brédif, M.; Vallet, B.
2015-08-01
Despite of the popularity of Delauney structure for mesh generation, octree based approaches remain an interesting solution for a first step surface reconstruction. In this paper, we propose a generic framework for a octree cell based mesh generation. Its input is a set of Lidar-based 3D measurements or other inputs which are formulated as a set of mass functions that characterize the level of confidence on the occupancy of each octree's leaf. The output is a binary segmentation of the space between occupied and empty areas by taking into account the uncertainty of data. To this end, the problem is then reduced to a global energy optimization framework efficiently optimized with a min-cut approach. We use the approach for producing a large scale surface reconstruction algorithm by merging data from ubiquitous sources like airborne, terrestrial Lidar data, occupancy map and extra cues. Once the surface is computed, a solution is proposed for texturing the mesh.
An adaptive mesh-moving and refinement procedure for one-dimensional conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Flaherty, Joseph E.; Arney, David C.
1993-01-01
We examine the performance of an adaptive mesh-moving and /or local mesh refinement procedure for the finite difference solution of one-dimensional hyperbolic systems of conservation laws. Adaptive motion of a base mesh is designed to isolate spatially distinct phenomena, and recursive local refinement of the time step and cells of the stationary or moving base mesh is performed in regions where a refinement indicator exceeds a prescribed tolerance. These adaptive procedures are incorporated into a computer code that includes a MacCormack finite difference scheme wih Davis' artificial viscosity model and a discretization error estimate based on Richardson's extrapolation. Experiments are conducted on three problems in order to qualify the advantages of adaptive techniques relative to uniform mesh computations and the relative benefits of mesh moving and refinement. Key results indicate that local mesh refinement, with and without mesh moving, can provide reliable solutions at much lower computational cost than possible on uniform meshes; that mesh motion can be used to improve the results of uniform mesh solutions for a modest computational effort; that the cost of managing the tree data structure associated with refinement is small; and that a combination of mesh motion and refinement reliably produces solutions for the least cost per unit accuracy.
A General-Purpose Mesh Generator for Finite Element Codes.
1984-02-28
Version 00 INGEN is a general-purpose mesh generator for use in conjunction with two and three dimensional finite element programs. The basic components of INGEN are surface and three-dimensional region generators that use linear-blending interpolation formulae. These generators are based on an i, j, k index scheme, which is used to number nodal points, construct elements, and develop displacement and traction boundary conditions.
Adaptive mesh refinement and adjoint methods in geophysics simulations
NASA Astrophysics Data System (ADS)
Burstedde, Carsten
2013-04-01
It is an ongoing challenge to increase the resolution that can be achieved by numerical geophysics simulations. This applies to considering sub-kilometer mesh spacings in global-scale mantle convection simulations as well as to using frequencies up to 1 Hz in seismic wave propagation simulations. One central issue is the numerical cost, since for three-dimensional space discretizations, possibly combined with time stepping schemes, a doubling of resolution can lead to an increase in storage requirements and run time by factors between 8 and 16. A related challenge lies in the fact that an increase in resolution also increases the dimensionality of the model space that is needed to fully parametrize the physical properties of the simulated object (a.k.a. earth). Systems that exhibit a multiscale structure in space are candidates for employing adaptive mesh refinement, which varies the resolution locally. An example that we found well suited is the mantle, where plate boundaries and fault zones require a resolution on the km scale, while deeper area can be treated with 50 or 100 km mesh spacings. This approach effectively reduces the number of computational variables by several orders of magnitude. While in this case it is possible to derive the local adaptation pattern from known physical parameters, it is often unclear what are the most suitable criteria for adaptation. We will present the goal-oriented error estimation procedure, where such criteria are derived from an objective functional that represents the observables to be computed most accurately. Even though this approach is well studied, it is rarely used in the geophysics community. A related strategy to make finer resolution manageable is to design methods that automate the inference of model parameters. Tweaking more than a handful of numbers and judging the quality of the simulation by adhoc comparisons to known facts and observations is a tedious task and fundamentally limited by the turnaround times
Generating unstructured nuclear reactor core meshes in parallel
Jain, Rajeev; Tautges, Timothy J.
2014-10-24
Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor core examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.
Loft: An Automated Mesh Generator for Stiffened Shell Aerospace Vehicles
NASA Technical Reports Server (NTRS)
Eldred, Lloyd B.
2011-01-01
Loft is an automated mesh generation code that is designed for aerospace vehicle structures. From user input, Loft generates meshes for wings, noses, tanks, fuselage sections, thrust structures, and so on. As a mesh is generated, each element is assigned properties to mark the part of the vehicle with which it is associated. This property assignment is an extremely powerful feature that enables detailed analysis tasks, such as load application and structural sizing. This report is presented in two parts. The first part is an overview of the code and its applications. The modeling approach that was used to create the finite element meshes is described. Several applications of the code are demonstrated, including a Next Generation Launch Technology (NGLT) wing-sizing study, a lunar lander stage study, a launch vehicle shroud shape study, and a two-stage-to-orbit (TSTO) orbiter. Part two of the report is the program user manual. The manual includes in-depth tutorials and a complete command reference.
Generating unstructured nuclear reactor core meshes in parallel
Jain, Rajeev; Tautges, Timothy J.
2014-10-24
Recent advances in supercomputers and parallel solver techniques have enabled users to run large simulations problems using millions of processors. Techniques for multiphysics nuclear reactor core simulations are under active development in several countries. Most of these techniques require large unstructured meshes that can be hard to generate in a standalone desktop computers because of high memory requirements, limited processing power, and other complexities. We have previously reported on a hierarchical lattice-based approach for generating reactor core meshes. Here, we describe efforts to exploit coarse-grained parallelism during reactor assembly and reactor core mesh generation processes. We highlight several reactor coremore » examples including a very high temperature reactor, a full-core model of the Korean MONJU reactor, a ¼ pressurized water reactor core, the fast reactor Experimental Breeder Reactor-II core with a XX09 assembly, and an advanced breeder test reactor core. The times required to generate large mesh models, along with speedups obtained from running these problems in parallel, are reported. A graphical user interface to the tools described here has also been developed.« less
A Spectral Adaptive Mesh Refinement Method for the Burgers equation
NASA Astrophysics Data System (ADS)
Nasr Azadani, Leila; Staples, Anne
2013-03-01
Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh.
ENZO: AN ADAPTIVE MESH REFINEMENT CODE FOR ASTROPHYSICS
Bryan, Greg L.; Turk, Matthew J.; Norman, Michael L.; Bordner, James; Xu, Hao; Kritsuk, Alexei G.; O'Shea, Brian W.; Smith, Britton; Abel, Tom; Wang, Peng; Skillman, Samuel W.; Wise, John H.; Reynolds, Daniel R.; Collins, David C.; Harkness, Robert P.; Kim, Ji-hoon; Kuhlen, Michael; Goldbaum, Nathan; Hummels, Cameron; Collaboration: Enzo Collaboration; and others
2014-04-01
This paper describes the open-source code Enzo, which uses block-structured adaptive mesh refinement to provide high spatial and temporal resolution for modeling astrophysical fluid flows. The code is Cartesian, can be run in one, two, and three dimensions, and supports a wide variety of physics including hydrodynamics, ideal and non-ideal magnetohydrodynamics, N-body dynamics (and, more broadly, self-gravity of fluids and particles), primordial gas chemistry, optically thin radiative cooling of primordial and metal-enriched plasmas (as well as some optically-thick cooling models), radiation transport, cosmological expansion, and models for star formation and feedback in a cosmological context. In addition to explaining the algorithms implemented, we present solutions for a wide range of test problems, demonstrate the code's parallel performance, and discuss the Enzo collaboration's code development methodology.
Adaptive Mesh Refinement in Computational Astrophysics -- Methods and Applications
NASA Astrophysics Data System (ADS)
Balsara, D.
2001-12-01
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so because the physics associated with astrophysical phenomena evolves in multi-scale fashion and we wish to arrive at a multi-scale simulational capability to represent the physics. Because astrophysical systems have magnetic fields, multi-scale magnetohydrodynamics (MHD) is of especial interest. In this paper we first discuss general issues in adaptive mesh refinement (AMR). We then focus on the important issues in carrying out divergence-free AMR-MHD and catalogue the progress we have made in that area. We show that AMR methods lend themselves to easy parallelization. We then discuss applications of the RIEMANN framework for AMR-MHD to problems in computational astophysics.
Structured adaptive mesh refinement on the connection machine
Berger, M.J. . Courant Inst. of Mathematical Sciences); Saltzman, J.S. )
1993-01-01
Adaptive mesh refinement has proven itself to be a useful tool in a large collection of applications. By refining only a small portion of the computational domain, computational savings of up to a factor of 80 in 3 dimensional calculations have been obtained on serial machines. A natural question is, can this algorithm be used on massively parallel machines and still achieve the same efficiencies We have designed a data layout scheme for mapping grid points to processors that preserves locality and minimizes global communication for the CM-200. The effect of the data layout scheme is that at the finest level nearby grid points from adjacent grids in physical space are in adjacent memory locations. Furthermore, coarse grid points are arranged in memory to be near their associated fine grid points. We show applications of the algorithm to inviscid compressible fluid flow in two space dimensions.
Finite element adaptive mesh analysis using a cluster of workstations
NASA Astrophysics Data System (ADS)
Wang, K. P.; Bruch, J. C., Jr.
1998-01-01
Parallel computation on clusters of workstations is becoming one of the major trends in the study of parallel computations, because of their high computing speed, cost effectiveness and scalability. This paper presents studies of using a cluster of workstations for the finite element adaptive mesh analysis of a free surface seepage problem. A parallel algorithm proven to be simple to implement and efficient is used to perform the analysis. A network of workstations is used as the hardware of a parallel system. Two parallel software packages, P4 and PVM (parallel virtual machine), are used to handle communications among networked workstations. Computational issues to be discussed are domain decomposition, load balancing, and communication time.
Production-quality Tools for Adaptive Mesh RefinementVisualization
Weber, Gunther H.; Childs, Hank; Bonnell, Kathleen; Meredith,Jeremy; Miller, Mark; Whitlock, Brad; Bethel, E. Wes
2007-10-25
Adaptive Mesh Refinement (AMR) is a highly effectivesimulation method for spanning a large range of spatiotemporal scales,such as astrophysical simulations that must accommodate ranges frominterstellar to sub-planetary. Most mainstream visualization tools stilllack support for AMR as a first class data type and AMR code teams usecustom built applications for AMR visualization. The Department ofEnergy's (DOE's) Science Discovery through Advanced Computing (SciDAC)Visualization and Analytics Center for Enabling Technologies (VACET) isextending and deploying VisIt, an open source visualization tool thataccommodates AMR as a first-class data type, for use asproduction-quality, parallel-capable AMR visual data analysisinfrastructure. This effort will help science teams that use AMR-basedsimulations and who develop their own AMR visual data analysis softwareto realize cost and labor savings.
A Finite Element Mesh Generation Code System with On-Line Graphic Display.
1980-05-30
Version 00 LOOM-P is a two-dimensional mesh generation program which produces a best finite element mesh network for a reactor core geometry. This is an on-line automatic mesh generating program which can produce triangular mesh elements as an edit program to QMESH-RENUM.
Adaptive surface meshing and multiresolution terrain depiction for SVS
NASA Astrophysics Data System (ADS)
Wiesemann, Thorsten; Schiefele, Jens; Kubbat, Wolfgang
2001-08-01
Many of today's and tomorrow's aviation applications demand accurate and reliable digital terrain elevation databases. Particularly future Vertical Cut Displays or 3D Synthetic Vision Systems (SVS) require accurate and hi-resolution data to offer a reliable terrain depiction. On the other hand, optimized or reduced terrain models are necessary to ensure real-time rendering and computing performance. In this paper a new method for adaptive terrain meshing and depiction for SVS is presented. The initial data set is decomposed by using a wavelet transform. By examining the wavelet coefficients, an adaptive surface approximation for various Level-of-Detail is determined. Additionally, the dyadic scaling of the wavelet transform is used to build a hierarchical quad-tree representation for the terrain data. This representation enhances fast interactive computations and real-time rendering methods. The proposed terrain representation is integrated into a standard navigation display. Due to the multi-resolution data organization, terrain depiction e.g. resolution is adaptive to a selected zooming level or flight phase. Moreover, the wavelet decomposition helps to define local regions of interest. A depicted terrain resolution has a finer grain nearby the current airplane position and gets coarser with increasing aircraft distance. In addition, flight critical regions can be depicted in a higher resolution.
NASA Astrophysics Data System (ADS)
Combet, F.; Gelman, L.
2011-04-01
In this paper, a novel adaptive demodulation technique including a new diagnostic feature is proposed for gear diagnosis in conditions of variable amplitudes of the mesh harmonics. This vibration technique employs the time synchronous average (TSA) of vibration signals. The new adaptive diagnostic feature is defined as the ratio of the sum of the sideband components of the envelope spectrum of a mesh harmonic to the measured power of the mesh harmonic. The proposed adaptation of the technique is justified theoretically and experimentally by the high level of the positive covariance between amplitudes of the mesh harmonics and the sidebands in conditions of variable amplitudes of the mesh harmonics. It is shown that the adaptive demodulation technique preserves effectiveness of local fault detection of gears operating in conditions of variable mesh amplitudes.
A geometry-independent fine-mesh-based Monte Carlo importance generator
Liu, L.; Gardner, R.P.
1997-02-01
A new importance map approach for Monte Carlo simulation that can be used in an adaptive fashion has been identified and developed. It is based on using a mesh-based system of weight windows that are independent of any physical geometric cells. It consists of an importance map generator and a splitting and Russian roulette algorithm for a mesh-based weight windows game that is used in an iterative fashion to obtain increasingly efficient results. The general purpose Monte Carlo code MCNP is modified to incorporate this new mesh-based importance map generator and matching weight window technique for variance reduction. Two nuclear well logging problems--one for neutrons and the other for gamma rays--are used to test the new importance map generator. Results show that the new generator is able to produce four to six times larger figures of merit than MCNP`s physical geometry cell-based importance map generator. More importantly, the superior user friendliness of this new mesh-based generator makes variance reduction easy to accomplish.
Adaptive Multiresolution or Adaptive Mesh Refinement? A Case Study for 2D Euler Equations
Deiterding, Ralf; Domingues, Margarete O.; Gomes, Sonia M.; Roussel, Olivier; Schneider, Kai
2009-01-01
We present adaptive multiresolution (MR) computations of the two-dimensional compressible Euler equations for a classical Riemann problem. The results are then compared with respect to accuracy and computational efficiency, in terms of CPU time and memory requirements, with the corresponding finite volume scheme on a regular grid. For the same test-case, we also perform computations using adaptive mesh refinement (AMR) imposing similar accuracy requirements. The results thus obtained are compared in terms of computational overhead and compression of the computational grid, using in addition either local or global time stepping strategies. We preliminarily conclude that the multiresolution techniques yield improved memory compression and gain in CPU time with respect to the adaptive mesh refinement method.
Analysis of hypersonic aircraft inlets using flow adaptive mesh algorithms
NASA Astrophysics Data System (ADS)
Neaves, Michael Dean
The numerical investigation into the dynamics of unsteady inlet flowfields is applied to a three-dimensional scramjet inlet-isolator-diffuser geometry designed for hypersonic type applications. The Reynolds-Averaged Navier-Stokes equations are integrated in time using a subiterating, time-accurate implicit algorithm. Inviscid fluxes are calculated using the Low Diffusion Flux Splitting Scheme of Edwards. A modified version of the dynamic solution-adaptive point movement algorithm of Benson and McRae is used in a coupled mode to dynamically resolve the features of the flow by enhancing the spatial accuracy of the simulations. The unsteady mesh terms are incorporated into the flow solver via the inviscid fluxes. The dynamic solution-adaptive grid algorithm of Benson and McRae is modified to improve orthogonality at the boundaries to ensure accurate application of boundary conditions and properly resolve turbulent boundary layers. Shock tube simulations are performed to ascertain the effectiveness of the algorithm for unsteady flow situations on fixed and moving grids. Unstarts due to a combustor and freestream angle of attack perturbations are simulated in a three-dimensional inlet-isolator-diffuser configuration.
Adaptive Mesh Refinement in Reactive Transport Modeling of Subsurface Environments
NASA Astrophysics Data System (ADS)
Molins, S.; Day, M.; Trebotich, D.; Graves, D. T.
2015-12-01
Adaptive mesh refinement (AMR) is a numerical technique for locally adjusting the resolution of computational grids. AMR makes it possible to superimpose levels of finer grids on the global computational grid in an adaptive manner allowing for more accurate calculations locally. AMR codes rely on the fundamental concept that the solution can be computed in different regions of the domain with different spatial resolutions. AMR codes have been applied to a wide range of problem including (but not limited to): fully compressible hydrodynamics, astrophysical flows, cosmological applications, combustion, blood flow, heat transfer in nuclear reactors, and land ice and atmospheric models for climate. In subsurface applications, in particular, reactive transport modeling, AMR may be particularly useful in accurately capturing concentration gradients (hence, reaction rates) that develop in localized areas of the simulation domain. Accurate evaluation of reaction rates is critical in many subsurface applications. In this contribution, we will discuss recent applications that bring to bear AMR capabilities on reactive transport problems from the pore scale to the flood plain scale.
Kaminsky, Jan; Rodt, Thomas; Gharabaghi, Alireza; Forster, Jan; Brand, Gerd; Samii, Madjid
2005-06-01
The FE-modeling of complex anatomical structures is not solved satisfyingly so far. Voxel-based as opposed to contour-based algorithms allow an automated mesh generation based on the image data. Nonetheless their geometric precision is limited. We developed an automated mesh-generator that combines the advantages of voxel-based generation with improved representation of the geometry by displacement of nodes on the object-surface. Models of an artificial 3D-pipe-section and a skullbase were generated with different mesh-densities using the newly developed geometric, unsmoothed and smoothed voxel generators. Compared to the analytic calculation of the 3D-pipe-section model the normalized RMS error of the surface stress was 0.173-0.647 for the unsmoothed voxel models, 0.111-0.616 for the smoothed voxel models with small volume error and 0.126-0.273 for the geometric models. The highest element-energy error as a criterion for the mesh quality was 2.61x10(-2) N mm, 2.46x10(-2) N mm and 1.81x10(-2) N mm for unsmoothed, smoothed and geometric voxel models, respectively. The geometric model of the 3D-skullbase resulted in the lowest element-energy error and volume error. This algorithm also allowed the best representation of anatomical details. The presented geometric mesh-generator is universally applicable and allows an automated and accurate modeling by combining the advantages of the voxel-technique and of improved surface-modeling.
Automatically Generated, Anatomically Accurate Meshes for Cardiac Electrophysiology Problems
Prassl, Anton J.; Kickinger, Ferdinand; Ahammer, Helmut; Grau, Vicente; Schneider, Jürgen E.; Hofer, Ernst; Vigmond, Edward J.; Trayanova, Natalia A.
2010-01-01
Significant advancements in imaging technology and the dramatic increase in computer power over the last few years broke the ground for the construction of anatomically realistic models of the heart at an unprecedented level of detail. To effectively make use of high-resolution imaging datasets for modeling purposes, the imaged objects have to be discretized. This procedure is trivial for structured grids. However, to develop generally applicable heart models, unstructured grids are much preferable. In this study, a novel image-based unstructured mesh generation technique is proposed. It uses the dual mesh of an octree applied directly to segmented 3-D image stacks. The method produces conformal, boundary-fitted, and hexahedra-dominant meshes. The algorithm operates fully automatically with no requirements for interactivity and generates accurate volume-preserving representations of arbitrarily complex geometries with smooth surfaces. The method is very well suited for cardiac electrophysiological simulations. In the myocardium, the algorithm minimizes variations in element size, whereas in the surrounding medium, the element size is grown larger with the distance to the myocardial surfaces to reduce the computational burden. The numerical feasibility of the approach is demonstrated by discretizing and solving the monodomain and bidomain equations on the generated grids for two preparations of high experimental relevance, a left ventricular wedge preparation, and a papillary muscle. PMID:19203877
An object-oriented approach for parallel self adaptive mesh refinement on block structured grids
NASA Technical Reports Server (NTRS)
Lemke, Max; Witsch, Kristian; Quinlan, Daniel
1993-01-01
Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.
NASA Technical Reports Server (NTRS)
Steger, J. L.; Dougherty, F. C.; Benek, J. A.
1983-01-01
A mesh system composed of multiple overset body-conforming grids is described for adapting finite-difference procedures to complex aircraft configurations. In this so-called 'chimera mesh,' a major grid is generated about a main component of the configuration and overset minor grids are used to resolve all other features. Methods for connecting overset multiple grids and modifications of flow-simulation algorithms are discussed. Computational tests in two dimensions indicate that the use of multiple overset grids can simplify the task of grid generation without an adverse effect on flow-field algorithms and computer code complexity.
CONSTRAINED-TRANSPORT MAGNETOHYDRODYNAMICS WITH ADAPTIVE MESH REFINEMENT IN CHARM
Miniati, Francesco; Martin, Daniel F. E-mail: DFMartin@lbl.gov
2011-07-01
We present the implementation of a three-dimensional, second-order accurate Godunov-type algorithm for magnetohydrodynamics (MHD) in the adaptive-mesh-refinement (AMR) cosmological code CHARM. The algorithm is based on the full 12-solve spatially unsplit corner-transport-upwind (CTU) scheme. The fluid quantities are cell-centered and are updated using the piecewise-parabolic method (PPM), while the magnetic field variables are face-centered and are evolved through application of the Stokes theorem on cell edges via a constrained-transport (CT) method. The so-called multidimensional MHD source terms required in the predictor step for high-order accuracy are applied in a simplified form which reduces their complexity in three dimensions without loss of accuracy or robustness. The algorithm is implemented on an AMR framework which requires specific synchronization steps across refinement levels. These include face-centered restriction and prolongation operations and a reflux-curl operation, which maintains a solenoidal magnetic field across refinement boundaries. The code is tested against a large suite of test problems, including convergence tests in smooth flows, shock-tube tests, classical two- and three-dimensional MHD tests, a three-dimensional shock-cloud interaction problem, and the formation of a cluster of galaxies in a fully cosmological context. The magnetic field divergence is shown to remain negligible throughout.
Parallel adaptive mesh refinement techniques for plasticity problems
NASA Technical Reports Server (NTRS)
Barry, W. J.; Jones, M. T.; Plassmann, P. E.
1997-01-01
The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.
Numerical study of Taylor bubbles with adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Percival, James; Pain, Chris; Matar, Omar; Hasan, Abbas; Azzopardi, Barry
2014-11-01
The Taylor bubble is a single long bubble which nearly fills the entire cross section of a liquid-filled circular tube. This type of bubble flow regime often occurs in gas-liquid slug flows in many industrial applications, including oil-and-gas production, chemical and nuclear reactors, and heat exchangers. The objective of this study is to investigate the fluid dynamics of Taylor bubbles rising in a vertical pipe filled with oils of extremely high viscosity (mimicking the ``heavy oils'' found in the oil-and-gas industry). A modelling and simulation framework is presented here which can modify and adapt anisotropic unstructured meshes to better represent the underlying physics of bubble rise and reduce the computational effort without sacrificing accuracy. The numerical framework consists of a mixed control-volume and finite-element formulation, a ``volume of fluid''-type method for the interface capturing based on a compressive control volume advection method, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of Taylor bubbles are presented to show the capability of this method. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
A Novel Coarsening Method for Scalable and Efficient Mesh Generation
Yoo, A; Hysom, D; Gunney, B
2010-12-02
matrix-vector multiplication can be performed locally on each processor and hence to minimize communication. Furthermore, a good graph partitioning scheme ensures the equal amount of computation performed on each processor. Graph partitioning is a well known NP-complete problem, and thus the most commonly used graph partitioning algorithms employ some forms of heuristics. These algorithms vary in terms of their complexity, partition generation time, and the quality of partitions, and they tend to trade off these factors. A significant challenge we are currently facing at the Lawrence Livermore National Laboratory is how to partition very large meshes on massive-size distributed memory machines like IBM BlueGene/P, where scalability becomes a big issue. For example, we have found that the ParMetis, a very popular graph partitioning tool, can only scale to 16K processors. An ideal graph partitioning method on such an environment should be fast and scale to very large meshes, while producing high quality partitions. This is an extremely challenging task, as to scale to that level, the partitioning algorithm should be simple and be able to produce partitions that minimize inter-processor communications and balance the load imposed on the processors. Our goals in this work are two-fold: (1) To develop a new scalable graph partitioning method with good load balancing and communication reduction capability. (2) To study the performance of the proposed partitioning method on very large parallel machines using actual data sets and compare the performance to that of existing methods. The proposed method achieves the desired scalability by reducing the mesh size. For this, it coarsens an input mesh into a smaller size mesh by coalescing the vertices and edges of the original mesh into a set of mega-vertices and mega-edges. A new coarsening method called brick algorithm is developed in this research. In the brick algorithm, the zones in a given mesh are first grouped into fixed size
MeSH indexing based on automatically generated summaries
2013-01-01
Background MEDLINE citations are manually indexed at the U.S. National Library of Medicine (NLM) using as reference the Medical Subject Headings (MeSH) controlled vocabulary. For this task, the human indexers read the full text of the article. Due to the growth of MEDLINE, the NLM Indexing Initiative explores indexing methodologies that can support the task of the indexers. Medical Text Indexer (MTI) is a tool developed by the NLM Indexing Initiative to provide MeSH indexing recommendations to indexers. Currently, the input to MTI is MEDLINE citations, title and abstract only. Previous work has shown that using full text as input to MTI increases recall, but decreases precision sharply. We propose using summaries generated automatically from the full text for the input to MTI to use in the task of suggesting MeSH headings to indexers. Summaries distill the most salient information from the full text, which might increase the coverage of automatic indexing approaches based on MEDLINE. We hypothesize that if the results were good enough, manual indexers could possibly use automatic summaries instead of the full texts, along with the recommendations of MTI, to speed up the process while maintaining high quality of indexing results. Results We have generated summaries of different lengths using two different summarizers, and evaluated the MTI indexing on the summaries using different algorithms: MTI, individual MTI components, and machine learning. The results are compared to those of full text articles and MEDLINE citations. Our results show that automatically generated summaries achieve similar recall but higher precision compared to full text articles. Compared to MEDLINE citations, summaries achieve higher recall but lower precision. Conclusions Our results show that automatic summaries produce better indexing than full text articles. Summaries produce similar recall to full text but much better precision, which seems to indicate that automatic summaries can
Adaptive Phase Delay Generator
NASA Technical Reports Server (NTRS)
Greer, Lawrence
2013-01-01
There are several experimental setups involving rotating machinery that require some form of synchronization. The adaptive phase delay generator (APDG) the Bencic-1000 is a flexible instrument that allows the user to generate pulses synchronized to the rising edge of a tachometer signal from any piece of rotating machinery. These synchronized pulses can vary by the delay angle, pulse width, number of pulses per period, number of skipped pulses, and total number of pulses. Due to the design of the pulse generator, any and all of these parameters can be changed independently, yielding an unparalleled level of versatility. There are two user interfaces to the APDG. The first is a LabVIEW program that has the advantage of displaying all of the pulse parameters and input signal data within one neatly organized window on the PC monitor. Furthermore, the LabVIEW interface plots the rpm of the two input signal channels in real time. The second user interface is a handheld portable device that goes anywhere a computer is not accessible. It consists of a liquid-crystal display and keypad, which enable the user to control the unit by scrolling through a host of command menus and parameter listings. The APDG combines all of the desired synchronization control into one unit. The experimenter can adjust the delay, pulse width, pulse count, number of skipped pulses, and produce a specified number of pulses per revolution. Each of these parameters can be changed independently, providing an unparalleled level of versatility when synchronizing hardware to a host of rotating machinery. The APDG allows experimenters to set up quickly and generate a host of synchronizing configurations using a simple user interface, which hopefully leads to faster results.
Global Load Balancing with Parallel Mesh Adaption on Distributed-Memory Systems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Oliker, Leonid; Sohn, Andrew
1996-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load imbalance among processors on a parallel machine. This paper describes the parallel implementation of a tetrahedral mesh adaption scheme and a new global load balancing method. A heuristic remapping algorithm is presented that assigns partitions to processors such that the redistribution cost is minimized. Results indicate that the parallel performance of the mesh adaption code depends on the nature of the adaption region and show a 35.5X speedup on 64 processors of an SP2 when 35% of the mesh is randomly adapted. For large-scale scientific computations, our load balancing strategy gives almost a sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remapper yields processor assignments that are less than 3% off the optimal solutions but requires only 1% of the computational time.
A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes
NASA Technical Reports Server (NTRS)
Lou, John Z.; Norton, Charles D.; Cwik, Thomas A.
1999-01-01
The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.
MESH2D GRID GENERATOR DESIGN AND USE
Flach, G.; Smith, F.
2012-01-20
Mesh2d is a Fortran90 program designed to generate two-dimensional structured grids of the form [x(i),y(i,j)] where [x,y] are grid coordinates identified by indices (i,j). The x(i) coordinates alone can be used to specify a one-dimensional grid. Because the x-coordinates vary only with the i index, a two-dimensional grid is composed in part of straight vertical lines. However, the nominally horizontal y(i,j{sub 0}) coordinates along index i are permitted to undulate or otherwise vary. Mesh2d also assigns an integer material type to each grid cell, mtyp(i,j), in a user-specified manner. The complete grid is specified through three separate input files defining the x(i), y(i,j), and mtyp(i,j) variations. The overall mesh is constructed from grid zones that are typically then subdivided into a collection of smaller grid cells. The grid zones usually correspond to distinct materials or larger-scale geometric shapes. The structured grid zones are identified through uppercase indices (I,J). Subdivision of zonal regions into grid cells can be done uniformly, or nonuniformly using either a polynomial or geometric skewing algorithm. Grid cells may be concentrated backward, forward, or toward both ends. Figure 1 illustrates the above concepts in the context of a simple four zone grid.
Cell-based Adaptive Mesh Refinement on the GPU with Applications to Exascale Supercomputing
NASA Astrophysics Data System (ADS)
Trujillo, Dennis; Robey, Robert; Davis, Neal; Nicholaeff, David
2011-10-01
We present an OpenCL implementation of a cell-based adaptive mesh refinement (AMR) scheme for the shallow water equations. The challenges associated with ensuring the locality of algorithm architecture to fully exploit the massive number of parallel threads on the GPU is discussed. This includes a proof of concept that a cell-based AMR code can be effectively implemented, even on a small scale, in the memory and threading model provided by OpenCL. Additionally, the program requires dynamic memory in order to properly implement the mesh; as this is not supported in the OpenCL 1.1 standard, a combination of CPU memory management and GPU computation effectively implements a dynamic memory allocation scheme. Load balancing is achieved through a new stencil-based implementation of a space-filling curve, eliminating the need for a complete recalculation of the indexing on the mesh. A cartesian grid hash table scheme to allow fast parallel neighbor accesses is also discussed. Finally, the relative speedup of the GPU-enabled AMR code is compared to the original serial version. We conclude that parallelization using the GPU provides significant speedup for typical numerical applications and is feasible for scientific applications in the next generation of supercomputing.
Using Adaptive Mesh Refinment to Simulate Storm Surge
NASA Astrophysics Data System (ADS)
Mandli, K. T.; Dawson, C.
2012-12-01
Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these storms, and their prediction and mitigation through numerical simulations is of great interest to coastal communities that need to plan for the subsequent rise in sea level during these storms. Unfortunately these simulations require a large amount of resolution in regions of interest to capture relevant effects resulting in a computational cost that may be intractable. This problem is exacerbated in situations where a large number of similar runs is needed such as in design of infrastructure or forecasting with ensembles of probable storms. One solution to address the problem of computational cost is to employ adaptive mesh refinement (AMR) algorithms. AMR functions by decomposing the computational domain into regions which may vary in resolution as time proceeds. Decomposing the domain as the flow evolves makes this class of methods effective at ensuring that computational effort is spent only where it is needed. AMR also allows for placement of computational resolution independent of user interaction and expectation of the dynamics of the flow as well as particular regions of interest such as harbors. The simulation of many different applications have only been made possible by using AMR-type algorithms, which have allowed otherwise impractical simulations to be performed for much less computational expense. Our work involves studying how storm surge simulations can be improved with AMR algorithms. We have implemented relevant storm surge physics in the GeoClaw package and tested how Hurricane Ike's surge into Galveston Bay and up the Houston Ship Channel compares to available tide gauge data. We will also discuss issues dealing with refinement criteria, optimal resolution and refinement ratios, and inundation.
RAM: a Relativistic Adaptive Mesh Refinement Hydrodynamics Code
Zhang, Wei-Qun; MacFadyen, Andrew I.; /Princeton, Inst. Advanced Study
2005-06-06
The authors have developed a new computer code, RAM, to solve the conservative equations of special relativistic hydrodynamics (SRHD) using adaptive mesh refinement (AMR) on parallel computers. They have implemented a characteristic-wise, finite difference, weighted essentially non-oscillatory (WENO) scheme using the full characteristic decomposition of the SRHD equations to achieve fifth-order accuracy in space. For time integration they use the method of lines with a third-order total variation diminishing (TVD) Runge-Kutta scheme. They have also implemented fourth and fifth order Runge-Kutta time integration schemes for comparison. The implementation of AMR and parallelization is based on the FLASH code. RAM is modular and includes the capability to easily swap hydrodynamics solvers, reconstruction methods and physics modules. In addition to WENO they have implemented a finite volume module with the piecewise parabolic method (PPM) for reconstruction and the modified Marquina approximate Riemann solver to work with TVD Runge-Kutta time integration. They examine the difficulty of accurately simulating shear flows in numerical relativistic hydrodynamics codes. They show that under-resolved simulations of simple test problems with transverse velocity components produce incorrect results and demonstrate the ability of RAM to correctly solve these problems. RAM has been tested in one, two and three dimensions and in Cartesian, cylindrical and spherical coordinates. they have demonstrated fifth-order accuracy for WENO in one and two dimensions and performed detailed comparison with other schemes for which they show significantly lower convergence rates. Extensive testing is presented demonstrating the ability of RAM to address challenging open questions in relativistic astrophysics.
Patch-based Adaptive Mesh Refinement for Multimaterial Hydrodynamics
Lomov, I; Pember, R; Greenough, J; Liu, B
2005-10-18
We present a patch-based direct Eulerian adaptive mesh refinement (AMR) algorithm for modeling real equation-of-state, multimaterial compressible flow with strength. Our approach to AMR uses a hierarchical, structured grid approach first developed by (Berger and Oliger 1984), (Berger and Oliger 1984). The grid structure is dynamic in time and is composed of nested uniform rectangular grids of varying resolution. The integration scheme on the grid hierarchy is a recursive procedure in which the coarse grids are advanced, then the fine grids are advanced multiple steps to reach the same time, and finally the coarse and fine grids are synchronized to remove conservation errors during the separate advances. The methodology presented here is based on a single grid algorithm developed for multimaterial gas dynamics by (Colella et al. 1993), refined by(Greenough et al. 1995), and extended to the solution of solid mechanics problems with significant strength by (Lomov and Rubin 2003). The single grid algorithm uses a second-order Godunov scheme with an approximate single fluid Riemann solver and a volume-of-fluid treatment of material interfaces. The method also uses a non-conservative treatment of the deformation tensor and an acoustic approximation for shear waves in the Riemann solver. This departure from a strict application of the higher-order Godunov methodology to the equation of solid mechanics is justified due to the fact that highly nonlinear behavior of shear stresses is rare. This algorithm is implemented in two codes, Geodyn and Raptor, the latter of which is a coupled rad-hydro code. The present discussion will be solely concerned with hydrodynamics modeling. Results from a number of simulations for flows with and without strength will be presented.
Studies in computational geometry motivated by mesh generation
Smith, W.D.
1989-01-01
This thesis sprawls over most of discrete and computational geometry. There are four loose bodies of theory developed. (1) A quantitative and algorithmic theory of crossing number and crossing-free line segment graphs in the plane. As five applications of this theory: the author disproves two long - standing conjectures on the crossing number of the complete and complete bipartite graphs, he presents the first exponential algorithm for planar minimum Steiner tree, and the first subexponential algorithms for planar traveling salesman tour and optimum triangulation, and he presents an algorithm for generating all non-isomorphic V-vertex planar graphs, in O(V{sup 3)}time per graph, using O(V) total workspace. (2) Mesh generation, and the triangulation of polytopes: He has the strongest bounds on the number of d-simplices required to triangulate the d-cube, and new triangulation methods in the plane. A quantitative and qualitative - and practical - theory of finite element mesh quality suggest a new, simple strategy for generating good meshes. (3) The theory of geometrical graphs on N point sites in d-space. This subsumes many new results in: geometrical probability, sphere packing, and extremal configurations. An array of new multidimensional search date structures are used to devise fast algorithms for construction many geometrical graphs. (4) Useful new results concerning the mensuration and structure of d-polytopes. In particular he extensively generalizes the famous formula of Heron and Alexandria (75 AD), for the area of a triangle, and he presents the first linear time congruence algorithm for 3 -dimensional polyhedra. He closes with the largest bibliography of the field, containing over 3000 references.
Unconstrained paving and plastering method for generating finite element meshes
Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert
2010-03-02
Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.
NASA Technical Reports Server (NTRS)
Barnard, Stephen T.; Simon, Horst; Lasinski, T. A. (Technical Monitor)
1994-01-01
The design of a parallel implementation of multilevel recursive spectral bisection is described. The goal is to implement a code that is fast enough to enable dynamic repartitioning of adaptive meshes.
Kohn, S.; Weare, J.; Ong, E.; Baden, S.
1997-05-01
We have applied structured adaptive mesh refinement techniques to the solution of the LDA equations for electronic structure calculations. Local spatial refinement concentrates memory resources and numerical effort where it is most needed, near the atomic centers and in regions of rapidly varying charge density. The structured grid representation enables us to employ efficient iterative solver techniques such as conjugate gradient with FAC multigrid preconditioning. We have parallelized our solver using an object- oriented adaptive mesh refinement framework.
NASA Astrophysics Data System (ADS)
Todarello, Giovanni; Vonck, Floris; Bourasseau, Sébastien; Peter, Jacques; Désidéri, Jean-Antoine
2016-05-01
A new goal-oriented mesh adaptation method for finite volume/finite difference schemes is extended from the structured mesh framework to a more suitable setting for adaptation of unstructured meshes. The method is based on the total derivative of the goal with respect to volume mesh nodes that is computable after the solution of the goal discrete adjoint equation. The asymptotic behaviour of this derivative is assessed on regularly refined unstructured meshes. A local refinement criterion is derived from the requirement of limiting the first order change in the goal that an admissible node displacement may cause. Mesh adaptations are then carried out for classical test cases of 2D Euler flows. Efficiency and local density of the adapted meshes are presented. They are compared with those obtained with a more classical mesh adaptation method in the framework of finite volume/finite difference schemes [46]. Results are very close although the present method only makes usage of the current grid.
Isoparametric 3-D Finite Element Mesh Generation Using Interactive Computer Graphics
NASA Technical Reports Server (NTRS)
Kayrak, C.; Ozsoy, T.
1985-01-01
An isoparametric 3-D finite element mesh generator was developed with direct interface to an interactive geometric modeler program called POLYGON. POLYGON defines the model geometry in terms of boundaries and mesh regions for the mesh generator. The mesh generator controls the mesh flow through the 2-dimensional spans of regions by using the topological data and defines the connectivity between regions. The program is menu driven and the user has a control of element density and biasing through the spans and can also apply boundary conditions, loads interactively.
Star formation with adaptive mesh refinement and magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Collins, David C.
2009-01-01
In this thesis, we develop an adaptive mesh refinement (AMR) code including magnetic fields, and use it to perform high resolution simulations of magnetized molecular clouds. The purpose of these simulations is to study present day star formation in the presence of turbulence and magnetic fields. We first present MHDEnzo, the extension of the cosmology and astrophysics code Enzo to include the effects magnetic fields. We use a higher order Godunov Riemann solver for the computation of interface fluxes; constrained transport to compute the electric field from those interface fluxes, which advances the induction equation in a divergence free manner; divergence free reconstruction technique to interpolate the magnetic fields to fine grids; operator splitting to include gravity and cosmological expansion. We present a series of test problems to demonstrate the quality of solution achieved. Additionally, we present several other solvers that were developed along the way. Finally we present the results from several AMR simulations that study isothermal turbulence in the presence of magnetic fields and self gravity. Ten simulations with initial Mach number 8.9 were studied varying several parameters; virial parameter a from 0.52 to 3.1; whether they were continuously stirred or allowed to decay; and the number of refinement levels (4 or 6). Measurements of the density probability density function (PDF) were made, showing both the expected log normal distribution and an additional power law. Measurements of the line of sight magnetic field vs. column density are done, giving excellent agreement with recent observations. The line width vs. size relationship is measured and compared with good agreement to observations, reproducing both turbulent and collapse signatures The core mass distribution is measured and agrees well with observations of Serpens and Perseus core samples, but the power-law distribution in Ophiuchus is not reproduced by our simulations. Finally we
NASA Astrophysics Data System (ADS)
Weller, Hilary; Browne, Philip; Budd, Chris; Cullen, Mike
2016-03-01
An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistributed with respect to a monitor function. Optimal transport generates meshes that keep the same connectivity as the original mesh, making them suitable for r-adaptive simulations, in which the equations of motion can be solved in a moving frame of reference in order to avoid mapping the solution between old and new meshes and to avoid load balancing problems on parallel computers. The semi-implicit solution of the Monge-Ampère type equation involves a new linearisation of the Hessian term, and exponential maps are used to map from old to new meshes on the sphere. The determinant of the Hessian is evaluated as the change in volume between old and new mesh cells, rather than using numerical approximations to the gradients. OT meshes are generated to compare with centroidal Voronoi tessellations on the sphere and are found to have advantages and disadvantages; OT equidistribution is more accurate, the number of iterations to convergence is independent of the mesh size, face skewness is reduced and the connectivity does not change. However anisotropy is higher and the OT meshes are non-orthogonal. It is shown that optimal transport on the sphere leads to meshes that do not tangle. However, tangling can be introduced by numerical errors in calculating the gradient of the mesh potential. Methods for alleviating this problem are explored. Finally, OT meshes are generated using observed precipitation as a monitor function, in order to demonstrate the potential power of the technique.
Yaqi Wang; Jean C. Ragusa
2011-02-01
Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.
Huang, W.; Zheng, Lingyun; Zhan, X.
2002-01-01
Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.
Three-dimensional modeling and highly refined mesh generation of the aorta artery and its tunics
NASA Astrophysics Data System (ADS)
Cazotto, J. A.; Neves, L. A.; Machado, J. M.; Momente, J. C.; Shiyou, Y.; Godoy, M. F.; Zafalon, G. F. D.; Pinto, A. R.; Valêncio, C. R.
2013-02-01
This paper describes strategies and techniques to perform modeling and automatic mesh generation of the aorta artery and its tunics (adventitia, media and intima walls), using open source codes. The models were constructed in the Blender package and Python scripts were used to export the data necessary for the mesh generation in TetGen. The strategies proposed are able to provide meshes of complicated and irregular volumes, with a large number of mesh elements involved (12,000,000 tetrahedrons approximately). These meshes can be used to perform computational simulations by Finite Element Method (FEM).
An adaptive computation mesh for the solution of singular perturbation problems
NASA Technical Reports Server (NTRS)
Brackbill, J. U.; Saltzman, J.
1980-01-01
In singular perturbation problems, control of zone size variation can affect the effort required to obtain accurate, numerical solutions of finite difference equations. The mesh is generated by the solution of potential equations. Numerical results for a singular perturbation problem in two dimensions are presented. The mesh was used in calculations of resistive magnetohydrodynamic flow in two dimensions.
NASA Astrophysics Data System (ADS)
Anderson, Robert; Pember, Richard; Elliott, Noah
2001-11-01
We present a method, ALE-AMR, for modeling unsteady compressible flow that combines a staggered grid arbitrary Lagrangian-Eulerian (ALE) scheme with structured local adaptive mesh refinement (AMR). The ALE method is a three step scheme on a staggered grid of quadrilateral cells: Lagrangian advance, mesh relaxation, and remap. The AMR scheme uses a mesh hierarchy that is dynamic in time and is composed of nested structured grids of varying resolution. The integration algorithm on the hierarchy is a recursive procedure in which the coarse grids are advanced a single time step, the fine grids are advanced to the same time, and the coarse and fine grid solutions are synchronized. The novel details of ALE-AMR are primarily motivated by the need to reconcile and extend AMR techniques typically employed for stationary rectangular meshes with cell-centered quantities to the moving quadrilateral meshes with staggered quantities used in the ALE scheme. Solutions of several test problems are discussed.
Advances in Parallelization for Large Scale Oct-Tree Mesh Generation
NASA Technical Reports Server (NTRS)
O'Connell, Matthew; Karman, Steve L.
2015-01-01
Despite great advancements in the parallelization of numerical simulation codes over the last 20 years, it is still common to perform grid generation in serial. Generating large scale grids in serial often requires using special "grid generation" compute machines that can have more than ten times the memory of average machines. While some parallel mesh generation techniques have been proposed, generating very large meshes for LES or aeroacoustic simulations is still a challenging problem. An automated method for the parallel generation of very large scale off-body hierarchical meshes is presented here. This work enables large scale parallel generation of off-body meshes by using a novel combination of parallel grid generation techniques and a hybrid "top down" and "bottom up" oct-tree method. Meshes are generated using hardware commonly found in parallel compute clusters. The capability to generate very large meshes is demonstrated by the generation of off-body meshes surrounding complex aerospace geometries. Results are shown including a one billion cell mesh generated around a Predator Unmanned Aerial Vehicle geometry, which was generated on 64 processors in under 45 minutes.
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods.
Li, Zhilin; Song, Peng
2012-01-01
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy.
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods
Li, Zhilin; Song, Peng
2012-01-01
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy. PMID:22670155
Multifluid adaptive-mesh simulation of the solar wind interaction with the local interstellar medium
Kryukov, I. A.; Borovikov, S. N.; Pogorelov, N. V.; Zank, G. P.
2006-09-26
DOE's SciDAC adaptive mesh refinement code Chombo has been modified for solution of compressible MHD flows with the application of high resolution, shock-capturing numerical schemes. The code developed is further extended to involve multiple fluids and applied to the problem of the solar wind interaction with the local interstellar medium. For this purpose, a set of MHD equations is solved together with a few sets of the Euler gas dynamics equations, depending on the number of neutral fluids included in the model. Our first results are presented that were obtained in the framework of an axially symmetric multifluid model which is applicable to magnetic-field-aligned flows. Details are shown of the generation and development of Rayleigh-Taylor and Kelvin-Helmholtz instabilities of the heliopause. A comparison is given of the results obtained with a two- and four-fluid models.
ENZO+MORAY: radiation hydrodynamics adaptive mesh refinement simulations with adaptive ray tracing
NASA Astrophysics Data System (ADS)
Wise, John H.; Abel, Tom
2011-07-01
We describe a photon-conserving radiative transfer algorithm, using a spatially-adaptive ray-tracing scheme, and its parallel implementation into the adaptive mesh refinement cosmological hydrodynamics code ENZO. By coupling the solver with the energy equation and non-equilibrium chemistry network, our radiation hydrodynamics framework can be utilized to study a broad range of astrophysical problems, such as stellar and black hole feedback. Inaccuracies can arise from large time-steps and poor sampling; therefore, we devised an adaptive time-stepping scheme and a fast approximation of the optically-thin radiation field with multiple sources. We test the method with several radiative transfer and radiation hydrodynamics tests that are given in Iliev et al. We further test our method with more dynamical situations, for example, the propagation of an ionization front through a Rayleigh-Taylor instability, time-varying luminosities and collimated radiation. The test suite also includes an expanding H II region in a magnetized medium, utilizing the newly implemented magnetohydrodynamics module in ENZO. This method linearly scales with the number of point sources and number of grid cells. Our implementation is scalable to 512 processors on distributed memory machines and can include the radiation pressure and secondary ionizations from X-ray radiation. It is included in the newest public release of ENZO.
An Adaptive Course Generation Framework
ERIC Educational Resources Information Center
Li, Frederick W. B.; Lau, Rynson W. H.; Dharmendran, Parthiban
2010-01-01
Existing adaptive e-learning methods are supported by student (user) profiling for capturing student characteristics, and course structuring for organizing learning materials according to topics and levels of difficulties. Adaptive courses are then generated by extracting materials from the course structure to match the criteria specified in the…
An adaptive mesh finite volume method for the Euler equations of gas dynamics
NASA Astrophysics Data System (ADS)
Mungkasi, Sudi
2016-06-01
The Euler equations have been used to model gas dynamics for decades. They consist of mathematical equations for the conservation of mass, momentum, and energy of the gas. For a large time value, the solution may contain discontinuities, even when the initial condition is smooth. A standard finite volume numerical method is not able to give accurate solutions to the Euler equations around discontinuities. Therefore we solve the Euler equations using an adaptive mesh finite volume method. In this paper, we present a new construction of the adaptive mesh finite volume method with an efficient computation of the refinement indicator. The adaptive method takes action automatically at around places having inaccurate solutions. Inaccurate solutions are reconstructed to reduce the error by refining the mesh locally up to a certain level. On the other hand, if the solution is already accurate, then the mesh is coarsened up to another certain level to minimize computational efforts. We implement the numerical entropy production as the mesh refinement indicator. As a test problem, we take the Sod shock tube problem. Numerical results show that the adaptive method is more promising than the standard one in solving the Euler equations of gas dynamics.
The direct simulation Monte Carlo method using unstructured adaptive mesh and its application
NASA Astrophysics Data System (ADS)
Wu, J.-S.; Tseng, K.-C.; Kuo, C.-H.
2002-02-01
The implementation of an adaptive mesh-embedding (h-refinement) scheme using unstructured grid in two-dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an-isotropic refinement in the interfacial cells between refined and non-refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high-speed driven cavity flow. The results show an improved flow resolution as compared with that of un-adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near-continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non-uniform density variations throughout the flow field. Copyright
Pamgen, a library for parallel generation of simple finite element meshes.
Foucar, James G.; Drake, Richard Roy; Hensinger, David M.; Gardiner, Thomas Anthony
2008-04-01
Generating finite-element meshes is a serious bottleneck for large parallel simulations. When mesh generation is limited to serial machines and element counts approach a billion, this bottleneck becomes a roadblock. Pamgen is a parallel mesh generation library that allows on-the-fly scalable generation of hexahedral and quadrilateral finite element meshes for several simple geometries. It has been used to generate more that 1.1 billion elements on 17,576 processors. Pamgen generates an unstructured finite element mesh on each processor at the start of a simulation. The mesh is specified by commands passed to the library as a 'C'-programming language string. The resulting mesh geometry, topology, and communication information can then be queried through an API. pamgen allows specification of boundary condition application regions using sidesets (element faces) and nodesets (collections of nodes). It supports several simple geometry types. It has multiple alternatives for mesh grading. It has several alternatives for the initial domain decomposition. Pamgen makes it easy to change details of the finite element mesh and is very useful for performance studies and scoping calculations.
SU-D-207-04: GPU-Based 4D Cone-Beam CT Reconstruction Using Adaptive Meshing Method
Zhong, Z; Gu, X; Iyengar, P; Mao, W; Wang, J; Guo, X
2015-06-15
Purpose: Due to the limited number of projections at each phase, the image quality of a four-dimensional cone-beam CT (4D-CBCT) is often degraded, which decreases the accuracy of subsequent motion modeling. One of the promising methods is the simultaneous motion estimation and image reconstruction (SMEIR) approach. The objective of this work is to enhance the computational speed of the SMEIR algorithm using adaptive feature-based tetrahedral meshing and GPU-based parallelization. Methods: The first step is to generate the tetrahedral mesh based on the features of a reference phase 4D-CBCT, so that the deformation can be well captured and accurately diffused from the mesh vertices to voxels of the image volume. After the mesh generation, the updated motion model and other phases of 4D-CBCT can be obtained by matching the 4D-CBCT projection images at each phase with the corresponding forward projections of the deformed reference phase of 4D-CBCT. The entire process of this 4D-CBCT reconstruction method is implemented on GPU, resulting in significantly increasing the computational efficiency due to its tremendous parallel computing ability. Results: A 4D XCAT digital phantom was used to test the proposed mesh-based image reconstruction algorithm. The image Result shows both bone structures and inside of the lung are well-preserved and the tumor position can be well captured. Compared to the previous voxel-based CPU implementation of SMEIR, the proposed method is about 157 times faster for reconstructing a 10 -phase 4D-CBCT with dimension 256×256×150. Conclusion: The GPU-based parallel 4D CBCT reconstruction method uses the feature-based mesh for estimating motion model and demonstrates equivalent image Result with previous voxel-based SMEIR approach, with significantly improved computational speed.
Block-structured adaptive meshes and reduced grids for atmospheric general circulation models.
Jablonowski, Christiane; Oehmke, Robert C; Stout, Quentin F
2009-11-28
Adaptive mesh refinement techniques offer a flexible framework for future variable-resolution climate and weather models since they can focus their computational mesh on certain geographical areas or atmospheric events. Adaptive meshes can also be used to coarsen a latitude-longitude grid in polar regions. This allows for the so-called reduced grid setups. A spherical, block-structured adaptive grid technique is applied to the Lin-Rood finite-volume dynamical core for weather and climate research. This hydrostatic dynamics package is based on a conservative and monotonic finite-volume discretization in flux form with vertically floating Lagrangian layers. The adaptive dynamical core is built upon a flexible latitude-longitude computational grid and tested in two- and three-dimensional model configurations. The discussion is focused on static mesh adaptations and reduced grids. The two-dimensional shallow water setup serves as an ideal testbed and allows the use of shallow water test cases like the advection of a cosine bell, moving vortices, a steady-state flow, the Rossby-Haurwitz wave or cross-polar flows. It is shown that reduced grid configurations are viable candidates for pure advection applications but should be used moderately in nonlinear simulations. In addition, static grid adaptations can be successfully used to resolve three-dimensional baroclinic waves in the storm-track region.
Using Multi-threading for the Automatic Load Balancing of 2D Adaptive Finite Element Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Thulasiraman, Parimala; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1998-01-01
In this paper, we present a multi-threaded approach for the automatic load balancing of adaptive finite element (FE) meshes The platform of our choice is the EARTH multi-threaded system which offers sufficient capabilities to tackle this problem. We implement the adaption phase of FE applications oil triangular meshes and exploit the EARTH token mechanism to automatically balance the resulting irregular and highly nonuniform workload. We discuss the results of our experiments oil EARTH-SP2, on implementation of EARTH on the IBM SP2 with different load balancing strategies that are built into the runtime system.
Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2014-01-01
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.
Thickness-based adaptive mesh refinement methods for multi-phase flow simulations with thin regions
Chen, Xiaodong; Yang, Vigor
2014-07-15
In numerical simulations of multi-scale, multi-phase flows, grid refinement is required to resolve regions with small scales. A notable example is liquid-jet atomization and subsequent droplet dynamics. It is essential to characterize the detailed flow physics with variable length scales with high fidelity, in order to elucidate the underlying mechanisms. In this paper, two thickness-based mesh refinement schemes are developed based on distance- and topology-oriented criteria for thin regions with confining wall/plane of symmetry and in any situation, respectively. Both techniques are implemented in a general framework with a volume-of-fluid formulation and an adaptive-mesh-refinement capability. The distance-oriented technique compares against a critical value, the ratio of an interfacial cell size to the distance between the mass center of the cell and a reference plane. The topology-oriented technique is developed from digital topology theories to handle more general conditions. The requirement for interfacial mesh refinement can be detected swiftly, without the need of thickness information, equation solving, variable averaging or mesh repairing. The mesh refinement level increases smoothly on demand in thin regions. The schemes have been verified and validated against several benchmark cases to demonstrate their effectiveness and robustness. These include the dynamics of colliding droplets, droplet motions in a microchannel, and atomization of liquid impinging jets. Overall, the thickness-based refinement technique provides highly adaptive meshes for problems with thin regions in an efficient and fully automatic manner.
Multiphase flow modelling of explosive volcanic eruptions using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Jacobs, Christian T.; Collins, Gareth S.; Piggott, Matthew D.; Kramer, Stephan C.
2014-05-01
Explosive volcanic eruptions generate highly energetic plumes of hot gas and ash particles that produce diagnostic deposits and pose an extreme environmental hazard. The formation, dispersion and collapse of these volcanic plumes are complex multiscale processes that are extremely challenging to simulate numerically. Accurate description of particle and droplet aggregation, movement and settling requires a model capable of capturing the dynamics on a range of scales (from cm to km) and a model that can correctly describe the important multiphase interactions that take place. However, even the most advanced models of eruption dynamics to date are restricted by the fixed mesh-based approaches that they employ. The research presented herein describes the development of a compressible multiphase flow model within Fluidity, a combined finite element / control volume computational fluid dynamics (CFD) code, for the study of explosive volcanic eruptions. Fluidity adopts a state-of-the-art adaptive unstructured mesh-based approach to discretise the domain and focus numerical resolution only in areas important to the dynamics, while decreasing resolution where it is not needed as a simulation progresses. This allows the accurate but economical representation of the flow dynamics throughout time, and potentially allows large multi-scale problems to become tractable in complex 3D domains. The multiphase flow model is verified with the method of manufactured solutions, and validated by simulating published gas-solid shock tube experiments and comparing the numerical results against pressure gauge data. The application of the model considers an idealised 7 km by 7 km domain in which the violent eruption of hot gas and volcanic ash high into the atmosphere is simulated. Although the simulations do not correspond to a particular eruption case study, the key flow features observed in a typical explosive eruption event are successfully captured. These include a shock wave resulting
Adaptation of Block-Structured Adaptive Mesh Refinement to Particle-In-Cell simulations
NASA Astrophysics Data System (ADS)
Vay, Jean-Luc; Colella, Phillip; McCorquodale, Peter; Friedman, Alex; Grote, Dave
2001-10-01
Particle-In-Cell (PIC) methods which solve the Maxwell equations (or a simplification) on a regular Cartesian grid are routinely used to simulate plasma and particle beam systems. Several techniques have been developed to accommodate irregular boundaries and scale variations. We describe here an ongoing effort to adapt the block-structured Adaptive Mesh Refinement (AMR) algorithm (http://seesar.lbl.gov/AMR/) to the Particle-In-Cell method. The AMR technique connects grids having different resolutions, using interpolation. Special care has to be taken to avoid the introduction of spurious forces close to the boundary of the inner, high-resolution grid, or at least to reduce such forces to an acceptable level. The Berkeley AMR library CHOMBO has been modified and coupled to WARP3d (D.P. Grote et al., Fusion Engineering and Design), 32-33 (1996), 193-200, a PIC code which is used for the development of high current accelerators for Heavy Ion Fusion. The methods and preliminary results will be presented.
Yeom, Han-Ju; Park, Jae-Hyeung
2016-08-22
We propose a method to obtain a computer-generated hologram that renders reflectance distributions of individual mesh surfaces of three-dimensional objects. Unlike previous methods which find phase distribution inside each mesh, the proposed method performs convolution of angular spectrum of the mesh to obtain desired reflectance distribution. Manipulation in the angular spectrum domain enables its application to fully-analytic mesh based computer generated hologram, removing the necessity for resampling of the spatial frequency grid. It is also computationally inexpensive as the convolution can be performed efficiently using Fourier transform. In this paper, we present principle, error analysis, simulation, and experimental verification results of the proposed method.
Multilevel Error Estimation and Adaptive h-Refinement for Cartesian Meshes with Embedded Boundaries
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
This paper presents the development of a mesh adaptation module for a multilevel Cartesian solver. While the module allows mesh refinement to be driven by a variety of different refinement parameters, a central feature in its design is the incorporation of a multilevel error estimator based upon direct estimates of the local truncation error using tau-extrapolation. This error indicator exploits the fact that in regions of uniform Cartesian mesh, the spatial operator is exactly the same on the fine and coarse grids, and local truncation error estimates can be constructed by evaluating the residual on the coarse grid of the restricted solution from the fine grid. A new strategy for adaptive h-refinement is also developed to prevent errors in smooth regions of the flow from being masked by shocks and other discontinuous features. For certain classes of error histograms, this strategy is optimal for achieving equidistribution of the refinement parameters on hierarchical meshes, and therefore ensures grid converged solutions will be achieved for appropriately chosen refinement parameters. The robustness and accuracy of the adaptation module is demonstrated using both simple model problems and complex three dimensional examples using meshes with from 10(exp 6), to 10(exp 7) cells.
Development of a scalable gas-dynamics solver with adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Korkut, Burak
There are various computational physics areas in which Direct Simulation Monte Carlo (DSMC) and Particle in Cell (PIC) methods are being employed. The accuracy of results from such simulations depend on the fidelity of the physical models being used. The computationally demanding nature of these problems make them ideal candidates to make use of modern supercomputers. The software developed to run such simulations also needs special attention so that the maintainability and extendability is considered with the recent numerical methods and programming paradigms. Suited for gas-dynamics problems, a software called SUGAR (Scalable Unstructured Gas dynamics with Adaptive mesh Refinement) has recently been developed and written in C++ and MPI. Physical and numerical models were added to this framework to simulate ion thruster plumes. SUGAR is used to model the charge-exchange (CEX) reactions occurring between the neutral and ion species as well as the induced electric field effect due to ions. Multiple adaptive mesh refinement (AMR) meshes were used in order to capture different physical length scales present in the flow. A multiple-thruster configuration was run to extend the studies to cases for which there is no axial or radial symmetry present that could only be modeled with a three-dimensional simulation capability. The combined plume structure showed interactions between individual thrusters where AMR capability captured this in an automated way. The back flow for ions was found to occur when CEX and momentum-exchange (MEX) collisions are present and strongly enhanced when the induced electric field is considered. The ion energy distributions in the back flow region were obtained and it was found that the inclusion of the electric field modeling is the most important factor in determining its shape. The plume back flow structure was also examined for a triple-thruster, 3-D geometry case and it was found that the ion velocity in the back flow region appears to be
NASA Astrophysics Data System (ADS)
Commerçon, B.; Debout, V.; Teyssier, R.
2014-03-01
Context. Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. Aims: We present a new method for implicit adaptive time-stepping on adaptive mesh-refinement grids. We implement it in the radiation-hydrodynamics solver we designed for the RAMSES code for astrophysical purposes and, more particularly, for protostellar collapse. Methods: We briefly recall the radiation-hydrodynamics equations and the adaptive time-stepping methodology used for hydrodynamical solvers. We then introduce the different types of boundary conditions (Dirichlet, Neumann, and Robin) that are used at the interface between levels and present our implementation of the new method in the RAMSES code. The method is tested against classical diffusion and radiation-hydrodynamics tests, after which we present an application for protostellar collapse. Results: We show that using Dirichlet boundary conditions at level interfaces is a good compromise between robustness and accuracy and that it can be used in structure formation calculations. The gain in computational time over our former unique time step method ranges from factors of 5 to 50 depending on the level of adaptive time-stepping and on the problem. We successfully compare the old and new methods for protostellar collapse calculations that involve highly non linear physics. Conclusions: We have developed a simple but robust method for adaptive time-stepping of implicit scheme on adaptive mesh-refinement grids. It can be applied to a wide variety of physical problems that involve diffusion processes.
ARANEA, a program for generating unstructured triangular meshes with a JAVA Graphics User Interface*
NASA Astrophysics Data System (ADS)
Marchand, Richard; Charbonneau-Lefort, Mathieu; Dumberry, Mathieu; Pronovost, Benoit
2001-09-01
ARANEA is a program that automatically generates unstructured triangular meshes on two-dimensional planar domains. The program implements a Graphics User Interface (GUI) that enables the user to read, edit and save a number of components required in the construction of a mesh. The program is written in JAVA, version 1.1. It is useful for constructing meshes of the type required to solve partial differential equations with finite elements over complex two-dimensional domains.
Generating meshes for finite-difference analysis using a solid modeler
NASA Astrophysics Data System (ADS)
Laguna, G. W.; White, W. T.; Cabral, B. K.
1987-09-01
One tool used by the Engineering Research Division of LLNL to help analyze the behavior of electronic systems in hostile environments is 3D finite-difference time-domain (FDTD) computation. FDTD codes solve Maxwell's equations,the differential equations of electromagnetism, on a uniform lattice of points. It is this uniform lattice, or mesh, that distinguishes finite-difference codes from other codes. The simple mesh makes FDTD codes computationally more efficient than other codes, which enables them to run larger problems and to run faster (up to thirty times faster than finite-element codes, for example). Therefore, within the Engineering Department at LLNL, Electronics Engineering (EE) has initiated a project to develop a mesh generator that will provide meshes suitable for FDTD analysis. This report describes the results of the first year of EE's FDTD Mesh Generation Project. During this year a preliminary version of an automated mesh generator was built and used to create a mesh of an object of interest to the High-Power Microwave Program, namely an electrically detonatable land mine. The code was verified by meshing basic solids such as spheres and cylinders. Because of the design of the code, there is no software limitation to the size of meshes that can be accommodated. The algorithm with a mesh space of approximately 500,000 cells has been demonstrated. The mesh generator can detect certain objects with walls that are thinner than the width of a cell. The code has internal graphics for viewing objects as they appear prior to being converted to a finite-difference representation. Additionally, via data files, the code is coupled to two external graphics packages for visually checking the meshes, namely TAURUS on the Cray and a new code, IMAGE, on the Silicon Graphics IRIS workstation.
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems.
Li, Zhilin; Song, Peng
2013-06-01
In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515-527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method.
Adaptive mesh refinement techniques for the immersed interface method applied to flow problems
Li, Zhilin; Song, Peng
2013-01-01
In this paper, we develop an adaptive mesh refinement strategy of the Immersed Interface Method for flow problems with a moving interface. The work is built on the AMR method developed for two-dimensional elliptic interface problems in the paper [12] (CiCP, 12(2012), 515–527). The interface is captured by the zero level set of a Lipschitz continuous function φ(x, y, t). Our adaptive mesh refinement is built within a small band of |φ(x, y, t)| ≤ δ with finer Cartesian meshes. The AMR-IIM is validated for Stokes and Navier-Stokes equations with exact solutions, moving interfaces driven by the surface tension, and classical bubble deformation problems. A new simple area preserving strategy is also proposed in this paper for the level set method. PMID:23794763
Hornung, R.D.
1996-12-31
An adaptive local mesh refinement (AMR) algorithm originally developed for unsteady gas dynamics is extended to multi-phase flow in porous media. Within the AMR framework, we combine specialized numerical methods to treat the different aspects of the partial differential equations. Multi-level iteration and domain decomposition techniques are incorporated to accommodate elliptic/parabolic behavior. High-resolution shock capturing schemes are used in the time integration of the hyperbolic mass conservation equations. When combined with AMR, these numerical schemes provide high resolution locally in a more efficient manner than if they were applied on a uniformly fine computational mesh. We will discuss the interplay of physical, mathematical, and numerical concerns in the application of adaptive mesh refinement to flow in porous media problems of practical interest.
A tuned mesh-generation strategy for image representation based on data-dependent triangulation.
Li, Ping; Adams, Michael D
2013-05-01
A mesh-generation framework for image representation based on data-dependent triangulation is proposed. The proposed framework is a modified version of the frameworks of Rippa and Garland and Heckbert that facilitates the development of more effective mesh-generation methods. As the proposed framework has several free parameters, the effects of different choices of these parameters on mesh quality are studied, leading to the recommendation of a particular set of choices for these parameters. A mesh-generation method is then introduced that employs the proposed framework with these best parameter choices. This method is demonstrated to produce meshes of higher quality (both in terms of squared error and subjectively) than those generated by several competing approaches, at a relatively modest computational and memory cost.
Failure of Anisotropic Unstructured Mesh Adaption Based on Multidimensional Residual Minimization
NASA Technical Reports Server (NTRS)
Wood, William A.; Kleb, William L.
2003-01-01
An automated anisotropic unstructured mesh adaptation strategy is proposed, implemented, and assessed for the discretization of viscous flows. The adaption criteria is based upon the minimization of the residual fluctuations of a multidimensional upwind viscous flow solver. For scalar advection, this adaption strategy has been shown to use fewer grid points than gradient based adaption, naturally aligning mesh edges with discontinuities and characteristic lines. The adaption utilizes a compact stencil and is local in scope, with four fundamental operations: point insertion, point deletion, edge swapping, and nodal displacement. Evaluation of the solution-adaptive strategy is performed for a two-dimensional blunt body laminar wind tunnel case at Mach 10. The results demonstrate that the strategy suffers from a lack of robustness, particularly with regard to alignment of the bow shock in the vicinity of the stagnation streamline. In general, constraining the adaption to such a degree as to maintain robustness results in negligible improvement to the solution. Because the present method fails to consistently or significantly improve the flow solution, it is rejected in favor of simple uniform mesh refinement.
Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations
NASA Technical Reports Server (NTRS)
Bibb, Karen L.; Gnoffo, Peter A.; Park, Michael A.; Jones, William T.
2006-01-01
Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.
Towards a large-scale scalable adaptive heart model using shallow tree meshes
NASA Astrophysics Data System (ADS)
Krause, Dorian; Dickopf, Thomas; Potse, Mark; Krause, Rolf
2015-10-01
Electrophysiological heart models are sophisticated computational tools that place high demands on the computing hardware due to the high spatial resolution required to capture the steep depolarization front. To address this challenge, we present a novel adaptive scheme for resolving the deporalization front accurately using adaptivity in space. Our adaptive scheme is based on locally structured meshes. These tensor meshes in space are organized in a parallel forest of trees, which allows us to resolve complicated geometries and to realize high variations in the local mesh sizes with a minimal memory footprint in the adaptive scheme. We discuss both a non-conforming mortar element approximation and a conforming finite element space and present an efficient technique for the assembly of the respective stiffness matrices using matrix representations of the inclusion operators into the product space on the so-called shallow tree meshes. We analyzed the parallel performance and scalability for a two-dimensional ventricle slice as well as for a full large-scale heart model. Our results demonstrate that the method has good performance and high accuracy.
Laser ray tracing in a parallel arbitrary Lagrangian-Eulerian adaptive mesh refinement hydrocode
NASA Astrophysics Data System (ADS)
Masters, N. D.; Kaiser, T. B.; Anderson, R. W.; Eder, D. C.; Fisher, A. C.; Koniges, A. E.
2010-08-01
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray tracing in ALE-AMR. We present the basic concepts of laser ray tracing and our approach to efficiently traverse the adaptive mesh hierarchy.
Performance Characteristics of an Adaptive Mesh RefinementCalculation on Scalar and Vector Platforms
Welcome, Michael; Rendleman, Charles; Oliker, Leonid; Biswas, Rupak
2006-01-31
Adaptive mesh refinement (AMR) is a powerful technique thatreduces the resources necessary to solve otherwise in-tractable problemsin computational science. The AMR strategy solves the problem on arelatively coarse grid, and dynamically refines it in regions requiringhigher resolution. However, AMR codes tend to be far more complicatedthan their uniform grid counterparts due to the software infrastructurenecessary to dynamically manage the hierarchical grid framework. Despitethis complexity, it is generally believed that future multi-scaleapplications will increasingly rely on adaptive methods to study problemsat unprecedented scale and resolution. Recently, a new generation ofparallel-vector architectures have become available that promise toachieve extremely high sustained performance for a wide range ofapplications, and are the foundation of many leadership-class computingsystems worldwide. It is therefore imperative to understand the tradeoffsbetween conventional scalar and parallel-vector platforms for solvingAMR-based calculations. In this paper, we examine the HyperCLaw AMRframework to compare and contrast performance on the Cray X1E, IBM Power3and Power5, and SGI Altix. To the best of our knowledge, this is thefirst work that investigates and characterizes the performance of an AMRcalculation on modern parallel-vector systems.
Mesh generation/refinement using fractal concepts and iterated function systems
NASA Technical Reports Server (NTRS)
Bova, S. W.; Carey, G. F.
1992-01-01
A novel method of mesh generation is proposed which is based on the use of fractal concepts to derive contractive, affine transformations. The transformations are constructed in such a manner that the attractors of the resulting maps are a union of the points, lines and surfaces in the domain. In particular, the mesh nodes may be generated recursively as a sequence of points which are obtained by applying the transformations to a coarse background mesh constructed from the given boundary data. A Delaunay triangulation or similar edge connection approach can then be performed on the resulting set of nodes in order to generate the mesh. Local refinement of an existing mesh can also be performed using the procedure. The method is easily extended to three dimensions, in which case the Delaunay triangulation is replaced by an analogous 3D tesselation.
NASA Astrophysics Data System (ADS)
Guo, Z.; Xiong, S. M.
2015-05-01
An algorithm comprising adaptive mesh refinement (AMR) and parallel (Para-) computing capabilities was developed to efficiently solve the coupled phase field equations in 3-D. The AMR was achieved based on a gradient criterion and the point clustering algorithm introduced by Berger (1991). To reduce the time for mesh generation, a dynamic regridding approach was developed based on the magnitude of the maximum phase advancing velocity. Local data at each computing process was then constructed and parallel computation was realized based on the hierarchical grid structure created during the AMR. Numerical tests and simulations on single and multi-dendrite growth were performed and results show that the proposed algorithm could shorten the computing time for 3-D phase field simulation for about two orders of magnitude and enable one to gain much more insight in understanding the underlying physics during dendrite growth in solidification.
Adaptive Mesh Refinement for High Accuracy Wall Loss Determination in Accelerating Cavity Design
Ge, L
2004-06-14
This paper presents the improvement in wall loss determination when adaptive mesh refinement (AMR) methods are used with the parallel finite element eigensolver Omega3P. We show that significant reduction in the number of degrees of freedom (DOFs) as well as a faster rate of convergence can be achieved as compared with results from uniform mesh refinement in determining cavity wall loss to a desired accuracy. Test cases for which measurements are available will be examined, and comparison with uniform refinement results will be discussed.
Laser Ray Tracing in a Parallel Arbitrary Lagrangian-Eulerian Adaptive Mesh Refinement Hydrocode
Masters, N D; Kaiser, T B; Anderson, R W; Eder, D C; Fisher, A C; Koniges, A E
2009-09-28
ALE-AMR is a new hydrocode that we are developing as a predictive modeling tool for debris and shrapnel formation in high-energy laser experiments. In this paper we present our approach to implementing laser ray-tracing in ALE-AMR. We present the equations of laser ray tracing, our approach to efficient traversal of the adaptive mesh hierarchy in which we propagate computational rays through a virtual composite mesh consisting of the finest resolution representation of the modeled space, and anticipate simulations that will be compared to experiments for code validation.
NASA Astrophysics Data System (ADS)
Burago, N. G.; Nikitin, I. S.; Yakushev, V. L.
2016-06-01
Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit-implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov-Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.
Masters, N D; Anderson, R W; Elliott, N S; Fisher, A C; Gunney, B T; Koniges, A E
2007-08-28
Modeling of high power laser and ignition facilities requires new techniques because of the higher energies and higher operational costs. We report on the development and application of a new interface reconstruction algorithm for chamber modeling code that combines ALE (Arbitrary Lagrangian Eulerian) techniques with AMR (Adaptive Mesh Refinement). The code is used for the simulation of complex target elements in the National Ignition Facility (NIF) and other similar facilities. The interface reconstruction scheme is required to adequately describe the debris/shrapnel (including fragments or droplets) resulting from energized materials that could affect optics or diagnostic sensors. Traditional ICF modeling codes that choose to implement ALE + AMR techniques will also benefit from this new scheme. The ALE formulation requires material interfaces (including those of generated particles or droplets) to be tracked. We present the interface reconstruction scheme developed for NIF's ALE-AMR and discuss how it is affected by adaptive mesh refinement and the ALE mesh. Results of the code are shown for NIF and OMEGA target configurations.
Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems
NASA Technical Reports Server (NTRS)
Steinthorsson, Erlendur; Modiano, David; Colella, Phillip
1995-01-01
To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.
Adaptive mesh refinement in curvilinear body-fitted grid systems
NASA Astrophysics Data System (ADS)
Steinthorsson, Erlendur; Modiano, David; Colella, Phillip
1995-10-01
To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.
Adaptive hp-FEM with dynamical meshes for transient heat and moisture transfer problems
NASA Astrophysics Data System (ADS)
Solin, Pavel; Dubcova, Lenka; Kruis, Jaroslav
2010-04-01
We are concerned with the time-dependent multiphysics problem of heat and moisture transfer in the context of civil engineering applications. The problem is challenging due to its multiscale nature (temperature usually propagates orders of magnitude faster than moisture), different characters of the two fields (moisture exhibits boundary layers which are not present in the temperature field), extremely long integration times (30 years or more), and lack of viable error control mechanisms. In order to solve the problem efficiently, we employ a novel multimesh adaptive higher-order finite element method (hp-FEM) based on dynamical meshes and adaptive time step control. We investigate the possibility to approximate the temperature and humidity fields on individual dynamical meshes equipped with mutually independent adaptivity mechanisms. Numerical examples related to a realistic nuclear reactor vessel simulation are presented.
An adaptive embedded mesh procedure for leading-edge vortex flows
NASA Technical Reports Server (NTRS)
Powell, Kenneth G.; Beer, Michael A.; Law, Glenn W.
1989-01-01
A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.
Integration over two-dimensional Brillouin zones by adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Henk, J.
2001-07-01
Adaptive mesh-refinement (AMR) schemes for integration over two-dimensional Brillouin zones are presented and their properties are investigated in detail. A salient feature of these integration techniques is that the grid of sampling points is automatically adapted to the integrand in such a way that regions with high accuracy demand are sampled with high density, while the other regions are sampled with low density. This adaptation may save a sizable amount of computation time in comparison with those integration methods without mesh refinement. Several AMR schemes for one- and two-dimensional integration are introduced. As an application, the spin-dependent conductance of electronic tunneling through planar junctions is investigated and discussed with regard to Brillouin zone integration.
PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes. Degree awarded by Colorado Univ.
NASA Technical Reports Server (NTRS)
Oliker, Leonid
1998-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.
ESCHER: An interactive mesh-generating editor for preparing finite-element input
NASA Technical Reports Server (NTRS)
Oakes, W. R., Jr.
1984-01-01
ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.
Practical improvements of multi-grid iteration for adaptive mesh refinement method
NASA Astrophysics Data System (ADS)
Miyashita, Hisashi; Yamada, Yoshiyuki
2005-03-01
Adaptive mesh refinement(AMR) is a powerful tool to efficiently solve multi-scaled problems. However, the vanilla AMR method has a well-known critical demerit, i.e., it cannot be applied to non-local problems. Although multi-grid iteration (MGI) can be regarded as a good remedy for a non-local problem such as the Poisson equation, we observed fundamental difficulties in applying the MGI technique in AMR to realistic problems under complicated mesh layouts because it does not converge or it requires too many iterations even if it does converge. To cope with the problem, when updating the next approximation in the MGI process, we calculate the precise total corrections that are relatively accurate to the current residual by introducing a new iteration for such a total correction. This procedure greatly accelerates the MGI convergence speed especially under complicated mesh layouts.
NASA Astrophysics Data System (ADS)
Leng, Wei; Zhong, Shijie
2011-04-01
Numerical modeling of mantle convection is challenging. Owing to the multiscale nature of mantle dynamics, high resolution is often required in localized regions, with coarser resolution being sufficient elsewhere. When investigating thermochemical mantle convection, high resolution is required to resolve sharp and often discontinuous boundaries between distinct chemical components. In this paper, we present a 2-D finite element code with adaptive mesh refinement techniques for simulating compressible thermochemical mantle convection. By comparing model predictions with a range of analytical and previously published benchmark solutions, we demonstrate the accuracy of our code. By refining and coarsening the mesh according to certain criteria and dynamically adjusting the number of particles in each element, our code can simulate such problems efficiently, dramatically reducing the computational requirements (in terms of memory and CPU time) when compared to a fixed, uniform mesh simulation. The resolving capabilities of the technique are further highlighted by examining plume-induced entrainment in a thermochemical mantle convection simulation.
Automatic generation of endocardial surface meshes with 1-to-1 correspondence from cine-MR images
NASA Astrophysics Data System (ADS)
Su, Yi; Teo, S.-K.; Lim, C. W.; Zhong, L.; Tan, R. S.
2015-03-01
In this work, we develop an automatic method to generate a set of 4D 1-to-1 corresponding surface meshes of the left ventricle (LV) endocardial surface which are motion registered over the whole cardiac cycle. These 4D meshes have 1- to-1 point correspondence over the entire set, and is suitable for advanced computational processing, such as shape analysis, motion analysis and finite element modelling. The inputs to the method are the set of 3D LV endocardial surface meshes of the different frames/phases of the cardiac cycle. Each of these meshes is reconstructed independently from border-delineated MR images and they have no correspondence in terms of number of vertices/points and mesh connectivity. To generate point correspondence, the first frame of the LV mesh model is used as a template to be matched to the shape of the meshes in the subsequent phases. There are two stages in the mesh correspondence process: (1) a coarse matching phase, and (2) a fine matching phase. In the coarse matching phase, an initial rough matching between the template and the target is achieved using a radial basis function (RBF) morphing process. The feature points on the template and target meshes are automatically identified using a 16-segment nomenclature of the LV. In the fine matching phase, a progressive mesh projection process is used to conform the rough estimate to fit the exact shape of the target. In addition, an optimization-based smoothing process is used to achieve superior mesh quality and continuous point motion.
Ray, Jaideep; Lefantzi, Sophia; Najm, Habib N.; Kennedy, Christopher A.
2006-01-01
Block-structured adaptively refined meshes (SAMR) strive for efficient resolution of partial differential equations (PDEs) solved on large computational domains by clustering mesh points only where required by large gradients. Previous work has indicated that fourth-order convergence can be achieved on such meshes by using a suitable combination of high-order discretizations, interpolations, and filters and can deliver significant computational savings over conventional second-order methods at engineering error tolerances. In this paper, we explore the interactions between the errors introduced by discretizations, interpolations and filters. We develop general expressions for high-order discretizations, interpolations, and filters, in multiple dimensions, using a Fourier approach, facilitating the high-order SAMR implementation. We derive a formulation for the necessary interpolation order for given discretization and derivative orders. We also illustrate this order relationship empirically using one and two-dimensional model problems on refined meshes. We study the observed increase in accuracy with increasing interpolation order. We also examine the empirically observed order of convergence, as the effective resolution of the mesh is increased by successively adding levels of refinement, with different orders of discretization, interpolation, or filtering.
Boundary treatments for 2D elliptic mesh generation in complex geometries
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents a boundary treatment method for 2D elliptic mesh generation in complex geometries. Corresponding to Neumann- Dirichlet boundary conditions (sliding boundary conditions), the proposed method aims at achieving orthogonal and smooth nodal distribution along irregular boundaries. In ...
Shape-model-based adaptation of 3D deformable meshes for segmentation of medical images
NASA Astrophysics Data System (ADS)
Pekar, Vladimir; Kaus, Michael R.; Lorenz, Cristian; Lobregt, Steven; Truyen, Roel; Weese, Juergen
2001-07-01
Segmentation methods based on adaptation of deformable models have found numerous applications in medical image analysis. Many efforts have been made in the recent years to improve their robustness and reliability. In particular, increasingly more methods use a priori information about the shape of the anatomical structure to be segmented. This reduces the risk of the model being attracted to false features in the image and, as a consequence, makes the need of close initialization, which remains the principal limitation of elastically deformable models, less crucial for the segmentation quality. In this paper, we present a novel segmentation approach which uses a 3D anatomical statistical shape model to initialize the adaptation process of a deformable model represented by a triangular mesh. As the first step, the anatomical shape model is parametrically fitted to the structure of interest in the image. The result of this global adaptation is used to initialize the local mesh refinement based on an energy minimization. We applied our approach to segment spine vertebrae in CT datasets. The segmentation quality was quantitatively assessed for 6 vertebrae, from 2 datasets, by computing the mean and maximum distance between the adapted mesh and a manually segmented reference shape. The results of the study show that the presented method is a promising approach for segmentation of complex anatomical structures in medical images.
Simulating Multi-scale Fluid Flows Using Adaptive Mesh Refinement Methods
NASA Astrophysics Data System (ADS)
Rowe, Kristopher; Lamb, Kevin
2015-11-01
When modelling flows with disparate length scales one must use a computational mesh that is fine enough to capture the smallest phenomena of interest. Traditional computational fluid dynamics models apply a mesh of uniform resolution to the entire computational domain; however, if the smallest scales of interest are isolated much of the computational resources used in these simulations will be wasted in regions where they are not needed. Adaptive mesh refinement methods seek to only apply resolution where it is needed. Beginning with a single coarse grid, a nested hierarchy of block structured grids is built in regions of the fluid flow where more resolution is necessary. As the fluid flow varies in time this hierarchy of grids is dynamically rebuilt to follow the phenomena of interest. Through the modelling of the interaction of vortices with wall boundary layers, it will be demonstrated that adaptive mesh refinement methods will produce equivalent results to traditional single resolution codes while using less processors, memory, and wall-clock time. Additionally, it is possible to model such flows to higher Reynolds numbers than have been feasible previously. This work was supported by NSERC and SHARCNET.
Effenberger, Frederic; Thust, Kay; Grauer, Rainer; Dreher, Juergen; Arnold, Lukas
2011-03-15
The formation of a thin current sheet in a magnetic quasiseparatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-{beta}, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al. [Astron. Astrophys. 444, 961 (2005)]. In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is finally limited by lack of resolution even in the AMR studies, the current sheet moves upward, following a global expansion of the magnetic structure during the quasistatic evolution. The sheet is locally one-dimensional and the plasma flow in its vicinity, when transformed into a comoving frame, qualitatively resembles a stagnation point flow. In conclusion, our simulations support the idea that extremely high current densities are generated in the vicinities of QSLs as a response to external perturbations, with no sign of saturation.
Fukuda, Jun-ichi; Yoneya, Makoto; Yokoyama, Hiroshi
2002-04-01
We investigate numerically the structure of topological defects close to a spherical particle immersed in a uniformly aligned nematic liquid crystal. To this end we have implemented an adaptive mesh refinement scheme in an axi-symmetric three-dimensional system, which makes it feasible to take into account properly the large length scale difference between the particle and the topological defects. The adaptive mesh refinement scheme proves to be quite efficient and useful in the investigation of not only the macroscopic properties such as the defect position but also the fine structure of defects. It can be shown that a hyperbolic hedgehog that accompanies a particle with strong homeotropic anchoring takes the structure of a ring.
NASA Astrophysics Data System (ADS)
Calder, A. C.; Curtis, B. C.; Dursi, L. J.; Fryxell, B.; Henry, G.; MacNeice, P.; Olson, K.; Ricker, P.; Rosner, R.; Timmes, F. X.; Tufo, H. M.; Truran, J. W.; Zingale, M.
We present simulations and performance results of nuclear burning fronts in supernovae on the largest domain and at the finest spatial resolution studied to date. These simulations were performed on the Intel ASCI-Red machine at Sandia National Laboratories using FLASH, a code developed at the Center for Astrophysical Thermonuclear Flashes at the University of Chicago. FLASH is a modular, adaptive mesh, parallel simulation code capable of handling compressible, reactive fluid flows in astrophysical environments. FLASH is written primarily in Fortran 90, uses the Message-Passing Interface library for inter-processor communication and portability, and employs the PARAMESH package to manage a block-structured adaptive mesh that places blocks only where the resolution is required and tracks rapidly changing flow features, such as detonation fronts, with ease. We describe the key algorithms and their implementation as well as the optimizations required to achieve sustained performance of 238 GLOPS on 6420 processors of ASCI-Red in 64-bit arithmetic.
Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver
NASA Technical Reports Server (NTRS)
Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.
2013-01-01
This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.
Anderson, R W; Pember, R B; Elliott, N S
2001-10-22
A new method that combines staggered grid Arbitrary Lagrangian-Eulerian (ALE) techniques with structured local adaptive mesh refinement (AMR) has been developed for solution of the Euler equations. This method facilitates the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required through dynamic adaption. Many of the core issues involved in the development of the combined ALEAMR method hinge upon the integration of AMR with a staggered grid Lagrangian integration method. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. Numerical examples are presented which demonstrate the accuracy and efficiency of the method.
Unstructured adaptive mesh computations of rotorcraft high-speed impulsive noise
NASA Technical Reports Server (NTRS)
Strawn, Roger; Garceau, Michael; Biswas, Rupak
1993-01-01
A new method is developed for modeling helicopter high-speed impulsive (HSI) noise. The aerodynamics and acoustics near the rotor blade tip are computed by solving the Euler equations on an unstructured grid. A stationary Kirchhoff surface integral is then used to propagate these acoustic signals to the far field. The near-field Euler solver uses a solution-adaptive grid scheme to improve the resolution of the acoustic signal. Grid points are locally added and/or deleted from the mesh at each adaptive step. An important part of this procedure is the choice of an appropriate error indicator. The error indicator is computed from the flow field solution and determines the regions for mesh coarsening and refinement. Computed results for HSI noise compare favorably with experimental data for three different hovering rotor cases.
Bas-Relief Generation and Shape Editing through Gradient-Based Mesh Deformation.
Zhang, Yu-Wei; Zhou, Yi-Qi; Li, Xue-Lin; Liu, Hui; Zhang, Li-Li
2015-03-01
In this paper, we introduce a novel approach to bas-relief generation and shape editing that uses gradient-based mesh deformation as the theoretical foundation. Our approach differs from image-based methods in that it operates directly on the triangular mesh, and ensures that the mesh topology remains unchanged during geometric processing. By implicitly deforming the input mesh through gradient manipulation, our approach is applicable to both plane surface bas-relief generation and curved surface bas-relief generation. We propose a series of gradient-based algorithms, such as height field deformation, high slope optimization, fine detail preservation, curved surface flattening and relief mapping. Additionally, we present two types of shape editing tools that allow the user to interactively modify the bas-relief to exhibit a desired shape. Experimental results indicate that the proposed approach is effective in producing plausible and impressive bas-reliefs. PMID:26357065
An Automatic 3D Mesh Generation Method for Domains with Multiple Materials.
Zhang, Yongjie; Hughes, Thomas J R; Bajaj, Chandrajit L
2010-01-01
This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single-material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided. PMID:20161555
TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh
Schnack, D.D.; Lottati, I.; Mikic, Z.
1995-07-01
The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.
Turner, C. David; Kotulski, Joseph Daniel; Pasik, Michael Francis
2005-12-01
This report investigates the feasibility of applying Adaptive Mesh Refinement (AMR) techniques to a vector finite element formulation for the wave equation in three dimensions. Possible error estimators are considered first. Next, approaches for refining tetrahedral elements are reviewed. AMR capabilities within the Nevada framework are then evaluated. We summarize our conclusions on the feasibility of AMR for time-domain vector finite elements and identify a path forward.
A 3-D adaptive mesh refinement algorithm for multimaterial gas dynamics
Puckett, E.G. ); Saltzman, J.S. )
1991-08-12
Adaptive Mesh Refinement (AMR) in conjunction with high order upwind finite difference methods has been used effectively on a variety of problems. In this paper we discuss an implementation of an AMR finite difference method that solves the equations of gas dynamics with two material species in three dimensions. An equation for the evolution of volume fractions augments the gas dynamics system. The material interface is preserved and tracked from the volume fractions using a piecewise linear reconstruction technique. 14 refs., 4 figs.
Lipnikov, Konstantin; Agouzal, Abdellatif; Vassilevski, Yuri
2009-01-01
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.
Automated hexahedral mesh generation from biomedical image data: applications in limb prosthetics.
Zachariah, S G; Sanders, J E; Turkiyyah, G M
1996-06-01
A general method to generate hexahedral meshes for finite element analysis of residual limbs and similar biomedical geometries is presented. The method utilizes skeleton-based subdivision of cross-sectional domains to produce simple subdomains in which structured meshes are easily generated. Application to a below-knee residual limb and external prosthetic socket is described. The residual limb was modeled as consisting of bones, soft tissue, and skin. The prosthetic socket model comprised a socket wall with an inner liner. The geometries of these structures were defined using axial cross-sectional contour data from X-ray computed tomography, optical scanning, and mechanical surface digitization. A tubular surface representation, using B-splines to define the directrix and generator, is shown to be convenient for definition of the structure geometries. Conversion of cross-sectional data to the compact tubular surface representation is direct, and the analytical representation simplifies geometric querying and numerical optimization within the mesh generation algorithms. The element meshes remain geometrically accurate since boundary nodes are constrained to lie on the tubular surfaces. Several element meshes of increasing mesh density were generated for two residual limbs and prosthetic sockets. Convergence testing demonstrated that approximately 19 elements are required along a circumference of the residual limb surface for a simple linear elastic model. A model with the fibula absent compared with the same geometry with the fibula present showed differences suggesting higher distal stresses in the absence of the fibula. Automated hexahedral mesh generation algorithms for sliced data represent an advancement in prosthetic stress analysis since they allow rapid modeling of any given residual limb and optimization of mesh parameters.
Divett, T; Vennell, R; Stevens, C
2013-02-28
At tidal energy sites, large arrays of hundreds of turbines will be required to generate economically significant amounts of energy. Owing to wake effects within the array, the placement of turbines within will be vital to capturing the maximum energy from the resource. This study presents preliminary results using Gerris, an adaptive mesh flow solver, to investigate the flow through four different arrays of 15 turbines each. The goal is to optimize the position of turbines within an array in an idealized channel. The turbines are represented as areas of increased bottom friction in an adaptive mesh model so that the flow and power capture in tidally reversing flow through large arrays can be studied. The effect of oscillating tides is studied, with interesting dynamics generated as the tidal current reverses direction, forcing turbulent flow through the array. The energy removed from the flow by each of the four arrays is compared over a tidal cycle. A staggered array is found to extract 54 per cent more energy than a non-staggered array. Furthermore, an array positioned to one side of the channel is found to remove a similar amount of energy compared with an array in the centre of the channel. PMID:23319710
An anisotropic scale-invariant unstructured mesh generator suitable for volumetric imaging data.
Kuprat, Andrew P; Einstein, Daniel R
2009-02-20
We present a boundary-fitted, scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local feature size. Given an input triangulated surface mesh, a feature size field is determined by casting rays normal to the surface and into the geometry and then performing gradient-limiting operations to enforce continuity of the resulting field. Surface mesh density is adjusted to be proportional to the feature size field and then a layered anisotropic volume mesh is generated. This mesh is "scale-invariant" in that roughly the same number of layers of mesh exist in mesh cross-sections, between a minimum scale size L(min) and a maximum scale size L(max). We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex biological surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[14]. Research funded by the National Heart and Blood Institute Award 1RO1HL073598-01A1. PMID:19784397
NASA Technical Reports Server (NTRS)
Steger, J. L.; Sorenson, R. L.
1979-01-01
Elliptic partial differential equations are used to generate a smooth grid that permits a one-to-one mapping in such a way that mesh lines of the same family do not cross. Problems that arise due to lack of clustering at crucial points or intersections of mesh lines at highly acute angles, are examined and various forcing or source terms are used (to correct the problems) that are either compatible with the maximum principle or are so locally controlled that mesh lines do not intersect. Attention is given to various schematics of unclustered grids and grid detail about (highly cambered) airfoils.
Fluidity: a fully-unstructured adaptive mesh computational framework for geodynamics
NASA Astrophysics Data System (ADS)
Kramer, S. C.; Davies, D.; Wilson, C. R.
2010-12-01
Fluidity is a finite element, finite volume fluid dynamics model developed by the Applied Modelling and Computation Group at Imperial College London. Several features of the model make it attractive for use in geodynamics. A core finite element library enables the rapid implementation and investigation of new numerical schemes. For example, the function spaces used for each variable can be changed allowing properties of the discretisation, such as stability, conservation and balance, to be easily varied and investigated. Furthermore, unstructured, simplex meshes allow the underlying resolution to vary rapidly across the computational domain. Combined with dynamic mesh adaptivity, where the mesh is periodically optimised to the current conditions, this allows significant savings in computational cost over traditional chessboard-like structured mesh simulations [1]. In this study we extend Fluidity (using the Portable, Extensible Toolkit for Scientific Computation [PETSc, 2]) to Stokes flow problems relevant to geodynamics. However, due to the assumptions inherent in all models, it is necessary to properly verify and validate the code before applying it to any large-scale problems. In recent years this has been made easier by the publication of a series of ‘community benchmarks’ for geodynamic modelling. We discuss the use of several of these to help validate Fluidity [e.g. 3, 4]. The experimental results of Vatteville et al. [5] are then used to validate Fluidity against laboratory measurements. This test case is also used to highlight the computational advantages of using adaptive, unstructured meshes - significantly reducing the number of nodes and total CPU time required to match a fixed mesh simulation. References: 1. C. C. Pain et al. Comput. Meth. Appl. M, 190:3771-3796, 2001. doi:10.1016/S0045-7825(00)00294-2. 2. B. Satish et al. http://www.mcs.anl.gov/petsc/petsc-2/, 2001. 3. Blankenbach et al. Geophys. J. Int., 98:23-28, 1989. 4. Busse et al. Geophys
From medical images to flow computations without user-generated meshes.
Dillard, Seth I; Mousel, John A; Shrestha, Liza; Raghavan, Madhavan L; Vigmostad, Sarah C
2014-10-01
Biomedical flow computations in patient-specific geometries require integrating image acquisition and processing with fluid flow solvers. Typically, image-based modeling processes involve several steps, such as image segmentation, surface mesh generation, volumetric flow mesh generation, and finally, computational simulation. These steps are performed separately, often using separate pieces of software, and each step requires considerable expertise and investment of time on the part of the user. In this paper, an alternative framework is presented in which the entire image-based modeling process is performed on a Cartesian domain where the image is embedded within the domain as an implicit surface. Thus, the framework circumvents the need for generating surface meshes to fit complex geometries and subsequent creation of body-fitted flow meshes. Cartesian mesh pruning, local mesh refinement, and massive parallelization provide computational efficiency; the image-to-computation techniques adopted are chosen to be suitable for distributed memory architectures. The complete framework is demonstrated with flow calculations computed in two 3D image reconstructions of geometrically dissimilar intracranial aneurysms. The flow calculations are performed on multiprocessor computer architectures and are compared against calculations performed with a standard multistep route.
From medical images to flow computations without user-generated meshes
Dillard, Seth I.; Mousel, John A.; Shrestha, Liza; Raghavan, Madhavan L.; Vigmostad, Sarah C.
2014-01-01
SUMMARY Biomedical flow computations in patient-specific geometries require integrating image acquisition and processing with fluid flow solvers. Typically, image-based modeling processes involve several steps, such as image segmentation, surface mesh generation, volumetric flow mesh generation, and finally computational simulation. These steps are performed separately, often using separate pieces of software, and each step requires considerable expertise and investment of time on the part of the user. In this paper an alternative framework is presented in which the entire image-based modeling process is performed on a Cartesian domain where the image is embedded within the domain as an implicit surface. Thus the framework circumvents the need for generating surface meshes to fit complex geometries and subsequent creation of body-fitted flow meshes. Cartesian mesh pruning, local mesh refinement, and massive parallelization provide computational efficiency; the image-to-computation techniques adopted are chosen to be suitable for distributed memory architectures. The complete framework is demonstrated with flow calculations computed in two 3D image reconstructions of geometrically dissimilar intracranial aneurysms. The flow calculations are performed on multiprocessor computer architectures and are compared against calculations performed with a standard multi-step route. PMID:24753504
Patched based methods for adaptive mesh refinement solutions of partial differential equations
Saltzman, J.
1997-09-02
This manuscript contains the lecture notes for a course taught from July 7th through July 11th at the 1997 Numerical Analysis Summer School sponsored by C.E.A., I.N.R.I.A., and E.D.F. The subject area was chosen to support the general theme of that year`s school which is ``Multiscale Methods and Wavelets in Numerical Simulation.`` The first topic covered in these notes is a description of the problem domain. This coverage is limited to classical PDEs with a heavier emphasis on hyperbolic systems and constrained hyperbolic systems. The next topic is difference schemes. These schemes are the foundation for the adaptive methods. After the background material is covered, attention is focused on a simple patched based adaptive algorithm and its associated data structures for square grids and hyperbolic conservation laws. Embellishments include curvilinear meshes, embedded boundary and overset meshes. Next, several strategies for parallel implementations are examined. The remainder of the notes contains descriptions of elliptic solutions on the mesh hierarchy, elliptically constrained flow solution methods and elliptically constrained flow solution methods with diffusion.
Error estimation and adaptive mesh refinement for parallel analysis of shell structures
NASA Technical Reports Server (NTRS)
Keating, Scott C.; Felippa, Carlos A.; Park, K. C.
1994-01-01
The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.
Error estimation and adaptive mesh refinement for parallel analysis of shell structures
NASA Astrophysics Data System (ADS)
Keating, Scott C.; Felippa, Carlos A.; Park, K. C.
1994-11-01
The formulation and application of element-level, element-independent error indicators is investigated. This research culminates in the development of an error indicator formulation which is derived based on the projection of element deformation onto the intrinsic element displacement modes. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited for obtaining error values and driving adaptive mesh refinements on parallel computers where access to neighboring elements residing on different processors may incur significant overhead. In addition such estimators are insensitive to the presence of physical interfaces and junctures. An error indicator qualifies as 'element-independent' when only visible quantities such as element stiffness and nodal displacements are used to quantify error. Error evaluation at the element level and element independence for the error indicator are highly desired properties for computing error in production-level finite element codes. Four element-level error indicators have been constructed. Two of the indicators are based on variational formulation of the element stiffness and are element-dependent. Their derivations are retained for developmental purposes. The second two indicators mimic and exceed the first two in performance but require no special formulation of the element stiffness mesh refinement which we demonstrate for two dimensional plane stress problems. The parallelizing of substructures and adaptive mesh refinement is discussed and the final error indicator using two-dimensional plane-stress and three-dimensional shell problems is demonstrated.
LAPS Grid generation and adaptation
NASA Astrophysics Data System (ADS)
Pagliantini, Cecilia; Delzanno, Gia Luca; Guo, Zehua; Srinivasan, Bhuvana; Tang, Xianzhu; Chacon, Luis
2011-10-01
LAPS uses a common-data framework in which a general purpose grid generation and adaptation package in toroidal and simply connected domains is implemented. The initial focus is on implementing the Winslow/Laplace-Beltrami method for generating non-overlapping block structured grids. This is to be followed by a grid adaptation scheme based on Monge-Kantorovich optimal transport method [Delzanno et al., J. Comput. Phys,227 (2008), 9841-9864], that equidistributes application-specified error. As an initial set of applications, we will lay out grids for an axisymmetric mirror, a field reversed configuration, and an entire poloidal cross section of a tokamak plasma reconstructed from a CMOD experimental shot. These grids will then be used for computing the plasma equilibrium and transport in accompanying presentations. A key issue for Monge-Kantorovich grid optimization is the choice of error or monitor function for equi-distribution. We will compare the Operator Recovery Error Source Detector (ORESD) [Lapenta, Int. J. Num. Meth. Eng,59 (2004) 2065-2087], the Tau method and a strategy based on the grid coarsening [Zhang et al., AIAA J,39 (2001) 1706-1715] to find an ``optimal'' grid. Work supported by DOE OFES.
Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes.
Bijar, Ahmad; Rohan, Pierre-Yves; Perrier, Pascal; Payan, Yohan
2016-01-01
Generation of subject-specific 3D finite element (FE) models requires the processing of numerous medical images in order to precisely extract geometrical information about subject-specific anatomy. This processing remains extremely challenging. To overcome this difficulty, we present an automatic atlas-based method that generates subject-specific FE meshes via a 3D registration guided by Magnetic Resonance images. The method extracts a 3D transformation by registering the atlas' volume image to the subject's one, and establishes a one-to-one correspondence between the two volumes. The 3D transformation field deforms the atlas' mesh to generate the subject-specific FE mesh. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline free-form deformations is used, which guarantees a non-folding and one-to-one transformation. Two evaluations of the method are provided. First, a publicly available CT-database is used to assess the capability to accurately capture the complexity of each subject-specific Lung's geometry. Second, FE tongue meshes are generated for two healthy volunteers and two patients suffering from tongue cancer using MR images. It is shown that the method generates an appropriate representation of the subject-specific geometry while preserving the quality of the FE meshes for subsequent FE analysis. To demonstrate the importance of our method in a clinical context, a subject-specific mesh is used to simulate tongue's biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.
Structured adaptive grid generation using algebraic methods
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.
1993-01-01
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration
KNUPP,PATRICK; MITCHELL,SCOTT A.
1999-11-01
In an attempt to automatically produce high-quality all-hex meshes, we investigated a mesh improvement strategy: given an initial poor-quality all-hex mesh, we iteratively changed the element connectivity, adding and deleting elements and nodes, and optimized the node positions. We found a set of hex reconnection primitives. We improved the optimization algorithms so they can untangle a negative-Jacobian mesh, even considering Jacobians on the boundary, and subsequently optimize the condition number of elements in an untangled mesh. However, even after applying both the primitives and optimization we were unable to produce high-quality meshes in certain regions. Our experiences suggest that many boundary configurations of quadrilaterals admit no hexahedral mesh with positive Jacobians, although we have no proof of this.
NASA Astrophysics Data System (ADS)
Shi, Lei; Wang, Z. J.
2015-08-01
Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.
A new adaptive mesh refinement data structure with an application to detonation
NASA Astrophysics Data System (ADS)
Ji, Hua; Lien, Fue-Sang; Yee, Eugene
2010-11-01
A new Cell-based Structured Adaptive Mesh Refinement (CSAMR) data structure is developed. In our CSAMR data structure, Cartesian-like indices are used to identify each cell. With these stored indices, the information on the parent, children and neighbors of a given cell can be accessed simply and efficiently. Owing to the usage of these indices, the computer memory required for storage of the proposed AMR data structure is only {5}/{8} word per cell, in contrast to the conventional oct-tree [P. MacNeice, K.M. Olson, C. Mobary, R. deFainchtein, C. Packer, PARAMESH: a parallel adaptive mesh refinement community toolkit, Comput. Phys. Commun. 330 (2000) 126] and the fully threaded tree (FTT) [A.M. Khokhlov, Fully threaded tree algorithms for adaptive mesh fluid dynamics simulations, J. Comput. Phys. 143 (1998) 519] data structures which require, respectively, 19 and 2{3}/{8} words per cell for storage of the connectivity information. Because the connectivity information (e.g., parent, children and neighbors) of a cell in our proposed AMR data structure can be accessed using only the cell indices, a tree structure which was required in previous approaches for the organization of the AMR data is no longer needed for this new data structure. Instead, a much simpler hash table structure is used to maintain the AMR data, with the entry keys in the hash table obtained directly from the explicitly stored cell indices. The proposed AMR data structure simplifies the implementation and parallelization of an AMR code. Two three-dimensional test cases are used to illustrate and evaluate the computational performance of the new CSAMR data structure.
Numerical Modelling of Volcanic Ash Settling in Water Using Adaptive Unstructured Meshes
NASA Astrophysics Data System (ADS)
Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R.
2011-12-01
At the bottom of the world's oceans lies layer after layer of ash deposited from past volcanic eruptions. Correct interpretation of these layers can provide important constraints on the duration and frequency of volcanism, but requires a full understanding of the complex multi-phase settling and deposition process. Analogue experiments of tephra settling through a tank of water demonstrate that small ash particles can either settle individually, or collectively as a gravitationally unstable ash-laden plume. These plumes are generated when the concentration of particles exceeds a certain threshold such that the density of the tephra-water mixture is sufficiently large relative to the underlying particle-free water for a gravitational Rayleigh-Taylor instability to develop. These ash-laden plumes are observed to descend as a vertical density current at a velocity much greater than that of single particles, which has important implications for the emplacement of tephra deposits on the seabed. To extend the results of laboratory experiments to large scales and explore the conditions under which vertical density currents may form and persist, we have developed a multi-phase extension to Fluidity, a combined finite element / control volume CFD code that uses adaptive unstructured meshes. As a model validation, we present two- and three-dimensional simulations of tephra plume formation in a water tank that replicate laboratory experiments (Carey, 1997, doi:10.1130/0091-7613(1997)025<0839:IOCSOT>2.3.CO;2). An inflow boundary condition at the top of the domain allows particles to flux in at a constant rate of 0.472 gm-2s-1, forming a near-surface layer of tephra particles, which initially settle individually at the predicted Stokes velocity of 1.7 mms-1. As more tephra enters the water and the particle concentration increases, the layer eventually becomes unstable and plumes begin to form, descending with velocities more than ten times greater than those of individual
ANTIPASTO: An interactive mesh generator and preprocessor for two-dimensional analysis programs
Nielan, P.E.; Perano, K.J; Mason, W.E.
1990-05-01
ANTIPASTO is an interactive two-dimensional preprocessor based on innovative user interface concepts, newly-developed geometric modeling and mesh generation algorithms, and device-independent graphics. It allows the analyst to generate, with greatly reduced effort, a complete input file for many finite-element programs including the DOE programs PASTA2D, TACO2D, GNATSII, NIKE2D, and DYNA2D. ANTIPASTO uses composite parametric cubics to store all lines and curves necessary to construct a mesh. Closed curves are supported because they allow more natural problem descriptions. The HPM algorithm developed at the University of California at Davis allows element meshes to be generated within arbitrarily complex regions with curved sides. ANTIPASTO currently supports the meshing of regions with one, two, three, four, five and six sides. Through the use of powerful grouping commands, elements, nodes, and boundary nodes can be identified and combined into named groups. The group names are available for use in specifying material properties, initial conditions, and boundary conditions such as constraints, loads, and slidelines. Groups can be specified in geometric terms. For example, all the elements within an arbitrary closed curve can be added to a group. This concept of geometric problem specification has several important implications. First, the analyst need not ever be concerned with node or element numbers. The model is completely described in terms of its geometry. Second, the mesh can be modified without the need to modify any other part of the model description. Finally, global mesh modification commands (such as a command to refine the entire mesh) can also be used without affecting any other part of the model description. ANTIPASTO presently runs on VAX computers under VMS and on CRAY computers under UNICOS. Versions for SUN and Macintosh workstations are being developed.
NASA Astrophysics Data System (ADS)
den, M.; Yamashita, K.; Ogawa, T.
A three-dimensional (3D) hydrodynamical (HD) and magneto-hydrodynamical (MHD) simulation codes using an adaptive mesh refinement (AMR) scheme are developed. This method places fine grids over areas of interest such as shock waves in order to obtain high resolution and places uniform grids with lower resolution in other area. Thus AMR scheme can provide a combination of high solution accuracy and computational robustness. We demonstrate numerical results for a simplified model of a shock propagation, which strongly indicate that the AMR techniques have the ability to resolve disturbances in an interplanetary space. We also present simulation results for MHD code.
Adaptive-mesh-based algorithm for fluorescence molecular tomography using an analytical solution.
Wang, Daifa; Song, Xiaolei; Bai, Jing
2007-07-23
Fluorescence molecular tomography (FMT) has become an important method for in-vivo imaging of small animals. It has been widely used for tumor genesis, cancer detection, metastasis, drug discovery, and gene therapy. In this study, an algorithm for FMT is proposed to obtain accurate and fast reconstruction by combining an adaptive mesh refinement technique and an analytical solution of diffusion equation. Numerical studies have been performed on a parallel plate FMT system with matching fluid. The reconstructions obtained show that the algorithm is efficient in computation time, and they also maintain image quality.
Transient thermal-structural analysis using adaptive unstructured remeshing and mesh movement
NASA Technical Reports Server (NTRS)
Dechaumphai, Pramote; Morgan, Kenneth
1990-01-01
An adaptive unstructured remeshing technique is applied to transient thermal-structural analysis. The effectiveness of the technique, together with the finite element method and an error estimation technique, is evaluated by two applications which have exact solutions: (1) the steady-state thermal analysis of a plate subjected to a highly localized surface heating, and (2) the transient thermal-structural analysis of a simulated convectively cooled leading edge subjected to a translating heat source. These applications demonstrate that the remeshing technique significantly reduces the problem size as well as the analysis solution error as compared to the results produced using standard structured meshes.
Cherry, Elizabeth M; Greenside, Henry S; Henriquez, Craig S
2003-09-01
A recently developed space-time adaptive mesh refinement algorithm (AMRA) for simulating isotropic one- and two-dimensional excitable media is generalized to simulate three-dimensional anisotropic media. The accuracy and efficiency of the algorithm is investigated for anisotropic and inhomogeneous 2D and 3D domains using the Luo-Rudy 1 (LR1) and FitzHugh-Nagumo models. For a propagating wave in a 3D slab of tissue with LR1 membrane kinetics and rotational anisotropy comparable to that found in the human heart, factors of 50 and 30 are found, respectively, for the speedup and for the savings in memory compared to an algorithm using a uniform space-time mesh at the finest resolution of the AMRA method. For anisotropic 2D and 3D media, we find no reduction in accuracy compared to a uniform space-time mesh. These results suggest that the AMRA will be able to simulate the 3D electrical dynamics of canine ventricles quantitatively for 1 s using 32 1-GHz Alpha processors in approximately 9 h.
Compact integration factor methods for complex domains and adaptive mesh refinement.
Liu, Xinfeng; Nie, Qing
2010-08-10
Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinate, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed.
Compact integration factor methods for complex domains and adaptive mesh refinement
Liu, Xinfeng; Nie, Qing
2010-01-01
Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinate, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed. PMID:20543883
A Predictive Model of Fragmentation using Adaptive Mesh Refinement and a Hierarchical Material Model
Koniges, A E; Masters, N D; Fisher, A C; Anderson, R W; Eder, D C; Benson, D; Kaiser, T B; Gunney, B T; Wang, P; Maddox, B R; Hansen, J F; Kalantar, D H; Dixit, P; Jarmakani, H; Meyers, M A
2009-03-03
Fragmentation is a fundamental material process that naturally spans spatial scales from microscopic to macroscopic. We developed a mathematical framework using an innovative combination of hierarchical material modeling (HMM) and adaptive mesh refinement (AMR) to connect the continuum to microstructural regimes. This framework has been implemented in a new multi-physics, multi-scale, 3D simulation code, NIF ALE-AMR. New multi-material volume fraction and interface reconstruction algorithms were developed for this new code, which is leading the world effort in hydrodynamic simulations that combine AMR with ALE (Arbitrary Lagrangian-Eulerian) techniques. The interface reconstruction algorithm is also used to produce fragments following material failure. In general, the material strength and failure models have history vector components that must be advected along with other properties of the mesh during remap stage of the ALE hydrodynamics. The fragmentation models are validated against an electromagnetically driven expanding ring experiment and dedicated laser-based fragmentation experiments conducted at the Jupiter Laser Facility. As part of the exit plan, the NIF ALE-AMR code was applied to a number of fragmentation problems of interest to the National Ignition Facility (NIF). One example shows the added benefit of multi-material ALE-AMR that relaxes the requirement that material boundaries must be along mesh boundaries.
Polgar, K; Viceconti, M; O'Connor, J J
2001-01-01
Finite element models of bone segments generated from computed tomography data using automatic mesh generation algorithms are becoming common not only in research but also in clinical applications such as computer aided orthopaedic surgery. Especially in the case of the latter application, the models cannot be verified against an experimental measurement, therefore their inherent accuracy should be well known before drawing conclusions based on the calculated results. This study was carried out to assess the performance of tetrahedral solid finite elements with linear and quadratic displacement functions when they are used to mesh the human femur in conjunction with automatic mesh generator methods. Ten-node quadratic tetrahedra (T10) having parabolic displacement functions were compared with four-node linear tetrahedron elements (T4) on the basis of accuracy and central processing unit (CPU) time. From the analyses of 11 finite element meshes, it was concluded that linear tetrahedral elements should be avoided and quadratic tetrahedral elements ought to be chosen for the purposes of finite element analysis of the human femur. When incremental loading and iterative solution is necessary, the coarsest possible T10 mesh compatible with accuracy is needed to minimize computer capacity and CPU time.
NASA Astrophysics Data System (ADS)
Bajc, Iztok; Hecht, Frédéric; Žumer, Slobodan
2016-09-01
This paper presents a 3D mesh adaptivity strategy on unstructured tetrahedral meshes by a posteriori error estimates based on metrics derived from the Hessian of a solution. The study is made on the case of a nonlinear finite element minimization scheme for the Landau-de Gennes free energy functional of nematic liquid crystals. Newton's iteration for tensor fields is employed with steepest descent method possibly stepping in. Aspects relating the driving of mesh adaptivity within the nonlinear scheme are considered. The algorithmic performance is found to depend on at least two factors: when to trigger each single mesh adaptation, and the precision of the correlated remeshing. Each factor is represented by a parameter, with its values possibly varying for every new mesh adaptation. We empirically show that the time of the overall algorithm convergence can vary considerably when different sequences of parameters are used, thus posing a question about optimality. The extensive testings and debugging done within this work on the simulation of systems of nematic colloids substantially contributed to the upgrade of an open source finite element-oriented programming language to its 3D meshing possibilities, as also to an outer 3D remeshing module.
Unstructured mesh algorithms for aerodynamic calculations
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1992-01-01
The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined.
Park, Jae-Hyeung; Kim, Seong-Bok; Yeom, Han-Ju; Kim, Hee-Jae; Zhang, HuiJun; Li, BoNi; Ji, Yeong-Min; Kim, Sang-Hoo; Ko, Seok-Bum
2015-12-28
Fully analytic mesh-based computer generated hologram enables efficient and precise representation of three-dimensional scene. Conventional method assigns uniform amplitude inside individual mesh, resulting in reconstruction of the three-dimensional scene of flat shading. In this paper, we report an extension of the conventional method to achieve the continuous shading where the amplitude in each mesh is continuously varying. The proposed method enables the continuous shading, while maintaining fully analytic framework of the conventional method without any sacrifice in the precision. The proposed method can also be extended to enable fast update of the shading for different illumination directions and the ambient-diffuse reflection ratio based on Phong reflection model. The feasibility of the proposed method is confirmed by the numerical and optical reconstruction of the generated hologram.
Ragusa, Jean C.
2015-01-01
In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement.
Computations of two- and three-dimensional flows using an adaptive mesh
NASA Astrophysics Data System (ADS)
Nakahashi, K.
1985-11-01
Two- and three-dimensional, steady and unsteady viscous flow fields are numerically simulated by solving the Navier-Stokes equations. A solution-adaptive-grid method is used to redistribute the grid points so as to improve the resolution of shock waves and shear layers without increasing the number of grid points. Flow fields considered include two-dimensional transonic flows about airfoils, two- and three-dimensional supersonic flow past an aerodynamic afterbody with a propulsive jet, supersonic flow over a blunt fin mounted on a wall, and supersonic flow over a bump. The computed results demonstrate a significant improvement in accuracy and quality of the solutions owing to the solution-adaptive mesh.
A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method
NASA Astrophysics Data System (ADS)
Bush, I. J.; Todorov, I. T.; Smith, W.
2006-09-01
The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.
Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation
Dione, Ibrahima; Briffard, Thomas; Doyon, Nicolas
2016-01-01
In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer. PMID:27548674
GAMER: A GRAPHIC PROCESSING UNIT ACCELERATED ADAPTIVE-MESH-REFINEMENT CODE FOR ASTROPHYSICS
Schive, H.-Y.; Tsai, Y.-C.; Chiueh Tzihong
2010-02-01
We present the newly developed code, GPU-accelerated Adaptive-MEsh-Refinement code (GAMER), which adopts a novel approach in improving the performance of adaptive-mesh-refinement (AMR) astrophysical simulations by a large factor with the use of the graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing total variation diminishing scheme for the hydrodynamic solver and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between the CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is diminished by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using one GPU with 4096{sup 3} effective resolution and 16 GPUs with 8192{sup 3} effective resolution, respectively.
Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.
Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas
2016-01-01
In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer.
Anderson, R W; Pember, R B; Elliot, N S
2000-09-26
A new method for the solution of the unsteady Euler equations has been developed. The method combines staggered grid Lagrangian techniques with structured local adaptive mesh refinement (AMR). This method is a precursor to a more general adaptive arbitrary Lagrangian Eulerian (ALE-AMR) algorithm under development, which will facilitate the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required. Many of the core issues involved in the development of the ALE-AMR method hinge upon the integration of AMR with a Lagrange step, which is the focus of the work described here. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. These new algorithmic components are first developed in one dimension and are then generalized to two dimensions. Solutions of several model problems involving shock hydrodynamics are presented and discussed.
Improved Simulation of Electrodiffusion in the Node of Ranvier by Mesh Adaptation.
Dione, Ibrahima; Deteix, Jean; Briffard, Thomas; Chamberland, Eric; Doyon, Nicolas
2016-01-01
In neural structures with complex geometries, numerical resolution of the Poisson-Nernst-Planck (PNP) equations is necessary to accurately model electrodiffusion. This formalism allows one to describe ionic concentrations and the electric field (even away from the membrane) with arbitrary spatial and temporal resolution which is impossible to achieve with models relying on cable theory. However, solving the PNP equations on complex geometries involves handling intricate numerical difficulties related either to the spatial discretization, temporal discretization or the resolution of the linearized systems, often requiring large computational resources which have limited the use of this approach. In the present paper, we investigate the best ways to use the finite elements method (FEM) to solve the PNP equations on domains with discontinuous properties (such as occur at the membrane-cytoplasm interface). 1) Using a simple 2D geometry to allow comparison with analytical solution, we show that mesh adaptation is a very (if not the most) efficient way to obtain accurate solutions while limiting the computational efforts, 2) We use mesh adaptation in a 3D model of a node of Ranvier to reveal details of the solution which are nearly impossible to resolve with other modelling techniques. For instance, we exhibit a non linear distribution of the electric potential within the membrane due to the non uniform width of the myelin and investigate its impact on the spatial profile of the electric field in the Debye layer. PMID:27548674
Automated Tetrahedral Mesh Generation for CFD Analysis of Aircraft in Conceptual Design
NASA Technical Reports Server (NTRS)
Ordaz, Irian; Li, Wu; Campbell, Richard L.
2014-01-01
The paper introduces an automation process of generating a tetrahedral mesh for computational fluid dynamics (CFD) analysis of aircraft configurations in early conceptual design. The method was developed for CFD-based sonic boom analysis of supersonic configurations, but can be applied to aerodynamic analysis of aircraft configurations in any flight regime.
An improved nearly-orthogonal structured mesh generation system with smoothness control functions
Technology Transfer Automated Retrieval System (TEKTRAN)
This paper presents an improved nearly-orthogonal structured mesh generation system with a set of smoothness control functions, which were derived based on the ratio between the Jacobian of the transformation matrix and the Jacobian of the metric tensor. The proposed smoothness control functions are...
Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow
NASA Astrophysics Data System (ADS)
Wood, William Alfred, III
production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
NASA Astrophysics Data System (ADS)
Goffin, Mark A.; Baker, Christopher M. J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.
2013-06-01
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k with directional dependence. General error estimators are derived for any given functional of the flux and applied to k to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Goffin, Mark A.; Baker, Christopher M.J.; Buchan, Andrew G.; Pain, Christopher C.; Eaton, Matthew D.; Smith, Paul N.
2013-06-01
This article presents a method for goal-based anisotropic adaptive methods for the finite element method applied to the Boltzmann transport equation. The neutron multiplication factor, k{sub eff}, is used as the goal of the adaptive procedure. The anisotropic adaptive algorithm requires error measures for k{sub eff} with directional dependence. General error estimators are derived for any given functional of the flux and applied to k{sub eff} to acquire the driving force for the adaptive procedure. The error estimators require the solution of an appropriately formed dual equation. Forward and dual error indicators are calculated by weighting the Hessian of each solution with the dual and forward residual respectively. The Hessian is used as an approximation of the interpolation error in the solution which gives rise to the directional dependence. The two indicators are combined to form a single error metric that is used to adapt the finite element mesh. The residual is approximated using a novel technique arising from the sub-grid scale finite element discretisation. Two adaptive routes are demonstrated: (i) a single mesh is used to solve all energy groups, and (ii) a different mesh is used to solve each energy group. The second method aims to capture the benefit from representing the flux from each energy group on a specifically optimised mesh. The k{sub eff} goal-based adaptive method was applied to three examples which illustrate the superior accuracy in criticality problems that can be obtained.
Manual for automatic generation of finite element models of spiral bevel gears in mesh
NASA Technical Reports Server (NTRS)
Bibel, G. D.; Reddy, S.; Kumar, A.
1994-01-01
The goal of this research is to develop computer programs that generate finite element models suitable for doing 3D contact analysis of faced milled spiral bevel gears in mesh. A pinion tooth and a gear tooth are created and put in mesh. There are two programs: Points.f and Pat.f to perform the analysis. Points.f is based on the equation of meshing for spiral bevel gears. It uses machine tool settings to solve for an N x M mesh of points on the four surfaces, pinion concave and convex, and gear concave and convex. Points.f creates the file POINTS.OUT, an ASCI file containing N x M points for each surface. (N is the number of node points along the length of the tooth, and M is nodes along the height.) Pat.f reads POINTS.OUT and creates the file tl.out. Tl.out is a series of PATRAN input commands. In addition to the mesh density on the tooth face, additional user specified variables are the number of finite elements through the thickness, and the number of finite elements along the tooth full fillet. A full fillet is assumed to exist for both the pinion and gear.
Interactive solution-adaptive grid generation
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Henderson, Todd L.
1992-01-01
TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.
Parallel octree-based hexahedral mesh generation for eulerian to lagrangian conversion.
Staten, Matthew L.; Owen, Steven James
2010-09-01
Computational simulation must often be performed on domains where materials are represented as scalar quantities or volume fractions at cell centers of an octree-based grid. Common examples include bio-medical, geotechnical or shock physics calculations where interface boundaries are represented only as discrete statistical approximations. In this work, we introduce new methods for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to ASC codes such as CTH and Alegra. New procedures for generating all-hexahedral finite element meshes from volume fraction data are introduced. A new primal-contouring approach is introduced for defining a geometric domain. New methods for refinement, node smoothing, resolving non-manifold conditions and defining geometry are also introduced as well as an extension of the algorithm to handle tetrahedral meshes. We also describe new scalable MPI-based implementations of these procedures. We describe a new software module, Sculptor, which has been developed for use as an embedded component of CTH. We also describe its interface and its use within the mesh generation code, CUBIT. Several examples are shown to illustrate the capabilities of Sculptor.
A unified approach for a posteriori high-order curved mesh generation using solid mechanics
NASA Astrophysics Data System (ADS)
Poya, Roman; Sevilla, Ruben; Gil, Antonio J.
2016-09-01
The paper presents a unified approach for the a posteriori generation of arbitrary high-order curvilinear meshes via a solid mechanics analogy. The approach encompasses a variety of methodologies, ranging from the popular incremental linear elastic approach to very sophisticated non-linear elasticity. In addition, an intermediate consistent incrementally linearised approach is also presented and applied for the first time in this context. Utilising a consistent derivation from energy principles, a theoretical comparison of the various approaches is presented which enables a detailed discussion regarding the material characterisation (calibration) employed for the different solid mechanics formulations. Five independent quality measures are proposed and their relations with existing quality indicators, used in the context of a posteriori mesh generation, are discussed. Finally, a comprehensive range of numerical examples, both in two and three dimensions, including challenging geometries of interest to the solids, fluids and electromagnetics communities, are shown in order to illustrate and thoroughly compare the performance of the different methodologies. This comparison considers the influence of material parameters and number of load increments on the quality of the generated high-order mesh, overall computational cost and, crucially, the approximation properties of the resulting mesh when considering an isoparametric finite element formulation.
Ying, Wenjun; Henriquez, Craig S
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.
Ying, Wenjun; Henriquez, Craig S.
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented. PMID:26581455
Unstructured 3D Delaunay mesh generation applied to planes, trains and automobiles
NASA Technical Reports Server (NTRS)
Blake, Kenneth R.; Spragle, Gregory S.
1993-01-01
Technical issues associated with domain-tessellation production, including initial boundary node triangulation and volume mesh refinement, are presented for the 'TGrid' 3D Delaunay unstructured grid generation program. The approach employed is noted to be capable of preserving predefined triangular surface facets in the final tessellation. The capabilities of the approach are demonstrated by generating grids about an entire fighter aircraft configuration, a train, and a wind tunnel model of an automobile.
A density-controlled triangular and quadrilateral element mesh automatic generation system
NASA Astrophysics Data System (ADS)
Sun, L.; Yeh, G.; Lin, F.; Zhao, G.
2013-12-01
We made an intensive study to develop an automatic mesh generation system based on the theory of Voronoi diagram and front advancing. The objective of this system is to create meshes for numerical modeling of practical engineering problems in the fields of geomechanics, hydrology, hydraulics, and water resources. The input data of the system is a set of given points to form the boundary contour of the analyzed geometry, containing the coordinates, the connections and the point spacing specified by users. Boundary points are generated by recursively inserting midpoints according to the spacing of the input points. For the curved boundaries, B-splines are constructed to interpolate midpoints. For the geometries with concave features and long thin domains, boundary loss problem may occur after generating the Voronoi diagram of boundary points. This problem is resolved by recursively inserting pseudo-points at the midpoints of the missing edges until all the original boundary edges are fully described. In order to ensure the curvature accuracy of curved boundaries, pseudo-points should be eliminated again by corresponding modes. Two criteria for selecting removal modes are employed, the Jacobian and minimum angle. Two methods are used to generate interior points. One is direct method and the other is pre-test method. A comparison of the two methods is also made. Laplacian method is used to smooth the interior points of triangles. For the geometries with several sub-domains, it is required to ensure the conformity of the elements and points on the intersecting boundaries between adjacent sub-domains. We establish corresponding methods to treat the overlapped boundary edges and implement the reasonable distribution and excellent conformity of the triangles and points on the overlapped boundaries. On the basis of the triangular mesh created by Delaunay triangulation, a front-advancing method is used to further generate quadrilateral mesh by combining two connected
Etienne, Zachariah B.; Liu, Yuk Tung; Shapiro, Stuart L.
2010-10-15
We have written and tested a new general relativistic magnetohydrodynamics code, capable of evolving magnetohydrodynamics (MHD) fluids in dynamical spacetimes with adaptive-mesh refinement (AMR). Our code solves the Einstein-Maxwell-MHD system of coupled equations in full 3+1 dimensions, evolving the metric via the Baumgarte-Shapiro Shibata-Nakamura formalism and the MHD and magnetic induction equations via a conservative, high-resolution shock-capturing scheme. The induction equations are recast as an evolution equation for the magnetic vector potential, which exists on a grid that is staggered with respect to the hydrodynamic and metric variables. The divergenceless constraint {nabla}{center_dot}B=0 is enforced by the curl of the vector potential. Our MHD scheme is fully compatible with AMR, so that fluids at AMR refinement boundaries maintain {nabla}{center_dot}B=0. In simulations with uniform grid spacing, our MHD scheme is numerically equivalent to a commonly used, staggered-mesh constrained-transport scheme. We present code validation test results, both in Minkowski and curved spacetimes. They include magnetized shocks, nonlinear Alfven waves, cylindrical explosions, cylindrical rotating disks, magnetized Bondi tests, and the collapse of a magnetized rotating star. Some of the more stringent tests involve black holes. We find good agreement between analytic and numerical solutions in these tests, and achieve convergence at the expected order.
Fakhari, Abbas; Lee, Taehun
2014-03-01
An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.
Efficient low-bit-rate adaptive mesh-based motion compensation technique
NASA Astrophysics Data System (ADS)
Mahmoud, Hanan A.; Bayoumi, Magdy A.
2001-08-01
This paper proposes a two-stage global motion estimation method using a novel quadtree block-based motion estimation technique and an active mesh model. In the first stage, motion parameters are estimated by fitting block-based motion vectors computed using a new efficient quadtree technique, that divides a frame into equilateral triangle blocks using the quad-tree structure. Arbitrary partition shapes are achieved by allowing 4-to-1, 3-to-1 and 2-1 merge/combine of sibling blocks having the same motion vector . In the second stage, the mesh is constructed using an adaptive triangulation procedure that places more triangles over areas with high motion content, these areas are estimated during the first stage. finally the motion compensation is achieved by using a novel algorithm that is carried by both the encoder and the decoder to determine the optimal triangulation of the resultant partitions followed by affine mapping at the encoder. Computer simulation results show that the proposed method gives better performance that the conventional ones in terms of the peak signal-to-noise ration (PSNR) and the compression ratio (CR).
White Dwarf Mergers on Adaptive Meshes. I. Methodology and Code Verification
NASA Astrophysics Data System (ADS)
Katz, Max P.; Zingale, Michael; Calder, Alan C.; Swesty, F. Douglas; Almgren, Ann S.; Zhang, Weiqun
2016-03-01
The Type Ia supernova (SN Ia) progenitor problem is one of the most perplexing and exciting problems in astrophysics, requiring detailed numerical modeling to complement observations of these explosions. One possible progenitor that has merited recent theoretical attention is the white dwarf (WD) merger scenario, which has the potential to naturally explain many of the observed characteristics of SNe Ia. To date there have been relatively few self-consistent simulations of merging WD systems using mesh-based hydrodynamics. This is the first paper in a series describing simulations of these systems using a hydrodynamics code with adaptive mesh refinement. In this paper we describe our numerical methodology and discuss our implementation in the compressible hydrodynamics code CASTRO, which solves the Euler equations, and the Poisson equation for self-gravity, and couples the gravitational and rotation forces to the hydrodynamics. Standard techniques for coupling gravitation and rotation forces to the hydrodynamics do not adequately conserve the total energy of the system for our problem, but recent advances in the literature allow progress and we discuss our implementation here. We present a set of test problems demonstrating the extent to which our software sufficiently models a system where large amounts of mass are advected on the computational domain over long timescales. Future papers in this series will describe our treatment of the initial conditions of these systems and will examine the early phases of the merger to determine its viability for triggering a thermonuclear detonation.
An Anisotropic Scale-Invariant Unstructured Mesh Generator Auitable for Volumetric Imaging Data
Kuprat, Andrew P.; Einstein, Daniel R.
2009-02-20
Mesh generation algorithms must consider the computational physics schemes to be adopted insomuch as tessellation should attempt to minimize discretization error metrics a priori, while placing elements judiciously yet economically. Basing local element size and shape on local geometric feature size is a promising approach, as the underlying physics may either be scale-invariant or may vary with scale in a predictable way. We present a boundary-fitted scale-invariant unstructured tetrahedral mesh generation algorithm that enables registration of element size to local geometric scale, given a triangulated mesh surface. The resulting tetrahedra are well-shaped and nearly orthogonal to the boundary. Unlike previous feature-based approaches, our algorithm does not require a background mesh, nor does it rely on the medial-axis. In contrast, as a first step, our algorithm produces a gradientlimited feature-size field over the input surface based on efficient ray casting. We illustrate how this field can be used to produce quality grids for computational fluid dynamics based simulations of challenging, topologically complex surfaces derived from magnetic resonance images. The algorithm is implemented in the Pacific Northwest National Laboratory (PNNL) version of the Los Alamos grid toolbox LaGriT[6].
3D active shape models of human brain structures: application to patient-specific mesh generation
NASA Astrophysics Data System (ADS)
Ravikumar, Nishant; Castro-Mateos, Isaac; Pozo, Jose M.; Frangi, Alejandro F.; Taylor, Zeike A.
2015-03-01
The use of biomechanics-based numerical simulations has attracted growing interest in recent years for computer-aided diagnosis and treatment planning. With this in mind, a method for automatic mesh generation of brain structures of interest, using statistical models of shape (SSM) and appearance (SAM), for personalised computational modelling is presented. SSMs are constructed as point distribution models (PDMs) while SAMs are trained using intensity profiles sampled from a training set of T1-weighted magnetic resonance images. The brain structures of interest are, the cortical surface (cerebrum, cerebellum & brainstem), lateral ventricles and falx-cerebri membrane. Two methods for establishing correspondences across the training set of shapes are investigated and compared (based on SSM quality): the Coherent Point Drift (CPD) point-set registration method and B-spline mesh-to-mesh registration method. The MNI-305 (Montreal Neurological Institute) average brain atlas is used to generate the template mesh, which is deformed and registered to each training case, to establish correspondence over the training set of shapes. 18 healthy patients' T1-weightedMRimages form the training set used to generate the SSM and SAM. Both model-training and model-fitting are performed over multiple brain structures simultaneously. Compactness and generalisation errors of the BSpline-SSM and CPD-SSM are evaluated and used to quantitatively compare the SSMs. Leave-one-out cross validation is used to evaluate SSM quality in terms of these measures. The mesh-based SSM is found to generalise better and is more compact, relative to the CPD-based SSM. Quality of the best-fit model instance from the trained SSMs, to test cases are evaluated using the Hausdorff distance (HD) and mean absolute surface distance (MASD) metrics.
Galaxy Mergers with Adaptive Mesh Refinement: Star Formation and Hot Gas Outflow
Kim, Ji-hoon; Wise, John H.; Abel, Tom; /KIPAC, Menlo Park /Stanford U., Phys. Dept.
2011-06-22
In hierarchical structure formation, merging of galaxies is frequent and known to dramatically affect their properties. To comprehend these interactions high-resolution simulations are indispensable because of the nonlinear coupling between pc and Mpc scales. To this end, we present the first adaptive mesh refinement (AMR) simulation of two merging, low mass, initially gas-rich galaxies (1.8 x 10{sup 10} M{sub {circle_dot}} each), including star formation and feedback. With galaxies resolved by {approx} 2 x 10{sup 7} total computational elements, we achieve unprecedented resolution of the multiphase interstellar medium, finding a widespread starburst in the merging galaxies via shock-induced star formation. The high dynamic range of AMR also allows us to follow the interplay between the galaxies and their embedding medium depicting how galactic outflows and a hot metal-rich halo form. These results demonstrate that AMR provides a powerful tool in understanding interacting galaxies.
Detached Eddy Simulation of the UH-60 Rotor Wake Using Adaptive Mesh Refinement
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.; Ahmad, Jasim U.
2012-01-01
Time-dependent Navier-Stokes flow simulations have been carried out for a UH-60 rotor with simplified hub in forward flight and hover flight conditions. Flexible rotor blades and flight trim conditions are modeled and established by loosely coupling the OVERFLOW Computational Fluid Dynamics (CFD) code with the CAMRAD II helicopter comprehensive code. High order spatial differences, Adaptive Mesh Refinement (AMR), and Detached Eddy Simulation (DES) are used to obtain highly resolved vortex wakes, where the largest turbulent structures are captured. Special attention is directed towards ensuring the dual time accuracy is within the asymptotic range, and verifying the loose coupling convergence process using AMR. The AMR/DES simulation produced vortical worms for forward flight and hover conditions, similar to previous results obtained for the TRAM rotor in hover. AMR proved to be an efficient means to capture a rotor wake without a priori knowledge of the wake shape.
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.; Fambri, F.
2016-05-01
We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an ”a-posteriori” sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.
3D Adaptive Mesh Refinement Simulations of Pellet Injection in Tokamaks
R. Samtaney; S.C. Jardin; P. Colella; D.F. Martin
2003-10-20
We present results of Adaptive Mesh Refinement (AMR) simulations of the pellet injection process, a proven method of refueling tokamaks. AMR is a computationally efficient way to provide the resolution required to simulate realistic pellet sizes relative to device dimensions. The mathematical model comprises of single-fluid MHD equations with source terms in the continuity equation along with a pellet ablation rate model. The numerical method developed is an explicit unsplit upwinding treatment of the 8-wave formulation, coupled with a MAC projection method to enforce the solenoidal property of the magnetic field. The Chombo framework is used for AMR. The role of the E x B drift in mass redistribution during inside and outside pellet injections is emphasized.
Dynamic Implicit 3D Adaptive Mesh Refinement for Non-Equilibrium Radiation Diffusion
Philip, Bobby; Wang, Zhen; Berrill, Mark A; Rodriguez Rodriguez, Manuel; Pernice, Michael
2014-01-01
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multiphysics systems: implicit time integration for efficient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent linear solver convergence.
On the Computation of Integral Curves in Adaptive Mesh Refinement Vector Fields
Deines, Eduard; Weber, Gunther H.; Garth, Christoph; Van Straalen, Brian; Borovikov, Sergey; Martin, Daniel F.; Joy, Kenneth I.
2011-06-27
Integral curves, such as streamlines, streaklines, pathlines, and timelines, are an essential tool in the analysis of vector field structures, offering straightforward and intuitive interpretation of visualization results. While such curves have a long-standing tradition in vector field visualization, their application to Adaptive Mesh Refinement (AMR) simulation results poses unique problems. AMR is a highly effective discretization method for a variety of physical simulation problems and has recently been applied to the study of vector fields in flow and magnetohydrodynamic applications. The cell-centered nature of AMR data and discontinuities in the vector field representation arising from AMR level boundaries complicate the application of numerical integration methods to compute integral curves. In this paper, we propose a novel approach to alleviate these problems and show its application to streamline visualization in an AMR model of the magnetic field of the solar system as well as to a simulation of two incompressible viscous vortex rings merging.
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
NASA Astrophysics Data System (ADS)
Wick, Thomas
2016-06-01
In this study, a posteriori error estimation and goal-oriented mesh adaptivity are developed for phase-field fracture propagation. Goal functionals are computed with the dual-weighted residual (DWR) method, which is realized by a recently introduced novel localization technique based on a partition-of-unity (PU). This technique is straightforward to apply since the weak residual is used. The influence of neighboring cells is gathered by the PU. Consequently, neither strong residuals nor jumps over element edges are required. Therefore, this approach facilitates the application of the DWR method to coupled (nonlinear) multiphysics problems such as fracture propagation. These developments then allow for a systematic investigation of the discretization error for certain quantities of interest. Specifically, our focus on the relationship between the phase-field regularization and the spatial discretization parameter in terms of goal functional evaluations is novel.
A Parallel Ocean Model With Adaptive Mesh Refinement Capability For Global Ocean Prediction
Herrnstein, Aaron R.
2005-12-01
An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration, and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO_{2} concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No
Single-pass GPU-raycasting for structured adaptive mesh refinement data
NASA Astrophysics Data System (ADS)
Kaehler, Ralf; Abel, Tom
2013-01-01
Structured Adaptive Mesh Refinement (SAMR) is a popular numerical technique to study processes with high spatial and temporal dynamic range. It reduces computational requirements by adapting the lattice on which the underlying differential equations are solved to most efficiently represent the solution. Particularly in astrophysics and cosmology such simulations now can capture spatial scales ten orders of magnitude apart and more. The irregular locations and extensions of the refined regions in the SAMR scheme and the fact that different resolution levels partially overlap, poses a challenge for GPU-based direct volume rendering methods. kD-trees have proven to be advantageous to subdivide the data domain into non-overlapping blocks of equally sized cells, optimal for the texture units of current graphics hardware, but previous GPU-supported raycasting approaches for SAMR data using this data structure required a separate rendering pass for each node, preventing the application of many advanced lighting schemes that require simultaneous access to more than one block of cells. In this paper we present the first single-pass GPU-raycasting algorithm for SAMR data that is based on a kD-tree. The tree is efficiently encoded by a set of 3D-textures, which allows to adaptively sample complete rays entirely on the GPU without any CPU interaction. We discuss two different data storage strategies to access the grid data on the GPU and apply them to several datasets to prove the benefits of the proposed method.
THE PLUTO CODE FOR ADAPTIVE MESH COMPUTATIONS IN ASTROPHYSICAL FLUID DYNAMICS
Mignone, A.; Tzeferacos, P.; Zanni, C.; Bodo, G.; Van Straalen, B.; Colella, P.
2012-01-01
We present a description of the adaptive mesh refinement (AMR) implementation of the PLUTO code for solving the equations of classical and special relativistic magnetohydrodynamics (MHD and RMHD). The current release exploits, in addition to the static grid version of the code, the distributed infrastructure of the CHOMBO library for multidimensional parallel computations over block-structured, adaptively refined grids. We employ a conservative finite-volume approach where primary flow quantities are discretized at the cell center in a dimensionally unsplit fashion using the Corner Transport Upwind method. Time stepping relies on a characteristic tracing step where piecewise parabolic method, weighted essentially non-oscillatory, or slope-limited linear interpolation schemes can be handily adopted. A characteristic decomposition-free version of the scheme is also illustrated. The solenoidal condition of the magnetic field is enforced by augmenting the equations with a generalized Lagrange multiplier providing propagation and damping of divergence errors through a mixed hyperbolic/parabolic explicit cleaning step. Among the novel features, we describe an extension of the scheme to include non-ideal dissipative processes, such as viscosity, resistivity, and anisotropic thermal conduction without operator splitting. Finally, we illustrate an efficient treatment of point-local, potentially stiff source terms over hierarchical nested grids by taking advantage of the adaptivity in time. Several multidimensional benchmarks and applications to problems of astrophysical relevance assess the potentiality of the AMR version of PLUTO in resolving flow features separated by large spatial and temporal disparities.
6th International Meshing Roundtable '97
White, D.
1997-09-01
The goal of the 6th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the pas~ the Roundtable has enjoyed significant participation born each of these groups from a wide variety of countries. The Roundtable will consist of technical presentations from contributed papers and abstracts, two invited speakers, and two invited panels of experts discussing topics related to the development and use of automatic mesh generation tools. In addition, this year we will feature a "Bring Your Best Mesh" competition and poster session to encourage discussion and participation from a wide variety of mesh generation tool users. The schedule and evening social events are designed to provide numerous opportunities for informal dialog. A proceedings will be published by Sandia National Laboratories and distributed at the Roundtable. In addition, papers of exceptionally high quaIity will be submitted to a special issue of the International Journal of Computational Geometry and Applications. Papers and one page abstracts were sought that present original results on the meshing process. Potential topics include but are got limited to: Unstructured triangular and tetrahedral mesh generation Unstructured quadrilateral and hexahedral mesh generation Automated blocking and structured mesh generation Mixed element meshing Surface mesh generation Geometry decomposition and clean-up techniques Geometry modification techniques related to meshing Adaptive mesh refinement and mesh quality control Mesh visualization Special purpose meshing algorithms for particular applications Theoretical or novel ideas with practical potential Technical presentations from industrial researchers.
2010-10-05
MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact with iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.
2010-10-05
MeshKit is an open-source library of mesh generation functionality. MeshKit has general mesh manipulation and generation functions such as Copoy, Move, Rotate and Extrude mesh. In addition, new quad mesh and embedded boundary Cartesian mesh algorithm (EB Mesh) are included. Interfaces to several public domain meshing algorithms (TetGen, netgen, triangle, Gmsh, camal) are also offered. This library interacts with mesh data mostly through iMesh including accessing the mesh in parallel. It also can interact withmore » iGeom interface to provide geometry functionality such as importing solid model based geometries. iGeom and IMesh are implemented in the CGM and MOAB packages, respectively. For some non-existing function in iMesh such as tree-construction and ray-tracing, MeshKit also interacts with MOAB functions directly.« less
Learning to use the finite-element mesh generator, ESCHER 3. 2
Oakes, W.R. Jr.
1989-08-01
ESCHER is a finite-element mesh generator designed to generate valid and well proportioned two-dimensional and three-dimensional meshes. It is intended for use in a loosely integrated analysis system. Edge-geometry data can be input to ESCHER from almost any computer-aided drafting program used today. ESCHER produces a finite-element model in a neutral file format that can be translated for input to specific finite-element analysis codes. This report describes how to use ESCHER. It explains what constitutes a valid geometrical model, how to construct one from edge geometry, how to define a finite-element model given a geometrical model, and how to verify that the created model is valid. The computer-hardware system required is explained, and ESCHER's relationship to other computer codes in the Integrated Design Engineering Analysis Library, IDEAL, is discussed. 5 refs., 11 figs.
Bohr, Adam; Beck-Broichsitter, Moritz
2015-01-01
Direct drug delivery to the lungs is considered the gold standard for the treatment of a variety of respiratory diseases, owing to the increased therapeutic selectivity of the inhalative approach. Airborne formulations with defined size characteristics are required to improve the deposition pattern within the airways. In this respect, different nebulizer systems have been conceived, which has enabled the generation of respirable medicament mists. Here, vibrating-mesh technology revealed significant potential to overcome the main shortcomings associated with 'traditional' devices. Tailored orifice dimensions and defined formulation characteristics are of special interest for the generation of suitable aerosol droplets for inhalative purposes. Ongoing developments in device and formulation design will optimize the clinical outcome of inhalative drug delivery under application of vibrating-mesh technology.
Shepherd, Jason; Mitchell, Scott A.; Jankovich, Steven R.; Benzley, Steven E.
2007-05-15
The present invention provides a meshing method, called grafting, that lifts the prior art constraint on abutting surfaces, including surfaces that are linking, source/target, or other types of surfaces of the trunk volume. The grafting method locally modifies the structured mesh of the linking surfaces allowing the mesh to conform to additional surface features. Thus, the grafting method can provide a transition between multiple sweep directions extending sweeping algorithms to 23/4-D solids. The method is also suitable for use with non-sweepable volumes; the method provides a transition between meshes generated by methods other than sweeping as well.
Mesh generation and energy group condensation studies for the jaguar deterministic transport code
Kennedy, R. A.; Watson, A. M.; Iwueke, C. I.; Edwards, E. J.
2012-07-01
The deterministic transport code Jaguar is introduced, and the modeling process for Jaguar is demonstrated using a two-dimensional assembly model of the Hoogenboom-Martin Performance Benchmark Problem. This single assembly model is being used to test and analyze optimal modeling methodologies and techniques for Jaguar. This paper focuses on spatial mesh generation and energy condensation techniques. In this summary, the models and processes are defined as well as thermal flux solution comparisons with the Monte Carlo code MC21. (authors)
NASA Astrophysics Data System (ADS)
Huang, Rongzong; Wu, Huiying
2016-06-01
A total enthalpy-based lattice Boltzmann (LB) method with adaptive mesh refinement (AMR) is developed in this paper to efficiently simulate solid-liquid phase change problem where variables vary significantly near the phase interface and thus finer grid is required. For the total enthalpy-based LB method, the velocity field is solved by an incompressible LB model with multiple-relaxation-time (MRT) collision scheme, and the temperature field is solved by a total enthalpy-based MRT LB model with the phase interface effects considered and the deviation term eliminated. With a kinetic assumption that the density distribution function for solid phase is at equilibrium state, a volumetric LB scheme is proposed to accurately realize the nonslip velocity condition on the diffusive phase interface and in the solid phase. As compared with the previous schemes, this scheme can avoid nonphysical flow in the solid phase. As for the AMR approach, it is developed based on multiblock grids. An indicator function is introduced to control the adaptive generation of multiblock grids, which can guarantee the existence of overlap area between adjacent blocks for information exchange. Since MRT collision schemes are used, the information exchange is directly carried out in the moment space. Numerical tests are firstly performed to validate the strict satisfaction of the nonslip velocity condition, and then melting problems in a square cavity with different Prandtl numbers and Rayleigh numbers are simulated, which demonstrate that the present method can handle solid-liquid phase change problem with high efficiency and accuracy.
NASA Astrophysics Data System (ADS)
Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long
2014-11-01
The authors have developed a method to automatically generate non-uniform CFD mesh for image-based human airway models. The sizes of generated tetrahedral elements vary in both radial and longitudinal directions to account for boundary layer and multiscale nature of pulmonary airflow. The proposed method takes advantage of our previously developed centerline-based geometry reconstruction method. In order to generate the mesh branch by branch in parallel, we used the open-source programs Gmsh and TetGen for surface and volume meshes, respectively. Both programs can specify element sizes by means of background mesh. The size of an arbitrary element in the domain is a function of wall distance, element size on the wall, and element size at the center of airway lumen. The element sizes on the wall are computed based on local flow rate and airway diameter. The total number of elements in the non-uniform mesh (10 M) was about half of that in the uniform mesh, although the computational time for the non-uniform mesh was about twice longer (170 min). The proposed method generates CFD meshes with fine elements near the wall and smooth variation of element size in longitudinal direction, which are required, e.g., for simulations with high flow rate. NIH Grants R01-HL094315, U01-HL114494, and S10-RR022421. Computer time provided by XSEDE.
Parameter studies of gear cooling using an automatic finites element mesh generator
NASA Technical Reports Server (NTRS)
El-Bayoumy, L. E.; Akin, L. S.; Townsend, D. P.
1984-01-01
The range of accuracies achieved in the gear tooth temperature using an automatic finite element mesh generator were investigated. Gear web contribution to the gear cooling process was studied by introducing a varying size hole at the center of the gear because of the versatility of program TARG in allowing different heat transfer coefficients in different areas of the gear tooth. A study was carried out to evaluate the contribution of the loaded and unloaded faces as well as the top and bottom lands. A general purpose two-dimensional finite element preprocessor ATOGEN has been developed for automatic generation of a finite element mesh over a pie-shaped sector of a gear. The program was used for facilitating the input to an upgraded version of a previously developed program for the thermal analysis of running gears (TARG). The latter program determined the steady state temperature distribution throughout the specified gear. The automatic mesh generator program includes a band width minimization routine for reducing computer cost.
CRASH: A BLOCK-ADAPTIVE-MESH CODE FOR RADIATIVE SHOCK HYDRODYNAMICS-IMPLEMENTATION AND VERIFICATION
Van der Holst, B.; Toth, G.; Sokolov, I. V.; Myra, E. S.; Fryxell, B.; Drake, R. P.; Powell, K. G.; Holloway, J. P.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.
2011-06-01
We describe the Center for Radiative Shock Hydrodynamics (CRASH) code, a block-adaptive-mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with a gray or multi-group method and uses a flux-limited diffusion approximation to recover the free-streaming limit. Electrons and ions are allowed to have different temperatures and we include flux-limited electron heat conduction. The radiation hydrodynamic equations are solved in the Eulerian frame by means of a conservative finite-volume discretization in either one-, two-, or three-dimensional slab geometry or in two-dimensional cylindrical symmetry. An operator-split method is used to solve these equations in three substeps: (1) an explicit step of a shock-capturing hydrodynamic solver; (2) a linear advection of the radiation in frequency-logarithm space; and (3) an implicit solution of the stiff radiation diffusion, heat conduction, and energy exchange. We present a suite of verification test problems to demonstrate the accuracy and performance of the algorithms. The applications are for astrophysics and laboratory astrophysics. The CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with a new radiation transfer and heat conduction library and equation-of-state and multi-group opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework.
NASA Astrophysics Data System (ADS)
Hatori, Tomoharu; Ito, Atsushi M.; Nunami, Masanori; Usui, Hideyuki; Miura, Hideaki
2016-08-01
We propose a numerical method to determine the artificial viscosity in magnetohydrodynamics (MHD) simulations with adaptive mesh refinement (AMR) method, where the artificial viscosity is adaptively changed due to the resolution level of the AMR hierarchy. Although the suitable value of the artificial viscosity depends on the governing equations and the model of target problem, it can be determined by von Neumann stability analysis. By means of the new method, "level-by-level artificial viscosity method," MHD simulations of Rayleigh-Taylor instability (RTI) are carried out with the AMR method. The validity of the level-by-level artificial viscosity method is confirmed by the comparison of the linear growth rates of RTI between the AMR simulations and the simple simulations with uniform grid and uniform artificial viscosity whose resolution is the same as that in the highest level of the AMR simulation. Moreover, in the nonlinear phase of RTI, the secondary instability is clearly observed where the hierarchical data structure of AMR calculation is visualized as high resolution region floats up like terraced fields. In the applications of the method to general fluid simulations, the growth of small structures can be sufficiently reproduced, while the divergence of numerical solutions can be suppressed.
Dynamically adaptive mesh refinement technique for image reconstruction in optical tomography.
Soloviev, Vadim Y; Krasnosselskaia, Lada V
2006-04-20
A novel adaptive mesh technique is introduced for problems of image reconstruction in luminescence optical tomography. A dynamical adaptation of the three-dimensional scheme based on the finite-volume formulation reduces computational time and balances the ill-posed nature of the inverse problem. The arbitrary shape of the bounding surface is handled by an additional refinement of computational cells on the boundary. Dynamical shrinking of the search volume is introduced to improve computational performance and accuracy while locating the luminescence target. Light propagation in the medium is modeled by the telegraph equation, and the image-reconstruction algorithm is derived from the Fredholm integral equation of the first kind. Stability and computational efficiency of the introduced method are demonstrated for image reconstruction of one and two spherical luminescent objects embedded within a breastlike tissue phantom. Experimental measurements are simulated by the solution of the forward problem on a grid of 5x5 light guides attached to the surface of the phantom.
An Application of the Mesh Generation and Refinement Tool to Mobile Bay, Alabama, USA
NASA Astrophysics Data System (ADS)
Aziz, Wali; Alarcon, Vladimir J.; McAnally, William; Martin, James; Cartwright, John
2009-08-01
A grid generation tool, called the Mesh Generation and Refinement Tool (MGRT), has been developed using Qt4. Qt4 is a comprehensive C++ application framework which includes GUI and container class-libraries and tools for cross-platform development. MGRT is capable of using several types of algorithms for grid generation. This paper presents an application of the MGRT grid generation tool for creating an unstructured grid of Mobile Bay (Alabama, USA) that will be used for hydrodynamics modeling. The algorithm used in this particular application is the Advancing-Front/Local-Reconnection (AFLR) [1] [2]. This research shows results of grids created with MGRT and compares them to grids (for the same geographical container) created using other grid generation tools. The superior quality of the grids generated by MGRT is shown.
Automated Generation of Finite-Element Meshes for Aircraft Conceptual Design
NASA Technical Reports Server (NTRS)
Li, Wu; Robinson, Jay
2016-01-01
This paper presents a novel approach for automated generation of fully connected finite-element meshes for all internal structural components and skins of a given wing-body geometry model, controlled by a few conceptual-level structural layout parameters. Internal structural components include spars, ribs, frames, and bulkheads. Structural layout parameters include spar/rib locations in wing chordwise/spanwise direction and frame/bulkhead locations in longitudinal direction. A simple shell thickness optimization problem with two load conditions is used to verify versatility and robustness of the automated meshing process. The automation process is implemented in ModelCenter starting from an OpenVSP geometry and ending with a NASTRAN 200 solution. One subsonic configuration and one supersonic configuration are used for numerical verification. Two different structural layouts are constructed for each configuration and five finite-element meshes of different sizes are generated for each layout. The paper includes various comparisons of solutions of 20 thickness optimization problems, as well as discussions on how the optimal solutions are affected by the stress constraint bound and the initial guess of design variables.
Interactive solution-adaptive grid generation procedure
NASA Technical Reports Server (NTRS)
Henderson, Todd L.; Choo, Yung K.; Lee, Ki D.
1992-01-01
TURBO-AD is an interactive solution adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution adaptive grid generation technique into a single interactive package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on the unit square in the parametric domain, and the new adapted grid is then mapped back to the physical domain. The grid adaption is achieved by adapting the control points to a numerical solution in the parametric domain using control sources obtained from the flow properties. Then a new modified grid is generated from the adapted control net. This process is efficient because the number of control points is much less than the number of grid points and the generation of the grid is an efficient algebraic process. TURBO-AD provides the user with both local and global controls.
INGRID: a three-dimensional mesh generator for modeling nonlinear systems
Stillman, D.W.; Hallquist, J.O.
1985-07-01
INGRID generates complete input files for the codes DYNA3D, NIKE3D, FACET, and TOPAZ3D. Geometries are described primarily using index space concepts which came from the program INGEN. The ideas used in INGEN were reworked into a new method which is both simple and powerful. Interactive graphics in INGRID are patterned after TAURUS, a three-dimensional post-processor, and MAZE, a two-dimensional mesh generator. Much of the coding from MAZE is directly incorporated in INGRID.
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2013-12-01
Accurate numerical simulations of global scale three-dimensional atmospheric chemical transport models (CTMs) are essential for studies of many important atmospheric chemistry problems such as adverse effect of air pollutants on human health, ecosystems and the Earth's climate. These simulations usually require large CPU time due to numerical difficulties associated with a wide range of spatial and temporal scales, nonlinearity and large number of reacting species. In our previous work we have shown that in order to achieve adequate convergence rate and accuracy, the mesh spacing in numerical simulation of global synoptic-scale pollution plume transport must be decreased to a few kilometers. This resolution is difficult to achieve for global CTMs on uniform or quasi-uniform grids. To address the described above difficulty we developed a three-dimensional Wavelet-based Adaptive Mesh Refinement (WAMR) algorithm. The method employs a highly non-uniform adaptive grid with fine resolution over the areas of interest without requiring small grid-spacing throughout the entire domain. The method uses multi-grid iterative solver that naturally takes advantage of a multilevel structure of the adaptive grid. In order to represent the multilevel adaptive grid efficiently, a dynamic data structure based on indirect memory addressing has been developed. The data structure allows rapid access to individual points, fast inter-grid operations and re-gridding. The WAMR method has been implemented on parallel computer architectures. The parallel algorithm is based on run-time partitioning and load-balancing scheme for the adaptive grid. The partitioning scheme maintains locality to reduce communications between computing nodes. The parallel scheme was found to be cost-effective. Specifically we obtained an order of magnitude increase in computational speed for numerical simulations performed on a twelve-core single processor workstation. We have applied the WAMR method for numerical
NASA Astrophysics Data System (ADS)
Lu, Yao; Ye, Hongwei; Xu, Yuesheng; Hu, Xiaofei; Vogelsang, Levon; Shen, Lixin; Feiglin, David; Lipson, Edward; Krol, Andrzej
2008-03-01
To improve the speed and quality of ordered-subsets expectation-maximization (OSEM) SPECT reconstruction, we have implemented a content-adaptive, singularity-based, mesh-domain, image model (CASMIM) with an accurate algorithm for estimation of the mesh-domain system matrix. A preliminary image, used to initialize CASMIM reconstruction, was obtained using pixel-domain OSEM. The mesh-domain representation of the image was produced by a 2D wavelet transform followed by Delaunay triangulation to obtain joint estimation of nodal locations and their activity values. A system matrix with attenuation compensation was investigated. Digital chest phantom SPECT was simulated and reconstructed. The quality of images reconstructed with OSEM-CASMIM is comparable to that from pixel-domain OSEM, but images are obtained five times faster by the CASMIM method.
Relativistic Flows Using Spatial And Temporal Adaptive Structured Mesh Refinement. I. Hydrodynamics
Wang, Peng; Abel, Tom; Zhang, Weiqun; /KIPAC, Menlo Park
2007-04-02
Astrophysical relativistic flow problems require high resolution three-dimensional numerical simulations. In this paper, we describe a new parallel three-dimensional code for simulations of special relativistic hydrodynamics (SRHD) using both spatially and temporally structured adaptive mesh refinement (AMR). We used method of lines to discrete SRHD equations spatially and used a total variation diminishing (TVD) Runge-Kutta scheme for time integration. For spatial reconstruction, we have implemented piecewise linear method (PLM), piecewise parabolic method (PPM), third order convex essentially non-oscillatory (CENO) and third and fifth order weighted essentially non-oscillatory (WENO) schemes. Flux is computed using either direct flux reconstruction or approximate Riemann solvers including HLL, modified Marquina flux, local Lax-Friedrichs flux formulas and HLLC. The AMR part of the code is built on top of the cosmological Eulerian AMR code enzo, which uses the Berger-Colella AMR algorithm and is parallel with dynamical load balancing using the widely available Message Passing Interface library. We discuss the coupling of the AMR framework with the relativistic solvers and show its performance on eleven test problems.
Collins, David C.; Norman, Michael L.; Padoan, Paolo; Xu Hao
2011-04-10
In this work, we present the mass and magnetic distributions found in a recent adaptive mesh refinement magnetohydrodynamic simulation of supersonic, super-Alfvenic, self-gravitating turbulence. Power-law tails are found in both mass density and magnetic field probability density functions, with P({rho}) {proportional_to} {rho}{sup -1.6} and P(B) {proportional_to} B{sup -2.7}. A power-law relationship is also found between magnetic field strength and density, with B {proportional_to} {rho}{sup 0.5}, throughout the collapsing gas. The mass distribution of gravitationally bound cores is shown to be in excellent agreement with recent observation of prestellar cores. The mass-to-flux distribution of cores is also found to be in excellent agreement with recent Zeeman splitting measurements. We also compare the relationship between velocity dispersion and density to the same cores, and find an increasing relationship between the two, with {sigma} {proportional_to} n{sup 0.25}, also in agreement with the observations. We then estimate the potential effects of ambipolar diffusion in our cores and find that due to the weakness of the magnetic field in our simulation, the inclusion of ambipolar diffusion in our simulation will not cause significant alterations of the flow dynamics.
Hummels, Cameron B.; Bryan, Greg L.
2012-04-20
We carry out adaptive mesh refinement cosmological simulations of Milky Way mass halos in order to investigate the formation of disk-like galaxies in a {Lambda}-dominated cold dark matter model. We evolve a suite of five halos to z = 0 and find a gas disk formation in each; however, in agreement with previous smoothed particle hydrodynamics simulations (that did not include a subgrid feedback model), the rotation curves of all halos are centrally peaked due to a massive spheroidal component. Our standard model includes radiative cooling and star formation, but no feedback. We further investigate this angular momentum problem by systematically modifying various simulation parameters including: (1) spatial resolution, ranging from 1700 to 212 pc; (2) an additional pressure component to ensure that the Jeans length is always resolved; (3) low star formation efficiency, going down to 0.1%; (4) fixed physical resolution as opposed to comoving resolution; (5) a supernova feedback model that injects thermal energy to the local cell; and (6) a subgrid feedback model which suppresses cooling in the immediate vicinity of a star formation event. Of all of these, we find that only the last (cooling suppression) has any impact on the massive spheroidal component. In particular, a simulation with cooling suppression and feedback results in a rotation curve that, while still peaked, is considerably reduced from our standard runs.
Nonaka, A.; Aspden, A. J.; Almgren, A. S.; Bell, J. B.; Zingale, M.; Woosley, S. E.
2012-01-20
We extend our previous three-dimensional, full-star simulations of the final hours of convection preceding ignition in Type Ia supernovae to higher resolution using the adaptive mesh refinement capability of our low Mach number code, MAESTRO. We report the statistics of the ignition of the first flame at an effective 4.34 km resolution and general flow field properties at an effective 2.17 km resolution. We find that off-center ignition is likely, with radius of 50 km most favored and a likely range of 40-75 km. This is consistent with our previous coarser (8.68 km resolution) simulations, implying that we have achieved sufficient resolution in our determination of likely ignition radii. The dynamics of the last few hot spots preceding ignition suggest that a multiple ignition scenario is not likely. With improved resolution, we can more clearly see the general flow pattern in the convective region, characterized by a strong outward plume with a lower speed recirculation. We show that the convective core is turbulent with a Kolmogorov spectrum and has a lower turbulent intensity and larger integral length scale than previously thought (on the order of 16 km s{sup -1} and 200 km, respectively), and we discuss the potential consequences for the first flames.
Skillman, Samuel W.; Hallman, Eric J.; Burns, Jack O.; Smith, Britton D.; O'Shea, Brian W.; Turk, Matthew J.
2011-07-10
Cosmological shocks are a critical part of large-scale structure formation, and are responsible for heating the intracluster medium in galaxy clusters. In addition, they are capable of accelerating non-thermal electrons and protons. In this work, we focus on the acceleration of electrons at shock fronts, which is thought to be responsible for radio relics-extended radio features in the vicinity of merging galaxy clusters. By combining high-resolution adaptive mesh refinement/N-body cosmological simulations with an accurate shock-finding algorithm and a model for electron acceleration, we calculate the expected synchrotron emission resulting from cosmological structure formation. We produce synthetic radio maps of a large sample of galaxy clusters and present luminosity functions and scaling relationships. With upcoming long-wavelength radio telescopes, we expect to see an abundance of radio emission associated with merger shocks in the intracluster medium. By producing observationally motivated statistics, we provide predictions that can be compared with observations to further improve our understanding of magnetic fields and electron shock acceleration.
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
B. Philip; Z. Wang; M.A. Berrill; M. Birke; M. Pernice
2014-04-01
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.
GPU accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid
NASA Astrophysics Data System (ADS)
Luo, Xisheng; Wang, Luying; Ran, Wei; Qin, Fenghua
2016-10-01
A GPU accelerated inviscid flow solver is developed on an unstructured quadrilateral grid in the present work. For the first time, the cell-based adaptive mesh refinement (AMR) is fully implemented on GPU for the unstructured quadrilateral grid, which greatly reduces the frequency of data exchange between GPU and CPU. Specifically, the AMR is processed with atomic operations to parallelize list operations, and null memory recycling is realized to improve the efficiency of memory utilization. It is found that results obtained by GPUs agree very well with the exact or experimental results in literature. An acceleration ratio of 4 is obtained between the parallel code running on the old GPU GT9800 and the serial code running on E3-1230 V2. With the optimization of configuring a larger L1 cache and adopting Shared Memory based atomic operations on the newer GPU C2050, an acceleration ratio of 20 is achieved. The parallelized cell-based AMR processes have achieved 2x speedup on GT9800 and 18x on Tesla C2050, which demonstrates that parallel running of the cell-based AMR method on GPU is feasible and efficient. Our results also indicate that the new development of GPU architecture benefits the fluid dynamics computing significantly.
Advances in Rotor Performance and Turbulent Wake Simulation Using DES and Adaptive Mesh Refinement
NASA Technical Reports Server (NTRS)
Chaderjian, Neal M.
2012-01-01
Time-dependent Navier-Stokes simulations have been carried out for a rigid V22 rotor in hover, and a flexible UH-60A rotor in forward flight. Emphasis is placed on understanding and characterizing the effects of high-order spatial differencing, grid resolution, and Spalart-Allmaras (SA) detached eddy simulation (DES) in predicting the rotor figure of merit (FM) and resolving the turbulent rotor wake. The FM was accurately predicted within experimental error using SA-DES. Moreover, a new adaptive mesh refinement (AMR) procedure revealed a complex and more realistic turbulent rotor wake, including the formation of turbulent structures resembling vortical worms. Time-dependent flow visualization played a crucial role in understanding the physical mechanisms involved in these complex viscous flows. The predicted vortex core growth with wake age was in good agreement with experiment. High-resolution wakes for the UH-60A in forward flight exhibited complex turbulent interactions and turbulent worms, similar to the V22. The normal force and pitching moment coefficients were in good agreement with flight-test data.
NASA Astrophysics Data System (ADS)
Wang, Cheng; Dong, XinZhuang; Shu, Chi-Wang
2015-10-01
For numerical simulation of detonation, computational cost using uniform meshes is large due to the vast separation in both time and space scales. Adaptive mesh refinement (AMR) is advantageous for problems with vastly different scales. This paper aims to propose an AMR method with high order accuracy for numerical investigation of multi-dimensional detonation. A well-designed AMR method based on finite difference weighted essentially non-oscillatory (WENO) scheme, named as AMR&WENO is proposed. A new cell-based data structure is used to organize the adaptive meshes. The new data structure makes it possible for cells to communicate with each other quickly and easily. In order to develop an AMR method with high order accuracy, high order prolongations in both space and time are utilized in the data prolongation procedure. Based on the message passing interface (MPI) platform, we have developed a workload balancing parallel AMR&WENO code using the Hilbert space-filling curve algorithm. Our numerical experiments with detonation simulations indicate that the AMR&WENO is accurate and has a high resolution. Moreover, we evaluate and compare the performance of the uniform mesh WENO scheme and the parallel AMR&WENO method. The comparison results provide us further insight into the high performance of the parallel AMR&WENO method.
Pavarino, E.; Neves, L. A.; Machado, J. M.; de Godoy, M. F.; Shiyou, Y.; Momente, J. C.; Zafalon, G. F. D.; Pinto, A. R.; Valêncio, C. R.
2013-01-01
The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. PMID:23762031
Pavarino, E; Neves, L A; Machado, J M; de Godoy, M F; Shiyou, Y; Momente, J C; Zafalon, G F D; Pinto, A R; Valêncio, C R
2013-01-01
The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. PMID:23762031
NASA Astrophysics Data System (ADS)
Power, C.; Read, J. I.; Hobbs, A.
2014-06-01
We simulate cosmological galaxy cluster formation using three different approaches to solving the equations of non-radiative hydrodynamics - classic smoothed particle hydrodynamics (SPH), novel SPH with a higher order dissipation switch (SPHS), and an adaptive mesh refinement (AMR) method. Comparing spherically averaged entropy profiles, we find that SPHS and AMR approaches result in a well-defined entropy core that converges rapidly with increasing mass and force resolution. In contrast, the central entropy profile in the SPH approach is sensitive to the cluster's assembly history and shows poor numerical convergence. We trace this disagreement to the known artificial surface tension in SPH that appears at phase boundaries. Varying systematically numerical dissipation in SPHS, we study the contributions of numerical and physical dissipation to the entropy core and argue that numerical dissipation is required to ensure single-valued fluid quantities in converging flows. However, provided it occurs only at the resolution limit and does not propagate errors to larger scales, its effect is benign - there is no requirement to build `sub-grid' models of unresolved turbulence for galaxy cluster simulations. We conclude that entropy cores in non-radiative galaxy cluster simulations are physical, resulting from entropy generation in shocked gas during cluster assembly.
NASA Astrophysics Data System (ADS)
Rasia, Elena; Lau, Erwin T.; Borgani, Stefano; Nagai, Daisuke; Dolag, Klaus; Avestruz, Camille; Granato, Gian Luigi; Mazzotta, Pasquale; Murante, Giuseppe; Nelson, Kaylea; Ragone-Figueroa, Cinthia
2014-08-01
Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10%-30%. The largest bias originates from both violation of hydrostatic equilibrium (HE) and an additional temperature bias caused by inhomogeneities in the X-ray-emitting intracluster medium (ICM). To elucidate this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle hydrodynamics (SPH) or adaptive-mesh refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in nonradiative simulations, whereas it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with that observed in the central regions of clusters. Around R 500 the temperature inhomogeneities of the SPH simulations can generate twice the typical HE mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high-sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii.
Rasia, Elena; Lau, Erwin T.; Nagai, Daisuke; Avestruz, Camille; Borgani, Stefano; Dolag, Klaus; Granato, Gian Luigi; Murante, Giuseppe; Ragone-Figueroa, Cinthia; Mazzotta, Pasquale; Nelson, Kaylea
2014-08-20
Analyses of cosmological hydrodynamic simulations of galaxy clusters suggest that X-ray masses can be underestimated by 10%-30%. The largest bias originates from both violation of hydrostatic equilibrium (HE) and an additional temperature bias caused by inhomogeneities in the X-ray-emitting intracluster medium (ICM). To elucidate this large dispersion among theoretical predictions, we evaluate the degree of temperature structures in cluster sets simulated either with smoothed-particle hydrodynamics (SPH) or adaptive-mesh refinement (AMR) codes. We find that the SPH simulations produce larger temperature variations connected to the persistence of both substructures and their stripped cold gas. This difference is more evident in nonradiative simulations, whereas it is reduced in the presence of radiative cooling. We also find that the temperature variation in radiative cluster simulations is generally in agreement with that observed in the central regions of clusters. Around R {sub 500} the temperature inhomogeneities of the SPH simulations can generate twice the typical HE mass bias of the AMR sample. We emphasize that a detailed understanding of the physical processes responsible for the complex thermal structure in ICM requires improved resolution and high-sensitivity observations in order to extend the analysis to higher temperature systems and larger cluster-centric radii.
NASA Technical Reports Server (NTRS)
Kleb, William L.; Batina, John T.; Williams, Marc H.
1990-01-01
A temporal adaptive algorithm for the time-integration of the two-dimensional Euler or Navier-Stokes equations is presented. The flow solver involves an upwind flux-split spatial discretization for the convective terms and central differencing for the shear-stress and heat flux terms on an unstructured mesh of triangles. The temporal adaptive algorithm is a time-accurate integration procedure which allows flows with high spatial and temporal gradients to be computed efficiently by advancing each grid cell near its maximum allowable time step. Results indicate that an appreciable computational savings can be achieved for both inviscid and viscous unsteady airfoil problems using unstructured meshes without degrading spatial or temporal accuracy.
NASA Astrophysics Data System (ADS)
Adam, A.; Pavlidis, D.; Percival, J. R.; Salinas, P.; Xie, Z.; Fang, F.; Pain, C. C.; Muggeridge, A. H.; Jackson, M. D.
2016-09-01
A general, higher-order, conservative and bounded interpolation for the dynamic and adaptive meshing of control-volume fields dual to continuous and discontinuous finite element representations is presented. Existing techniques such as node-wise interpolation are not conservative and do not readily generalise to discontinuous fields, whilst conservative methods such as Grandy interpolation are often too diffusive. The new method uses control-volume Galerkin projection to interpolate between control-volume fields. Bounded solutions are ensured by using a post-interpolation diffusive correction. Example applications of the method to interface capturing during advection and also to the modelling of multiphase porous media flow are presented to demonstrate the generality and robustness of the approach.
NASA Astrophysics Data System (ADS)
Zheng, J.; Zhu, J.; Wang, Z.; Fang, F.; Pain, C. C.; Xiang, J.
2015-10-01
An integrated method of advanced anisotropic hr-adaptive mesh and discretization numerical techniques has been, for first time, applied to modelling of multiscale advection-diffusion problems, which is based on a discontinuous Galerkin/control volume discretization on unstructured meshes. Over existing air quality models typically based on static-structured grids using a locally nesting technique, the advantage of the anisotropic hr-adaptive model has the ability to adapt the mesh according to the evolving pollutant distribution and flow features. That is, the mesh resolution can be adjusted dynamically to simulate the pollutant transport process accurately and effectively. To illustrate the capability of the anisotropic adaptive unstructured mesh model, three benchmark numerical experiments have been set up for two-dimensional (2-D) advection phenomena. Comparisons have been made between the results obtained using uniform resolution meshes and anisotropic adaptive resolution meshes. Performance achieved in 3-D simulation of power plant plumes indicates that this new adaptive multiscale model has the potential to provide accurate air quality modelling solutions effectively.
Generation and Computerized Simulation of Meshing and Contact of Modified Involute Helical Gears
NASA Technical Reports Server (NTRS)
Litvin, Faydor L.; Chen, Ningxin; Lu, Jian
1995-01-01
The design and generation of modified involute helical gears that have a localized and stable bearing contact, and reduced noise and vibration characteristics are described. The localization of the bearing contact is achieved by the mismatch of the two generating surfaces that are used for generation of the pinion and the gear. The reduction of noise and vibration will be achieved by application of a parabolic function of transmission errors that is able to absorb the almost linear function of transmission errors caused by gear misalignment. The meshing and contact of misaligned gear drives can be analyzed by application of computer programs that have been developed. The computations confirmed the effectiveness of the proposed modification of the gear geometry. A numerical example that illustrates the developed theory is provided.
De Colle, Fabio; Ramirez-Ruiz, Enrico; Granot, Jonathan; Lopez-Camara, Diego
2012-02-20
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with {rho}{proportional_to}r{sup -k}, bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the
Henshaw, W; Schwendeman, D
2007-11-15
This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.
NASA Astrophysics Data System (ADS)
De Colle, Fabio; Granot, Jonathan; López-Cámara, Diego; Ramirez-Ruiz, Enrico
2012-02-01
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with ρvpropr -k , bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the relativistic flow.
NASA Technical Reports Server (NTRS)
Litvin, F. L.; Tsung, W.-J.; Coy, J. J.
1985-01-01
There is proposed a method for generation of Gleason's spiral bevel gears which provides the following properties of meshing and contact: (1) the contact normal keeps its original direction within the neighborhood of the main contact point; (2) the contact ellipse moves along the gear tooth surface; and (3) the kinematical errors caused by Gleason's method of cutting are almost zero. Computer programs for the simulation of meshing and bearing contact are developed.
Raut, Samarth S.; Liu, Peng; Finol, Ender A.
2015-01-01
In this work, we present a computationally efficient image-derived volume mesh generation approach for vasculatures that implements spatially varying patient-specific wall thickness with a novel inward extrusion of the wall surface mesh. Multi-domain vascular meshes with arbitrary numbers, locations, and patterns of both iliac bifurcations and thrombi can be obtained without the need to specify features or landmark points as input. In addition, the mesh output is coordinate-frame independent and independent of the image grid resolution with high dimensional accuracy and mesh quality, devoid of errors typically found in off-the-shelf image-based model generation workflows. The absence of deformable template models or Cartesian grid-based methods enables the present approach to be robust by handling aneurysmatic geometries with highly irregular shapes, arterial branches nearly parallel to the image plane, and variable wall thickness. The assessment of the methodology was based on i) estimation of the surface reconstruction accuracy, ii) validation of the output mesh using an aneurysm phantom, and iii) benchmarking the volume mesh quality against other frameworks. For the phantom image dataset (pixel size 0.105 mm; slice spacing 0.7 mm; mean wall thickness 1.401 ± 0.120 mm), the average wall thickness in the mesh was 1.459 ± 0.123 mm. The absolute error in average wall thickness was 0.060 ± 0.036 mm, or about 8.6% of the largest image grid spacing (0.7 mm) and 4.36% of the actual mean wall thickness. Mesh quality metrics and the ability to reproduce regional variations of wall thickness were found superior to similar alternative frameworks. PMID:25976018
Carson, James P.; Kuprat, Andrew P.; Jiao, Xiangmin; Dyedov, Volodymyr; del Pin, Facundo; Guccione, Julius M.; Ratcliffe, Mark B.; Einstein, Daniel R.
2010-04-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where, the fluid and solid phases must match geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to share the same surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh.
Carson, J.P.; Kuprat, A.P; Jiao, X.; Dyedov, V.; del Pin, F.; Johnson, G.A.; Guccione, J.M.; Ratcliffe, M.B.; Einstein, D.R.
2009-01-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh. PMID:19727874
Requirements for mesh resolution in 3D computational hemodynamics.
Prakash, S; Ethier, C R
2001-04-01
Computational techniques are widely used for studying large artery hemodynamics. Current trends favor analyzing flow in more anatomically realistic arteries. A significant obstacle to such analyses is generation of computational meshes that accurately resolve both the complex geometry and the physiologically relevant flow features. Here we examine, for a single arterial geometry, how velocity and wall shear stress patterns depend on mesh characteristics. A well-validated Navier-Stokes solver was used to simulate flow in an anatomically realistic human right coronary artery (RCA) using unstructured high-order tetrahedral finite element meshes. Velocities, wall shear stresses (WSS), and wall shear stress gradients were computed on a conventional "high-resolution" mesh series (60,000 to 160,000 velocity nodes) generated with a commercial meshing package. Similar calculations were then performed in a series of meshes generated through an adaptive mesh refinement (AMR) methodology. Mesh-independent velocity fields were not very difficult to obtain for both the conventional and adaptive mesh series. However, wall shear stress fields, and, in particular, wall shear stress gradient fields, were much more difficult to accurately resolve. The conventional (nonadaptive) mesh series did not show a consistent trend towards mesh-independence of WSS results. For the adaptive series, it required approximately 190,000 velocity nodes to reach an r.m.s. error in normalized WSS of less than 10 percent. Achieving mesh-independence in computed WSS fields requires a surprisingly large number of nodes, and is best approached through a systematic solution-adaptive mesh refinement technique. Calculations of WSS, and particularly WSS gradients, show appreciable errors even on meshes that appear to produce mesh-independent velocity fields.
Optical breast shape capture and finite-element mesh generation for electrical impedance tomography.
Forsyth, J; Borsic, A; Halter, R J; Hartov, A; Paulsen, K D
2011-07-01
X-ray mammography is the standard for breast cancer screening. The development of alternative imaging modalities is desirable because mammograms expose patients to ionizing radiation. Electrical impedance tomography (EIT) may be used to determine tissue conductivity, a property which is an indicator of cancer presence. EIT is also a low-cost imaging solution and does not involve ionizing radiation. In breast EIT, impedance measurements are made using electrodes placed on the surface of the patient's breast. The complex conductivity of the volume of the breast is estimated by a reconstruction algorithm. EIT reconstruction is a severely ill-posed inverse problem. As a result, noisy instrumentation and incorrect modelling of the electrodes and domain shape produce significant image artefacts. In this paper, we propose a method that has the potential to reduce these errors by accurately modelling the patient breast shape. A 3D hand-held optical scanner is used to acquire the breast geometry and electrode positions. We develop methods for processing the data from the scanner and producing volume meshes accurately matching the breast surface and electrode locations, which can be used for image reconstruction. We demonstrate this method for a plaster breast phantom and a human subject. Using this approach will allow patient-specific finite-element meshes to be generated which has the potential to improve the clinical value of EIT for breast cancer diagnosis.
NASA Astrophysics Data System (ADS)
Pantano, Carlos
2005-11-01
We describe a hybrid finite difference method for large-eddy simulation (LES) of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). Numerical experiments and validation calculations are presented including a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability. The approach is a conservative flux-based SAMR formulation and as such, it utilizes refinement to computational advantage. The numerical method for the resolved scale terms encompasses the cases of scheme alternation and internal mesh interfaces resulting from SAMR. An explicit centered scheme that is consistent with a skew-symmetric finite difference formulation is used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. The subgrid stresses and transports are calculated by means of the streched-vortex model, Misra & Pullin (1997)
NASA Astrophysics Data System (ADS)
Pantano, C.; Deiterding, R.; Hill, D. J.; Pullin, D. I.
2007-01-01
We present a methodology for the large-eddy simulation of compressible flows with a low-numerical dissipation scheme and structured adaptive mesh refinement (SAMR). A description of a conservative, flux-based hybrid numerical method that uses both centered finite-difference and a weighted essentially non-oscillatory (WENO) scheme is given, encompassing the cases of scheme alternation and internal mesh interfaces resulting from SAMR. In this method, the centered scheme is used in turbulent flow regions while WENO is employed to capture shocks. One-, two- and three-dimensional numerical experiments and example simulations are presented including homogeneous shock-free turbulence, a turbulent jet and the strongly shock-driven mixing of a Richtmyer-Meshkov instability.
NASA Technical Reports Server (NTRS)
Steinthorsson, E.; Modiano, David; Colella, Phillip
1994-01-01
A methodology for accurate and efficient simulation of unsteady, compressible flows is presented. The cornerstones of the methodology are a special discretization of the Navier-Stokes equations on structured body-fitted grid systems and an efficient solution-adaptive mesh refinement technique for structured grids. The discretization employs an explicit multidimensional upwind scheme for the inviscid fluxes and an implicit treatment of the viscous terms. The mesh refinement technique is based on the AMR algorithm of Berger and Colella. In this approach, cells on each level of refinement are organized into a small number of topologically rectangular blocks, each containing several thousand cells. The small number of blocks leads to small overhead in managing data, while their size and regular topology means that a high degree of optimization can be achieved on computers with vector processors.
Adaptive Mesh Refinement Cosmological Simulations of Cosmic Rays in Galaxy Clusters
NASA Astrophysics Data System (ADS)
Skillman, Samuel William
2013-12-01
Galaxy clusters are unique astrophysical laboratories that contain many thermal and non-thermal phenomena. In particular, they are hosts to cosmic shocks, which propagate through the intracluster medium as a by-product of structure formation. It is believed that at these shock fronts, magnetic field inhomogeneities in a compressing flow may lead to the acceleration of cosmic ray electrons and ions. These relativistic particles decay and radiate through a variety of mechanisms, and have observational signatures in radio, hard X-ray, and Gamma-ray wavelengths. We begin this dissertation by developing a method to find shocks in cosmological adaptive mesh refinement simulations of structure formation. After describing the evolution of shock properties through cosmic time, we make estimates for the amount of kinetic energy processed and the total number of cosmic ray protons that could be accelerated at these shocks. We then use this method of shock finding and a model for the acceleration of and radio synchrotron emission from cosmic ray electrons to estimate the radio emission properties in large scale structures. By examining the time-evolution of the radio emission with respect to the X-ray emission during a galaxy cluster merger, we find that the relative timing of the enhancements in each are important consequences of the shock dynamics. By calculating the radio emission expected from a given mass galaxy cluster, we make estimates for future large-area radio surveys. Next, we use a state-of-the-art magnetohydrodynamic simulation to follow the electron acceleration in a massive merging galaxy cluster. We use the magnetic field information to calculate not only the total radio emission, but also create radio polarization maps that are compared to recent observations. We find that we can naturally reproduce Mpc-scale radio emission that resemble many of the known double radio relic systems. Finally, motivated by our previous studies, we develop and introduce a
NASA Technical Reports Server (NTRS)
Jou, W.-H.
1982-01-01
An attempt is made to develop a three-dimensional, finite volume computational code for highly swept, twisted, small aspect ratio propeller blades with supersonic tip speeds, in a way that accounts for cascade effects, hub-induced flow, and nonlinear transonic effects. Attention is presently given to the generation of a computational mesh for such a complex propeller configuration, with the aim of sharing developmental process experience. The problem treated is unique, in that blade chord, blade length, hub length and blade-to-blade distance represent several characteristic length scales among which there is considerable disparity. An ad hoc mesh-generation scheme is accordingly developed.
NASA Astrophysics Data System (ADS)
Patchimpattapong, Apisit
This dissertation develops an expert system for generating an effective spatial mesh distribution for the discrete ordinates particle transport method in a parallel environment. This expert system consists of two main parts: (1) an algorithm for generating an effective mesh distribution in a serial environment, and (2) an algorithm for inference of an effective domain decomposition strategy for parallel computing. The mesh generation algorithm consists of four steps: creation of a geometric model as partitioned into coarse meshes, determination of an approximate flux shape, selection of appropriate differencing schemes, and generation of an effective fine mesh distribution. A geometric model was created using AutoCAD. A parallel code PENFC (Parallel Environment Neutral-Particle First Collision) has been developed to calculate an uncollided flux in a 3-D Cartesian geometry. The appropriate differencing schemes were selected based on the uncollided flux distribution using a least squares methodology. A menu-driven serial code PENXMSH has been developed to generate an effective spatial mesh distribution that preserves problem geometry and physics. The domain decomposition selection process involves evaluation of the four factors that affect parallel performance, which include number of processors and memory available per processor, load balance, granularity, and degree-of-coupling among processors. These factors are used to derive a parallel-performance-index that provides expected performance of a parallel algorithm depending on computing environment and resources. A large index indicates a high granularity algorithm with relatively low coupling among processors. This expert system has been successfully tested within the PENTRAN (Parallel Environment Neutral-Particle Transport) code system for simulating real-life shielding problems: the VENUS-3 experimental facility and the BWR core shroud.
Lombardini, Manuel; Deiterding, Ralf
2010-01-01
This paper presents the use of a dynamically adaptive mesh refinement strategy for the simulations of shock-driven turbulent mixing. Large-eddy simulations are necessary due the high Reynolds number turbulent regime. In this approach, the large scales are simulated directly and small scales at which the viscous dissipation occurs are modeled. A low-numerical centered finite-difference scheme is used in turbulent flow regions while a shock-capturing method is employed to capture shocks. Three-dimensional parallel simulations of the Richtmyer-Meshkov instability performed in plane and converging geometries are described.
NASA Astrophysics Data System (ADS)
Foks, Nathan Leon
The interpretation of geophysical data plays an important role in the analysis of potential field data in resource exploration industries. Two categories of interpretation techniques are discussed in this thesis; boundary detection and geophysical inversion. Fault or boundary detection is a method to interpret the locations of subsurface boundaries from measured data, while inversion is a computationally intensive method that provides 3D information about subsurface structure. My research focuses on these two aspects of interpretation techniques. First, I develop a method to aid in the interpretation of faults and boundaries from magnetic data. These processes are traditionally carried out using raster grid and image processing techniques. Instead, I use unstructured meshes of triangular facets that can extract inferred boundaries using mesh edges. Next, to address the computational issues of geophysical inversion, I develop an approach to reduce the number of data in a data set. The approach selects the data points according to a user specified proxy for its signal content. The approach is performed in the data domain and requires no modification to existing inversion codes. This technique adds to the existing suite of compressive inversion algorithms. Finally, I develop an algorithm to invert gravity data for an interfacing surface using an unstructured mesh of triangular facets. A pertinent property of unstructured meshes is their flexibility at representing oblique, or arbitrarily oriented structures. This flexibility makes unstructured meshes an ideal candidate for geometry based interface inversions. The approaches I have developed provide a suite of algorithms geared towards large-scale interpretation of potential field data, by using an unstructured representation of both the data and model parameters.
Application of adaptive mesh refinement to particle-in-cell simulations of plasmas and beams
Vay, J.-L.; Colella, P.; Kwan, J.W.; McCorquodale, P.; Serafini, D.B.; Friedman, A.; Grote, D.P.; Westenskow, G.; Adam, J.-C.; Heron, A.; Haber, I.
2003-11-04
Plasma simulations are often rendered challenging by the disparity of scales in time and in space which must be resolved. When these disparities are in distinctive zones of the simulation domain, a method which has proven to be effective in other areas (e.g. fluid dynamics simulations) is the mesh refinement technique. We briefly discuss the challenges posed by coupling this technique with plasma Particle-In-Cell simulations, and present examples of application in Heavy Ion Fusion and related fields which illustrate the effectiveness of the approach. We also report on the status of a collaboration under way at Lawrence Berkeley National Laboratory between the Applied Numerical Algorithms Group (ANAG) and the Heavy Ion Fusion group to upgrade ANAG's mesh refinement library Chombo to include the tools needed by Particle-In-Cell simulation codes.
Cunningham, Andrew J.; Frank, Adam; Varniere, Peggy; Mitran, Sorin; Jones, Thomas W.
2009-06-15
A description is given of the algorithms implemented in the AstroBEAR adaptive mesh-refinement code for ideal magnetohydrodynamics. The code provides several high-resolution shock-capturing schemes which are constructed to maintain conserved quantities of the flow in a finite-volume sense. Divergence-free magnetic field topologies are maintained to machine precision by collating the components of the magnetic field on a cell-interface staggered grid and utilizing the constrained transport approach for integrating the induction equations. The maintenance of magnetic field topologies on adaptive grids is achieved using prolongation and restriction operators which preserve the divergence and curl of the magnetic field across collocated grids of different resolutions. The robustness and correctness of the code is demonstrated by comparing the numerical solution of various tests with analytical solutions or previously published numerical solutions obtained by other codes.
Fukuda, Jun-Ichi; Yoneya, Makoto; Yokoyama, Hiroshi
2004-01-01
We investigate the orientation profile and the structure of topological defects of a nematic liquid crystal around a spherical particle using an adaptive mesh refinement scheme developed by us previously. The previous work [J. Fukuda et al., Phys. Rev. E 65, 041709 (2002)] was devoted to the investigation of the fine structure of a hyperbolic hedgehog defect that the particle accompanies and in this paper we present the equilibrium profile of the Saturn ring configuration. The radius of the Saturn ring r(d) in units of the particle radius R(0) increases weakly with the increase of Epsilon, the ratio of the nematic coherence length to R(0). Next we discuss the energetic stability of a hedgehog and a Saturn ring. The use of adaptive mesh refinement scheme together with a tensor orientational order parameter Q (alpha, beta) allows us to calculate the elastic energy of a nematic liquid crystal without any assumption of the structure and the energy of the defect core as in the previous similar studies. The reduced free energy of a nematic liquid crystal, F= F/L1RO, with L(1) being the elastic constant, is almost independent of Epsilon in the hedgehog configuration, while it shows a logarithmic dependence in the Saturn ring configuration. This result clearly indicates that the energetic stability of a hedgehog to a Saturn ring for a large particle is definitely attributed to the large defect energy of the Saturn ring with a large radius.
Blacker, Teddy D.
1994-01-01
An automatic quadrilateral surface discretization method and apparatus is provided for automatically discretizing a geometric region without decomposing the region. The automated quadrilateral surface discretization method and apparatus automatically generates a mesh of all quadrilateral elements which is particularly useful in finite element analysis. The generated mesh of all quadrilateral elements is boundary sensitive, orientation insensitive and has few irregular nodes on the boundary. A permanent boundary of the geometric region is input and rows are iteratively layered toward the interior of the geometric region. Also, an exterior permanent boundary and an interior permanent boundary for a geometric region may be input and the rows are iteratively layered inward from the exterior boundary in a first counter clockwise direction while the rows are iteratively layered from the interior permanent boundary toward the exterior of the region in a second clockwise direction. As a result, a high quality mesh for an arbitrary geometry may be generated with a technique that is robust and fast for complex geometric regions and extreme mesh gradations.
Power generation using carbon mesh cathodes with different diffusion layers in microbial fuel cells
NASA Astrophysics Data System (ADS)
Luo, Yong; Zhang, Fang; Wei, Bin; Liu, Guangli; Zhang, Renduo; Logan, Bruce E.
An inexpensive carbon material, carbon mesh, was examined to replace the more expensive carbon cloth usually used to make cathodes in air-cathode microbial fuel cells (MFCs). Three different diffusion layers were tested using carbon mesh: poly(dimethylsiloxane) (PDMS), polytetrafluoroethylene (PTFE), and Goretex cloth. Carbon mesh with a mixture of PDMS and carbon black as a diffusion layer produced a maximum power density of 1355 ± 62 mW m -2 (normalized to the projected cathode area), which was similar to that obtained with a carbon cloth cathode (1390 ± 72 mW m -2). Carbon mesh with a PTFE diffusion layer produced only a slightly lower (6.6%) maximum power density (1303 ± 48 mW m -2). The Coulombic efficiencies were a function of current density, with the highest value for the carbon mesh and PDMS (79%) larger than that for carbon cloth (63%). The cost of the carbon mesh cathode with PDMS/Carbon or PTFE (excluding catalyst and binder costs) is only 2.5% of the cost of the carbon cloth cathode. These results show that low cost carbon materials such as carbon mesh can be used as the cathode in an MFC without reducing the performance compared to more expensive carbon cloth.
An adaptive-mesh finite-difference solution method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Luchini, Paolo
1987-02-01
An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.
You, Shi-Jie; Wang, Xiu-Heng; Zhang, Jin-Na; Wang, Jing-Yuan; Ren, Nan-Qi; Gong, Xiao-Bo
2011-01-15
This study reports the fabrication of a new membrane electrode assembly by using stainless steel mesh (SSM) as raw material and its effectiveness as gas diffusion electrode (GDE) for electrochemical oxygen reduction in microbial fuel cell (MFC). Based on feeding glucose (0.5 g L(-1)) substrate to a single-chambered MFC, power generation using SSM-based GDE was increased with the decrease of polytetrafluoroethylene (PTFE) content applied during fabrication, reaching the optimum power density of 951.6 mW m(-2) at 20% PTFE. Repeatable cell voltage of 0.51 V (external resistance of 400 Ω) and maximum power density of 951.6 mW m(-2) produced for the MFC with SSM-based GDE are comparable to that of 0.52 V and 972.6 mW m(-2), respectively obtained for the MFC containing typical carbon cloth (CC)-made GDE. Besides, Coulombic efficiency (CE) is found higher for GDE (SSM or CC) with membrane assembly than without, which results preliminarily from the mitigation of Coulombic loss being associated with oxygen diffusion and substrate crossover. This study demonstrates that with its good electrical conductivity and much lower cost, the SSM-made GDE suggests a promising alternative as efficient and more economically viable material to conventional typical carbon for power production from biomass in MFC.
Waldrep, J C; Dhand, R
2008-04-01
Recent technological advances and improved nebulizer designs have overcome many limitations of jet nebulizers. Newer devices employ a vibrating mesh or aperture plate (VM/AP) for the generation of therapeutic aerosols with consistent, increased efficiency, predominant aerosol fine particle fractions, low residuals, and the ability to nebulize even microliter volumes. These enhancements are achieved through several different design features and include improvements that promote patient compliance, such as compact design, portability, shorter treatment durations, and quiet operation. Current VM/AP devices in clinical use are the Omron MicroAir, the Nektar Aeroneb, and the Pari eFlow. However, some devices are only approved for use with specific medications. Development of "smart nebulizers" such as the Respironics I-neb couple VM technologies with coordinated delivery and optimized inhalation patterns to enhance inhaled drug delivery of specialized, expensive formulations. Ongoing development of advanced aerosol technologies should improve clinical outcomes and continue to expand therapeutic options as newer inhaled drugs become available. PMID:18393813
NASA Technical Reports Server (NTRS)
Rodriguez, David L. (Inventor); Sturdza, Peter (Inventor)
2013-01-01
Fluid-flow simulation over a computer-generated aircraft surface is generated using inviscid and viscous simulations. A fluid-flow mesh of fluid cells is obtained. At least one inviscid fluid property for the fluid cells is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. A set of intersecting fluid cells that intersects the aircraft surface are identified. One surface mesh polygon of the surface mesh is identified for each intersecting fluid cell. A boundary-layer prediction point for each identified surface mesh polygon is determined. At least one boundary-layer fluid property for each boundary-layer prediction point is determined using the at least one inviscid fluid property of the corresponding intersecting fluid cell and a boundary-layer simulation that simulates fluid viscous effects. At least one updated fluid property for at least one fluid cell is determined using the at least one boundary-layer fluid property and the inviscid fluid simulation.
NASA Astrophysics Data System (ADS)
Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian
2013-07-01
Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.
NASA Astrophysics Data System (ADS)
Torrano, I.; Martinez-Agirre, M.; Tutar, M.
2016-02-01
A passive grid-generated turbulence technique for generating turbulent inflow conditions in large-eddy simulation (LES) is developed on moderate number of mesh cells and the results are compared with synthetic methods and wind tunnel experiments performed at Reynolds (Re) number of order 100 (based on Taylor microscale). Consistent with previous investigations, it is found that the synthetic methods turbulence dissipate the turbulence kinetic energy very quickly while the present technique represents this decay more accurately. However, this pre-computation method usually requires considerable computational cost. The aim of this study is, therefore, to decrease the computational cost by employing a relatively coarse mesh resolution accompanied with an appropriate wall modelling approach in the solid boundary. The results are within an acceptable accuracy and, therefore, offer a cost-effective solution to generate inflow turbulence parameters for their use in different aerodynamic applications at low Re numbers.
Connectivity-based, all-hexahedral mesh generation method and apparatus
Tautges, T.J.; Mitchell, S.A.; Blacker, T.D.; Murdoch, P.
1998-06-16
The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as ``whisker chords.`` This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method. 79 figs.
Connectivity-based, all-hexahedral mesh generation method and apparatus
Tautges, Timothy James; Mitchell, Scott A.; Blacker, Ted D.; Murdoch, Peter
1998-01-01
The present invention is a computer-based method and apparatus for constructing all-hexahedral finite element meshes for finite element analysis. The present invention begins with a three-dimensional geometry and an all-quadrilateral surface mesh, then constructs hexahedral element connectivity from the outer boundary inward, and then resolves invalid connectivity. The result of the present invention is a complete representation of hex mesh connectivity only; actual mesh node locations are determined later. The basic method of the present invention comprises the step of forming hexahedral elements by making crossings of entities referred to as "whisker chords." This step, combined with a seaming operation in space, is shown to be sufficient for meshing simple block problems. Entities that appear when meshing more complex geometries, namely blind chords, merged sheets, and self-intersecting chords, are described. A method for detecting invalid connectivity in space, based on repeated edges, is also described, along with its application to various cases of invalid connectivity introduced and resolved by the method.
Mesh Quality Improvement Toolkit
2002-11-15
MESQUITE is a linkable software library to be used by simulation and mesh generation tools to improve the quality of meshes. Mesh quality is improved by node movement and/or local topological modifications. Various aspects of mesh quality such as smoothness, element shape, size, and orientation are controlled by choosing the appropriate mesh qualtiy metric, and objective function tempate, and a numerical optimization solver to optimize the quality of meshes, MESQUITE uses the TSTT mesh interfacemore » specification to provide an interoperable toolkit that can be used by applications which adopt the standard. A flexible code design makes it easy for meshing researchers to add additional mesh quality metrics, templates, and solvers to develop new quality improvement algorithms by making use of the MESQUITE infrastructure.« less
NASA Astrophysics Data System (ADS)
Angelidis, Dionysios; Sotiropoulos, Fotis
2015-11-01
The geometrical details of wind turbines determine the structure of the turbulence in the near and far wake and should be taken in account when performing high fidelity calculations. Multi-resolution simulations coupled with an immersed boundary method constitutes a powerful framework for high-fidelity calculations past wind farms located over complex terrains. We develop a 3D Immersed-Boundary Adaptive Mesh Refinement flow solver (IB-AMR) which enables turbine-resolving LES of wind turbines. The idea of using a hybrid staggered/non-staggered grid layout adopted in the Curvilinear Immersed Boundary Method (CURVIB) has been successfully incorporated on unstructured meshes and the fractional step method has been employed. The overall performance and robustness of the second order accurate, parallel, unstructured solver is evaluated by comparing the numerical simulations against conforming grid calculations and experimental measurements of laminar and turbulent flows over complex geometries. We also present turbine-resolving multi-scale LES considering all the details affecting the induced flow field; including the geometry of the tower, the nacelle and especially the rotor blades of a wind tunnel scale turbine. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482 and the Sandia National Laboratories.
Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems
NASA Astrophysics Data System (ADS)
Landry, Jonathan; Soulaïmani, Azzeddine; Luke, Edward; Ben Haj Ali, Amine
2016-12-01
A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.
Lopez-Camara, D.; Lazzati, Davide; Morsony, Brian J.; Begelman, Mitchell C.
2013-04-10
We present the results of special relativistic, adaptive mesh refinement, 3D simulations of gamma-ray burst jets expanding inside a realistic stellar progenitor. Our simulations confirm that relativistic jets can propagate and break out of the progenitor star while remaining relativistic. This result is independent of the resolution, even though the amount of turbulence and variability observed in the simulations is greater at higher resolutions. We find that the propagation of the jet head inside the progenitor star is slightly faster in 3D simulations compared to 2D ones at the same resolution. This behavior seems to be due to the fact that the jet head in 3D simulations can wobble around the jet axis, finding the spot of least resistance to proceed. Most of the average jet properties, such as density, pressure, and Lorentz factor, are only marginally affected by the dimensionality of the simulations and therefore results from 2D simulations can be considered reliable.
A more efficient anisotropic mesh adaptation for the computation of Lagrangian coherent structures
NASA Astrophysics Data System (ADS)
Fortin, A.; Briffard, T.; Garon, A.
2015-03-01
The computation of Lagrangian coherent structures is more and more used in fluid mechanics to determine subtle fluid flow structures. We present in this paper a new adaptive method for the efficient computation of Finite Time Lyapunov Exponent (FTLE) from which the coherent Lagrangian structures can be obtained. This new adaptive method considerably reduces the computational burden without any loss of accuracy on the FTLE field.
NASA Astrophysics Data System (ADS)
Guo, Zhikui; Chen, Chao; Tao, Chunhui
2016-04-01
Since 2007, there are four China Da yang cruises (CDCs), which have been carried out to investigate polymetallic sulfides in the southwest Indian ridge (SWIR) and have acquired both gravity data and bathymetry data on the corresponding survey lines(Tao et al., 2014). Sandwell et al. (2014) published a new global marine gravity model including the free air gravity data and its first order vertical gradient (Vzz). Gravity data and its gradient can be used to extract unknown density structure information(e.g. crust thickness) under surface of the earth, but they contain all the mass effect under the observation point. Therefore, how to get accurate gravity and its gradient effect of the existing density structure (e.g. terrain) has been a key issue. Using the bathymetry data or ETOPO1 (http://www.ngdc.noaa.gov/mgg/global/global.html) model at a full resolution to calculate the terrain effect could spend too much computation time. We expect to develop an effective method that takes less time but can still yield the desired accuracy. In this study, a constant-density polyhedral model is used to calculate the gravity field and its vertical gradient, which is based on the work of Tsoulis (2012). According to gravity field attenuation with distance and variance of bathymetry, we present an adaptive mesh refinement and coarsening strategies to merge both global topography data and multi-beam bathymetry data. The local coarsening or size of mesh depends on user-defined accuracy and terrain variation (Davis et al., 2011). To depict terrain better, triangular surface element and rectangular surface element are used in fine and coarse mesh respectively. This strategy can also be applied to spherical coordinate in large region and global scale. Finally, we applied this method to calculate Bouguer gravity anomaly (BGA), mantle Bouguer anomaly(MBA) and their vertical gradient in SWIR. Further, we compared the result with previous results in the literature. Both synthetic model
NASA Astrophysics Data System (ADS)
Moura, R. C.; Silva, A. F. C.; Bigarella, E. D. V.; Fazenda, A. L.; Ortega, M. A.
2016-08-01
This paper proposes two important improvements to shock-capturing strategies using a discontinuous Galerkin scheme, namely, accurate shock identification via finite-time Lyapunov exponent (FTLE) operators and efficient shock treatment through a point-implicit discretization of a PDE-based artificial viscosity technique. The advocated approach is based on the FTLE operator, originally developed in the context of dynamical systems theory to identify certain types of coherent structures in a flow. We propose the application of FTLEs in the detection of shock waves and demonstrate the operator's ability to identify strong and weak shocks equally well. The detection algorithm is coupled with a mesh refinement procedure and applied to transonic and supersonic flows. While the proposed strategy can be used potentially with any numerical method, a high-order discontinuous Galerkin solver is used in this study. In this context, two artificial viscosity approaches are employed to regularize the solution near shocks: an element-wise constant viscosity technique and a PDE-based smooth viscosity model. As the latter approach is more sophisticated and preferable for complex problems, a point-implicit discretization in time is proposed to reduce the extra stiffness introduced by the PDE-based technique, making it more competitive in terms of computational cost.
Feasibility of electrical impedance tomography in haemorrhagic stroke treatment using adaptive mesh
NASA Astrophysics Data System (ADS)
Nasehi Tehrani, J.; Anderson, C.; Jin, C.; van Schaik, A.; Holder, D.; McEwan, A.
2010-04-01
EIT has been proposed for acute stroke differentiation, specifically to determine the type of stroke, either ischaemia (clot) or haemorrhage (bleed) to allow the rapid use of clot-busting drugs in the former (Romsauerova et al 2006) . This addresses an important medical need, although there is little treatment offered in the case of haemorrhage. Also the demands on EIT are high with usually no availability to take a 'before' measurement, ruling out time difference imaging. Recently a new treatment option for haemorrhage has been proposed and is being studied in international randomised controlled trial: the early reduction of elevated blood pressure to attenuate the haematoma. This has been shown via CT to reduce bleeds by up to 1mL by Anderson et al 2008. The use of EIT as a continuous measure is desirable here to monitor the effect of blood pressure reduction. A 1mL increase of haemorrhagic lesion located near scalp on the right side of head caused a boundary voltage change of less than 0.05% at 50 kHz. This could be visually observed in a time difference 3D reconstruction with no change in electrode positions, mesh, background conductivity or drift when baseline noise was less than 0.005% but not when noise was increased to 0.01%. This useful result informs us that the EIT system must have noise of less than 0.005% at 50 kHz including instrumentation, physiological and other biases.
Vertical Scan (V-SCAN) for 3-D Grid Adaptive Mesh Refinement for an atmospheric Model Dynamical Core
NASA Astrophysics Data System (ADS)
Andronova, N. G.; Vandenberg, D.; Oehmke, R.; Stout, Q. F.; Penner, J. E.
2009-12-01
One of the major building blocks of a rigorous representation of cloud evolution in global atmospheric models is a parallel adaptive grid MPI-based communication library (an Adaptive Blocks for Locally Cartesian Topologies library -- ABLCarT), which manages the block-structured data layout, handles ghost cell updates among neighboring blocks and splits a block as refinements occur. The library has several modules that provide a layer of abstraction for adaptive refinement: blocks, which contain individual cells of user data; shells - the global geometry for the problem, including a sphere, reduced sphere, and now a 3D sphere; a load balancer for placement of blocks onto processors; and a communication support layer which encapsulates all data movement. A major performance concern with adaptive mesh refinement is how to represent calculations that have need to be sequenced in a particular order in a direction, such as calculating integrals along a specific path (e.g. atmospheric pressure or geopotential in the vertical dimension). This concern is compounded if the blocks have varying levels of refinement, or are scattered across different processors, as can be the case in parallel computing. In this paper we describe an implementation in ABLCarT of a vertical scan operation, which allows computing along vertical paths in the correct order across blocks transparent to their resolution and processor location. We test this functionality on a 2D and a 3D advection problem, which tests the performance of the model’s dynamics (transport) and physics (sources and sinks) for different model resolutions needed for inclusion of cloud formation.
NASA Astrophysics Data System (ADS)
Ferguson, J. O.; Jablonowski, C.; Johansen, H.; McCorquodale, P.; Ullrich, P. A.
2015-12-01
Complex multi-scale atmospheric phenomena such as tropical cyclones challenge the coarse uniform grids of convectional climate models. Adaptive mesh refinement (AMR) techniques seek to mitigate these problems by providing sufficiently high-resolution grid patches only over features of interests while limiting the computational burden of requiring such resolutions globally. One such model is the non-hydrostatic, finite-volume Chombo-AMR general circulation model (GCM), which implements refinement in both space and time on a cubed-sphere grid. The 2D shallow-water equations exhibit many of the complexities of 3D GCM dynamical cores and serve as an effective method for testing the dynamical core and the refinement strategies of adaptive atmospheric models. We implement a shallow-water test case consisting of a pair of interacting tropical cyclone-like vortices. Small changes in the initial conditions can lead to a variety of interactions that develop fine-scale spiral band structures and large-scale wave trains. We investigate the accuracy and efficiency of AMR's ability to capture and effectively follow the evolution of the vortices in time. These simulations serve to test the effectiveness of refinement for both static and dynamic grid configurations as well as the sensitivity of the model results to the refinement criteria.
Medical case-based retrieval: integrating query MeSH terms for query-adaptive multi-modal fusion
NASA Astrophysics Data System (ADS)
Seco de Herrera, Alba G.; Foncubierta-Rodríguez, Antonio; Müller, Henning
2015-03-01
Advances in medical knowledge give clinicians more objective information for a diagnosis. Therefore, there is an increasing need for bibliographic search engines that can provide services helping to facilitate faster information search. The ImageCLEFmed benchmark proposes a medical case-based retrieval task. This task aims at retrieving articles from the biomedical literature that are relevant for differential diagnosis of query cases including a textual description and several images. In the context of this campaign many approaches have been investigated showing that the fusion of visual and text information can improve the precision of the retrieval. However, fusion does not always lead to better results. In this paper, a new query-adaptive fusion criterion to decide when to use multi-modal (text and visual) or only text approaches is presented. The proposed method integrates text information contained in MeSH (Medical Subject Headings) terms extracted and visual features of the images to find synonym relations between them. Given a text query, the query-adaptive fusion criterion decides when it is suitable to also use visual information for the retrieval. Results show that this approach can decide if a text or multi{modal approach should be used with 77.15% of accuracy.
woptic: Optical conductivity with Wannier functions and adaptive k-mesh refinement
NASA Astrophysics Data System (ADS)
Assmann, E.; Wissgott, P.; Kuneš, J.; Toschi, A.; Blaha, P.; Held, K.
2016-05-01
We present an algorithm for the adaptive tetrahedral integration over the Brillouin zone of crystalline materials, and apply it to compute the optical conductivity, dc conductivity, and thermopower. For these quantities, whose contributions are often localized in small portions of the Brillouin zone, adaptive integration is especially relevant. Our implementation, the woptic package, is tied into the WIEN2WANNIER framework and allows including a local many-body self energy, e.g. from dynamical mean-field theory (DMFT). Wannier functions and dipole matrix elements are computed with the DFT package WIEN2k and Wannier90. For illustration, we show DFT results for fcc-Al and DMFT results for the correlated metal SrVO3.
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
Zhang, Yu; Prakash, Edmond C; Sung, Eric
2004-01-01
This paper presents a new physically-based 3D facial model based on anatomical knowledge which provides high fidelity for facial expression animation while optimizing the computation. Our facial model has a multilayer biomechanical structure, incorporating a physically-based approximation to facial skin tissue, a set of anatomically-motivated facial muscle actuators, and underlying skull structure. In contrast to existing mass-spring-damper (MSD) facial models, our dynamic skin model uses the nonlinear springs to directly simulate the nonlinear visco-elastic behavior of soft tissue and a new kind of edge repulsion spring is developed to prevent collapse of the skin model. Different types of muscle models have been developed to simulate distribution of the muscle force applied on the skin due to muscle contraction. The presence of the skull advantageously constrain the skin movements, resulting in more accurate facial deformation and also guides the interactive placement of facial muscles. The governing dynamics are computed using a local semi-implicit ODE solver. In the dynamic simulation, an adaptive refinement automatically adapts the local resolution at which potential inaccuracies are detected depending on local deformation. The method, in effect, ensures the required speedup by concentrating computational time only where needed while ensuring realistic behavior within a predefined error threshold. This mechanism allows more pleasing animation results to be produced at a reduced computational cost.
NASA Astrophysics Data System (ADS)
Zhang, Shuang; Parashar, Manish; Zabusky, Norman
2001-11-01
We merge the PPM compressible algorithm (VH-1 (M. Parashar, Grid Adaptive Computational Engine. 2001. http://www.caip.rutgers.edu/ parashar/TASSL/Projects/GrACE/Gmain.html)) with the new Grid Adaptive Computation Engine (GrACE ( J. M. Blondin and J. Hawley, Virginia Hydrodynamics Code. http://wonka.physics.ncsu.edu/pub/VH-1/index.html)). The latter environment uses the Berger-Oliger AMR algorithm and has many high-performance computation features such as data parallelism, data and computation locality, etc. We discuss the performance (scaling) resulting from examining the space of four parameters: top coarse level resolution; number of refinement levels; number of processors; duration of calculation. We validate the new code by applying it to the 2D shock-curtain interaction problem (N. J. Zabusky and S. Zhang. "Shock - planar curtain interactions in 2D: Emergence of vortex double layers, vortex projectiles and decaying stratified turbulence." Revised submitted Physics of Fluids, July, 2001.). We discuss the visualization and quantification of AMR data sets.
NASA Astrophysics Data System (ADS)
Heard, Gary Wayne
A new approach to solution-adaptive grid refinement using the finite element method and Flowfield-Dependent Variation (FDV) theory applied to the Navier-Stokes system of equations is discussed. Flowfield-Dependent Variation (FDV) parameters are introduced into a modified Taylor series expansion of the conservation variables, with the Navier-Stokes system of equations substituted into the Taylor series. The FDV parameters are calculated from the current Fowfield conditions, and automatically adjust the resulting equations from elliptic to parabolic to hyperbolic in type to assure solution accuracy in evolving fluid flowfields that may consist of interactions between regions of compressible and incompressible flow, viscous and inviscid flow, and turbulent and laminar flow. The system of equations is solved using an element-by-element iterative GMRES solver with the elements grouped together to allow the element operations to be performed in parallel. The FDV parameters play many roles in the numerical scheme. One of these roles is to control formations of shock wave discontinuities in high speeds and pressure oscillations in low speeds. To demonstrate these abilities, various example problems are shown, including supersonic flows over a flat plate and a compression corner, and flows involving triple shock waves generated on fin geometries for high speed compressible flows. Furthermore, analysis of low speed incompressible flows is presented in the form of flow in a lid-driven cavity at various Reynolds numbers. Another role of the FDV parameters is their use as error indicators for a solution-adaptive mesh. The finite element grid is refined as dictated by the magnitude of the FDV parameters. Examples of adaptive grids generated using the FDV parameters as error indicators are presented for supersonic flow over flat plate/compression ramp combinations in both two and three dimensions. Grids refined using the FDV parameters as error indicators are comparable to ones
Zhang, S.; Yuen, D.A.; Zhu, A.; Song, S.; George, D.L.
2011-01-01
We parallelized the GeoClaw code on one-level grid using OpenMP in March, 2011 to meet the urgent need of simulating tsunami waves at near-shore from Tohoku 2011 and achieved over 75% of the potential speed-up on an eight core Dell Precision T7500 workstation [1]. After submitting that work to SC11 - the International Conference for High Performance Computing, we obtained an unreleased OpenMP version of GeoClaw from David George, who developed the GeoClaw code as part of his PH.D thesis. In this paper, we will show the complementary characteristics of the two approaches used in parallelizing GeoClaw and the speed-up obtained by combining the advantage of each of the two individual approaches with adaptive mesh refinement (AMR), demonstrating the capabilities of running GeoClaw efficiently on many-core systems. We will also show a novel simulation of the Tohoku 2011 Tsunami waves inundating the Sendai airport and Fukushima Nuclear Power Plants, over which the finest grid distance of 20 meters is achieved through a 4-level AMR. This simulation yields quite good predictions about the wave-heights and travel time of the tsunami waves. ?? 2011 IEEE.
NASA Technical Reports Server (NTRS)
Combi, M. R.; Kabin, K.; Gombosi, T. I.; DeZeeuw, D. L.; Powell, K. G.
1998-01-01
The first results for applying a three-dimensional multimedia ideal MHD model for the mass-loaded flow of Jupiter's corotating magnetospheric plasma past Io are presented. The model is able to consider simultaneously physically realistic conditions for ion mass loading, ion-neutral drag, and intrinsic magnetic field in a full global calculation without imposing artificial dissipation. Io is modeled with an extended neutral atmosphere which loads the corotating plasma torus flow with mass, momentum, and energy. The governing equations are solved using adaptive mesh refinement on an unstructured Cartesian grid using an upwind scheme for AHMED. For the work described in this paper we explored a range of models without an intrinsic magnetic field for Io. We compare our results with particle and field measurements made during the December 7, 1995, flyby of to, as published by the Galileo Orbiter experiment teams. For two extreme cases of lower boundary conditions at Io, our model can quantitatively explain the variation of density along the spacecraft trajectory and can reproduce the general appearance of the variations of magnetic field and ion pressure and temperature. The net fresh ion mass-loading rates are in the range of approximately 300-650 kg/s, and equivalent charge exchange mass-loading rates are in the range approximately 540-1150 kg/s in the vicinity of Io.
NASA Astrophysics Data System (ADS)
Masterlark, T.; Lu, Z.; Rykhus, R.
2003-12-01
We construct finite element models (FEMs) of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine volcano, Alaska. Interferometric synthetic aperture radar (InSAR) imagery documents the consistent contraction of the PFD during 1992-2000. Three-dimensional problem domains of the FEMs include an elastic substrate overlain by a thermoelastic material representing the PFD. The geometry of the substrate is determined from a digital elevation model (DEM) and bathymetry data. The thickness of the PFD is initially determined from the difference between post- and pre-eruptive DEMs. Systematic prediction errors suggest the PFD thickness distribution, estimated from the DEM difference, is inaccurate. We combine InSAR images, FEMs, and an adaptive mesh algorithm to re-estimate the geometry of the PFD and optimize the thickness distribution for the PFD. Prediction errors from the FEM that includes an optimized PFD geometry are reduced by 20% with respect to those from an FEM that includes a PFD geometry derived from the DEM difference.
Generation of the 30 M-Mesh Global Digital Surface Model by Alos Prism
NASA Astrophysics Data System (ADS)
Tadono, T.; Nagai, H.; Ishida, H.; Oda, F.; Naito, S.; Minakawa, K.; Iwamoto, H.
2016-06-01
Topographical information is fundamental to many geo-spatial related information and applications on Earth. Remote sensing satellites have the advantage in such fields because they are capable of global observation and repeatedly. Several satellite-based digital elevation datasets were provided to examine global terrains with medium resolutions e.g. the Shuttle Radar Topography Mission (SRTM), the global digital elevation model by the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER GDEM). A new global digital surface model (DSM) dataset using the archived data of the Panchromatic Remote-sensing Instrument for Stereo Mapping (PRISM) onboard the Advanced Land Observing Satellite (ALOS, nicknamed "Daichi") has been completed on March 2016 by Japan Aerospace Exploration Agency (JAXA) collaborating with NTT DATA Corp. and Remote Sensing Technology Center, Japan. This project is called "ALOS World 3D" (AW3D), and its dataset consists of the global DSM dataset with 0.15 arcsec. pixel spacing (approx. 5 m mesh) and ortho-rectified PRISM image with 2.5 m resolution. JAXA is also processing the global DSM with 1 arcsec. spacing (approx. 30 m mesh) based on the AW3D DSM dataset, and partially releasing it free of charge, which calls "ALOS World 3D 30 m mesh" (AW3D30). The global AW3D30 dataset will be released on May 2016. This paper describes the processing status, a preliminary validation result of the AW3D30 DSM dataset, and its public release status. As a summary of the preliminary validation of AW3D30 DSM, 4.40 m (RMSE) of the height accuracy of the dataset was confirmed using 5,121 independent check points distributed in the world.
Condition Driven Adaptive Music Generation for Computer Games
NASA Astrophysics Data System (ADS)
Naushad, Alamgir; Muhammad, Tufail
2013-02-01
The video game industry has grown to a multi-billion dollar, worldwide industry. The background music tends adaptively in reference to the specific game content during the game length of the play. Adaptive music should be further explored by looking at the particular condition in the game; such condition is driven by generating a specific music in the background which best fits in with the active game content throughout the length of the gameplay. This research paper outlines the use of condition driven adaptive music generation for audio and video to dynamically incorporate adaptively.
Mesh-based enhancement schemes in diffuse optical tomography.
Gu, Xuejun; Xu, Yong; Jiang, Huabei
2003-05-01
Two mesh-based methods including dual meshing and adaptive meshing are developed to improve the finite element-based reconstruction of both absorption and scattering images of heterogeneous turbid media. The idea of dual meshing scheme is to use a fine mesh for the solution of photon propagation and a coarse mesh for the inversion of optical property distributions. The adaptive meshing method is accomplished by the automatic mesh refinement in the region of heterogeneity during reconstruction. These schemes are validated using tissue-like phantom measurements. Our results demonstrate the capabilities of the dual meshing and adaptive meshing in both qualitative and quantitative improvement of optical image reconstruction.
Practical Aspects of Formulation and Solution of Moving Mesh Partial Differential Equations
NASA Astrophysics Data System (ADS)
Huang, Weizhang
2001-08-01
Moving mesh partial differential equations (MMPDEs) are used in the MMPDE moving mesh method to generate adaptive moving meshes for the numerical solution of time dependent problems. How MMPDEs are formulated and solved is crucial to the efficiency and robustness of the method. In this paper, several practical aspects of formulating and solving MMPDEs are studied. They include spatial balance, scaling invariance, effective control of mesh concentration, bounds on time steps, multiple sub-steps, and two-level mesh movement. Numerical results are also given.
NASA Astrophysics Data System (ADS)
Pantano, C.; Deiterding, R.; Hill, D. J.; Pullin, D. I.
2006-09-01
This paper describes a hybrid finite-difference method for the large-eddy simulation of compressible flows with low-numerical dissipation and structured adaptive mesh refinement (SAMR). A conservative flux-based approach is described with an explicit centered scheme used in turbulent flow regions while a weighted essentially non-oscillatory (WENO) scheme is employed to capture shocks. Three-dimensional numerical simulations of a Richtmyer-Meshkov instability are presented.
Adapting your teaching to accommodate the net generation of learners.
Skiba, Diane J; Barton, Amy J
2006-05-01
Educators are faced with the challenge of adapting their teaching styles to accommodate a new generation of learners. The Net Generation or Millennials, who are now entering colleges and universities, have learning expectations, styles, and needs different from past students. This article assists educators in teaching the Net Generation by highlighting the characteristics of the Net Generation and providing examples of how to adapt teaching strategies to accommodate the Net Generation, in light of their preferences for digital literacy, experiential learning, interactivity, and immediacy. PMID:17201579
Generation of tunable plasma photonic crystals in meshed dielectric barrier discharge
Wang, Yongjie; Dong, Lifang Liu, Weibo; He, Yafeng; Li, Yonghui
2014-07-15
Tunable superlattice plasma photonic crystals are obtained in a meshed dielectric barrier discharge. These plasma photonic crystals are composed of thin artificial lattices and thick self-organized lattices, and can be tuned easily by adjusting the applied voltage. A plasma photonic crystal with self-organized hexagonal lattice coupled to artificial square lattice is first realized. The dispersion relations of the square sublattices with different radii, which are recorded by an intensified charge-coupled device camera, are calculated. The results show that the thick square sublattice has the higher band edge frequencies and wider band widths. Band gaps of superlattice plasma photonic crystals are actually temporal integrations of those of transient sublattices.
NASA Astrophysics Data System (ADS)
Dahdouh, S.; Varsier, N.; Serrurier, A.; De la Plata, J.-P.; Anquez, J.; Angelini, E. D.; Wiart, J.; Bloch, I.
2014-08-01
Fetal dosimetry studies require the development of accurate numerical 3D models of the pregnant woman and the fetus. This paper proposes a 3D articulated fetal growth model covering the main phases of pregnancy and a pregnant woman model combining the utero-fetal structures and a deformable non-pregnant woman body envelope. The structures of interest were automatically or semi-automatically (depending on the stage of pregnancy) segmented from a database of images and surface meshes were generated. By interpolating linearly between fetal structures, each one can be generated at any age and in any position. A method is also described to insert the utero-fetal structures in the maternal body. A validation of the fetal models is proposed, comparing a set of biometric measurements to medical reference charts. The usability of the pregnant woman model in dosimetry studies is also investigated, with respect to the influence of the abdominal fat layer.
NASA Astrophysics Data System (ADS)
Skutnik, Steven E.; Davis, David R.
2016-05-01
The use of passive gamma and neutron signatures from fission indicators is a common means of estimating used fuel burnup, enrichment, and cooling time. However, while characteristic fission product signatures such as 134Cs, 137Cs, 154Eu, and others are generally reliable estimators for used fuel burnup within the context where the assembly initial enrichment and the discharge time are known, in the absence of initial enrichment and/or cooling time information (such as when applying NDA measurements in a safeguards/verification context), these fission product indicators no longer yield a unique solution for assembly enrichment, burnup, and cooling time after discharge. Through the use of a new Mesh-Adaptive Direct Search (MADS) algorithm, it is possible to directly probe the shape of this "degeneracy space" characteristic of individual nuclides (and combinations thereof), both as a function of constrained parameters (such as the assembly irradiation history) and unconstrained parameters (e.g., the cooling time before measurement and the measurement precision for particular indicator nuclides). In doing so, this affords the identification of potential means of narrowing the uncertainty space of potential assembly enrichment, burnup, and cooling time combinations, thereby bounding estimates of assembly plutonium content. In particular, combinations of gamma-emitting nuclides with distinct half-lives (e.g., 134Cs with 137Cs and 154Eu) in conjunction with gross neutron counting (via 244Cm) are able to reasonably constrain the degeneracy space of possible solutions to a space small enough to perform useful discrimination and verification of fuel assemblies based on their irradiation history.
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
Henshaw, W D; Schwendeman, D W
2005-08-30
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach.
Confronting socially generated uncertainty in adaptive management.
Tyre, Andrew J; Michaels, Sarah
2011-05-01
As more and more organizations with responsibility for natural resource management adopt adaptive management as the rubric in which they wish to operate, it becomes increasingly important to consider the sources of uncertainty inherent in their endeavors. Without recognizing that uncertainty originates both in the natural world and in human undertakings, efforts to manage adaptively at the least will prove frustrating and at the worst will prove damaging to the very natural resources that are the management targets. There will be more surprises and those surprises potentially may prove at the very least unwanted and at the worst devastating. We illustrate how acknowledging uncertainty associated with the natural world is necessary but not sufficient to avoid surprise using case studies of efforts to manage three wildlife species; Hector's Dolphins, American Alligators and Pallid Sturgeon. Three characteristics of indeterminism are salient to all of them; non-stationarity, irreducibility and an inability to define objective probabilities. As an antidote, we recommend employing a holistic treatment of indeterminism, that includes recognizing that uncertainty originates in ecological systems and in how people perceive, interact and decide about the natural world of which they are integral players. PMID:20965642
Triangle Geometry Processing for Surface Modeling and Cartesian Grid Generation
NASA Technical Reports Server (NTRS)
Aftosmis, Michael J. (Inventor); Melton, John E. (Inventor); Berger, Marsha J. (Inventor)
2002-01-01
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
Triangle geometry processing for surface modeling and cartesian grid generation
Aftosmis, Michael J [San Mateo, CA; Melton, John E [Hollister, CA; Berger, Marsha J [New York, NY
2002-09-03
Cartesian mesh generation is accomplished for component based geometries, by intersecting components subject to mesh generation to extract wetted surfaces with a geometry engine using adaptive precision arithmetic in a system which automatically breaks ties with respect to geometric degeneracies. During volume mesh generation, intersected surface triangulations are received to enable mesh generation with cell division of an initially coarse grid. The hexagonal cells are resolved, preserving the ability to directionally divide cells which are locally well aligned.
NASA Technical Reports Server (NTRS)
Wood, William A., III
2002-01-01
A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two-dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. A Blasius flat plate viscous validation case reveals a more accurate upsilon-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably, the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. The second half of the report develops a local, compact, anisotropic unstructured mesh adaptation scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. The adaptation strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization.
Brown, D.; Freitag, L.; Glimm, J.
2002-03-28
We present an overview of the technical objectives of the Terascale Simulation Tools and Technologies center. The primary goal of this multi-institution collaboration is to develop technologies that enable application scientists to easily use multiple mesh and discretization strategies within a single simulation on terascale computers. The discussion focuses on our efforts to create interoperable mesh generation tools, high-order discretization techniques, and adaptive meshing strategies.
NASA Technical Reports Server (NTRS)
Litvin, Faydor L.; Feng, Pin-Hao; Lagutin, Sergei A.
2000-01-01
In this report, we propose a new geometry for low-noise, increased-strength helical gears of the Novikov-Wildhaber type. Contact stresses are reduced as a result of their convex-concave gear tooth surfaces. The gear tooth surfaces are crowned in the profile direction to localize bearing contact and in the longitudinal direction to obtain a parabolic function of transmission errors. Such a function results in the reduction of noise and vibrations. Methods for the generation of the proposed gear tooth surfaces by grinding and hobbing are considered, and a tooth contact analysis (TCA) computer program to simulate meshing and contact is applied. The report also investigates the influence of misalignment on transmission errors and shift of bearing contact. Numerical examples to illustrate the developed approaches are proposed. The proposed geometry was patented by Ford/UIC (Serial Number 09-340-824, pending) on June 28, 1999.
NASA Astrophysics Data System (ADS)
Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.
2003-04-01
An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.
An enhanced geometry-independent mesh weight window generator for MCNP
Evans, T.M.; Hendricks, J.S.
1997-12-31
A new, enhanced, weight window generator suite has been developed for MCNP{trademark}. The new generator correctly estimates importances in either an user-specified, geometry-independent orthogonal grid or in MCNP geometric cells. The geometry-independent option alleviates the need to subdivide the MCNP cell geometry for variance reduction purposes. In addition, the new suite corrects several pathologies in the existing MCNP weight window generator. To verify the correctness of the new implementation, comparisons are performed with the analytical solution for the cell importance. Using the new generator, differences between Monte Carlo generated and analytical importances are less than 0.1%. Also, assumptions implicit in the original MCNP generator are shown to be poor in problems with high scattering media. The new generator is fully compatible with MCNP`s AVATAR{trademark} automatic variance reduction method. The new generator applications, together with AVATAR, gives MCNP an enhanced suite of variance reduction methods. The flexibility and efficacy of this suite is demonstrated in a neutron porosity tool well-logging problem.
Implicit solvers for unstructured meshes
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, Dimitri J.
1991-01-01
Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.
Implicit solvers for unstructured meshes
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, Dimitri J.
1991-01-01
Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.
Keeney-Walker, J.; Bass, B.R.
1992-09-01
This report describes the ORNOZL finite-element mesh generator program for computational fracture mechanics analysis. The program automatically generates a three-dimensional (3-D) finite-element model for four different geometries of a comer crack in a nozzle-cylinder intersection. ORNOZL generates a core of special wedge or collapsed prism elements at the crack front to introduce the appropriate stress singularity at the crack tip. Regular 20-noded isoparametric brick elements are used away from the crack front in the modeling. Also, an option is included that allows for an embedded or penetrating crack in clad materials. As few as five input cards are required to execute the program. ORNOZL is part of a three-program system, ORNOZL-ADINA-ORVIRT, which addresses linear or nonlinear fracture in 2- or 3-D crack geometries. ORNOZL creates files containing nodal point coordinates and element connectivities that have formats compatible with the ADINA structural analysis program. ORVIRT is a postprocessor to ADINA and employs a virtual crack extension technique to compute energy release rates at specified positions along the crack front.
NASA Technical Reports Server (NTRS)
Hua, Chongyu; Volakis, John L.
1990-01-01
AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.
Neural adaptation in the generation of rhythmic behavior.
Pearson, K G
2000-01-01
Motor systems can adapt rapidly to changes in external conditions and to switching of internal goals. They can also adapt slowly in response to training, alterations in the mechanics of the system, and any changes in the system resulting from injury. This article reviews the mechanisms underlying short- and long-term adaptation in rhythmic motor systems. The neuronal networks underlying the generation of rhythmic motor patterns (central pattern generators; CPGs) are extremely flexible. Neuromodulators, central commands, and afferent signals all influence the pattern produced by a CPG by altering the cellular and synaptic properties of individual neurons and the coupling between different populations of neurons. This flexibility allows the generation of a variety of motor patterns appropriate for the mechanical requirements of different forms of a behavior. The matching of motor output to mechanical requirements depends on the capacity of pattern-generating networks to adapt to slow changes in body mechanics and persistent errors in performance. Afferent feedback from body and limb proprioceptors likely plays an important role in driving these long-term adaptive processes.
Bols, Joris; Taelman, L; De Santis, G; Degroote, J; Verhegghe, B; Segers, P; Vierendeels, J
2016-01-01
The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid-structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed. PMID:26208183
Bols, Joris; Taelman, L; De Santis, G; Degroote, J; Verhegghe, B; Segers, P; Vierendeels, J
2016-01-01
The trend towards realistic numerical models of (pathologic) patient-specific vascular structures brings along larger computational domains and more complex geometries, increasing both the computation time and the operator time. Hexahedral grids effectively lower the computational run time and the required computational infrastructure, but at high cost in terms of operator time and minimal cell quality, especially when the computational analyses are targeting complex geometries such as aneurysm necks, severe stenoses and bifurcations. Moreover, such grids generally do not allow local refinements. As an attempt to overcome these limitations, a novel approach to hexahedral meshing is proposed in this paper, which combines the automated generation of multi-block structures with a grid-based method. The robustness of the novel approach is tested on common complex geometries, such as tree-like structures (including trifurcations), stenoses, and aneurysms. Additionally, the performance of the generated grid is assessed using two numerical examples. In the first example, a grid sensitivity analysis is performed for blood flow simulated in an abdominal mouse aorta and compared to tetrahedral grids with a prismatic boundary layer. In the second example, the fluid-structure interaction in a model of an aorta with aortic coarctation is simulated and the effect of local grid refinement is analyzed.
MEAT: An Authoring Tool for Generating Adaptable Learning Resources
ERIC Educational Resources Information Center
Kuo, Yen-Hung; Huang, Yueh-Min
2009-01-01
Mobile learning (m-learning) is a new trend in the e-learning field. The learning services in m-learning environments are supported by fundamental functions, especially the content and assessment services, which need an authoring tool to rapidly generate adaptable learning resources. To fulfill the imperious demand, this study proposes an…
Greenough, Jeffrey A.; de Supinski, Bronis R.; Yates, Robert K.; Rendleman, Charles A.; Skinner, David; Beckner, Vince; Lijewski, Mike; Bell, John; Sexton, James C.
2005-04-25
We describe the performance of the block-structured Adaptive Mesh Refinement (AMR) code Raptor on the 32k node IBM BlueGene/L computer. This machine represents a significant step forward towards petascale computing. As such, it presents Raptor with many challenges for utilizing the hardware efficiently. In terms of performance, Raptor shows excellent weak and strong scaling when running in single level mode (no adaptivity). Hardware performance monitors show Raptor achieves an aggregate performance of 3:0 Tflops in the main integration kernel on the 32k system. Results from preliminary AMR runs on a prototype astrophysical problem demonstrate the efficiency of the current software when running at large scale. The BG/L system is enabling a physics problem to be considered that represents a factor of 64 increase in overall size compared to the largest ones of this type computed to date. Finally, we provide a description of the development work currently underway to address our inefficiencies.
Klein, R.I. |; Bell, J.; Pember, R.; Kelleher, T.
1993-04-01
The authors present results for high resolution hydrodynamic calculations of the growth and development of instabilities in shock driven imploding spherical geometries in both 2D and 3D. They solve the Eulerian equations of hydrodynamics with a high order Godunov approach using local adaptive mesh refinement to study the temporal and spatial development of the turbulent mixing layer resulting from both Richtmyer Meshkov and Rayleigh Taylor instabilities. The use of a high resolution Eulerian discretization with adaptive mesh refinement permits them to study the detailed three-dimensional growth of multi-mode perturbations far into the non-linear regime for converging geometries. They discuss convergence properties of the simulations by calculating global properties of the flow. They discuss the time evolution of the turbulent mixing layer and compare its development to a simple theory for a turbulent mix model in spherical geometry based on Plesset`s equation. Their 3D calculations show that the constant found in the planar incompressible experiments of Read and Young`s may not be universal for converging compressible flow. They show the 3D time trace of transitional onset to a mixing state using the temporal evolution of volume rendered imaging. Their preliminary results suggest that the turbulent mixing layer loses memory of its initial perturbations for classical Richtmyer Meshkov and Rayleigh Taylor instabilities in spherically imploding shells. They discuss the time evolution of mixed volume fraction and the role of vorticity in converging 3D flows in enhancing the growth of a turbulent mixing layer.
SUPERIMPOSED MESH PLOTTING IN MCNP
J. HENDRICKS
2001-02-01
The capability to plot superimposed meshes has been added to MCNP{trademark}. MCNP4C featured a superimposed mesh weight window generator which enabled users to set up geometries without having to subdivide geometric cells for variance reduction. The variance reduction was performed with weight windows on a rectangular or cylindrical mesh superimposed over the physical geometry. Experience with the new capability was favorable but also indicated that a number of enhancements would be very beneficial, particularly a means of visualizing the mesh and its values. The mathematics for plotting the mesh and its values is described here along with a description of other upgrades.
NASA Technical Reports Server (NTRS)
Gabrielson, V. K.
1975-01-01
The computer program DVMESH and the use of the Tektronix DVST graphics terminal were described for applications of preparing mesh data for use in various two-dimensional axisymmetric finite element stress analysis and heat transfer codes.
Adaptive node techniques for Maxwell's equations
Hewett, D W
2000-04-01
The computational mesh in numerical simulation provides a framework on which to monitor the spatial dependence of function and their derivatives. Spatial mesh is therefore essential to the ability to integrate systems in time without loss of fidelity. Several philosophies have emerged to provide such fidelity (Eulerian, Lagrangian, Arbitrary Lagrangian Eulerian ALE, Adaptive Mesh Refinement AMR, and adaptive node generation/deletion). Regardless of the type of mesh, a major difficulty is in setting up the initial mesh. Clearly a high density of grid points is essential in regions of high geometric complexity and/or regions of intense, energetic activity. For some problems, mesh generation is such a crucial part of the problem that it can take as much computational effort as the run itself, and these tasks are now taking weeks of massively parallel CPU time. Mesh generation is no less crucial to electromagnetic calculations. In fact EM problem set up can be even more challenging without the clues given by fluid motion in hydrodynamic systems. When the mesh is advected with the fluid (Lagrangian), mesh points naturally congregate in regions of high activity. Similarly in AMR algorithms, strong gradients in the fluid flow are one of the triggers for mesh refinement. In the hyperbolic Maxwell's equations without advection, mesh point placement/motion is not so intuitive. In fixed geometry systems, it at least feasible to finely mesh high leverage, geometrically challenged areas. For other systems, where the action takes place far from the boundaries and, likely, changes position in time, the options are limited to either using a high resolution (expensive) mesh in all regions that could require such resolution or adaptively generating nodes to resolve the physics as it evolves. The authors have developed a new time of adaptive node technique for Maxwell's equations to deal with this set of issues.
NASA Astrophysics Data System (ADS)
Bogdanov, P. B.; Gorobets, A. V.; Sukov, S. A.
2013-08-01
The design of efficient algorithms for large-scale gas dynamics computations with hybrid (heterogeneous) computing systems whose high performance relies on massively parallel accelerators is addressed. A high-order accurate finite volume algorithm with polynomial reconstruction on unstructured hybrid meshes is used to compute compressible gas flows in domains of complex geometry. The basic operations of the algorithm are implemented in detail for massively parallel accelerators, including AMD and NVIDIA graphics processing units (GPUs). Major optimization approaches and a computation transfer technique are covered. The underlying programming tool is the Open Computing Language (OpenCL) standard, which performs on accelerators of various architectures, both existing and emerging.
Parallel Adaptive Multi-Mechanics Simulations using Diablo
Parsons, D; Solberg, J
2004-12-03
Coupled multi-mechanics simulations (such as thermal-stress and fluidstructure interaction problems) are of substantial interest to engineering analysts. In addition, adaptive mesh refinement techniques present an attractive alternative to current mesh generation procedures and provide quantitative error bounds that can be used for model verification. This paper discusses spatially adaptive multi-mechanics implicit simulations using the Diablo computer code. (U)
Multigrid techniques for unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1995-01-01
An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.
On Optimal Bilinear Quadrilateral Meshes
D'Azevedo, E.
1998-10-26
The novelty of this work is in presenting interesting error properties of two types of asymptotically optimal quadrilateral meshes for bilinear approximation. The first type of mesh has an error equidistributing property where the maximum interpolation error is asymptotically the same over all elements. The second type has faster than expected super-convergence property for certain saddle-shaped data functions. The super-convergent mesh may be an order of magnitude more accurate than the error equidistributing mesh. Both types of mesh are generated by a coordinate transformation of a regular mesh of squares. The coordinate transformation is derived by interpreting the Hessian matrix of a data function as a metric tensor. The insights in this work may have application in mesh design near known corner or point singularities.
toolkit computational mesh conceptual model.
Baur, David G.; Edwards, Harold Carter; Cochran, William K.; Williams, Alan B.; Sjaardema, Gregory D.
2010-03-01
The Sierra Toolkit computational mesh is a software library intended to support massively parallel multi-physics computations on dynamically changing unstructured meshes. This domain of intended use is inherently complex due to distributed memory parallelism, parallel scalability, heterogeneity of physics, heterogeneous discretization of an unstructured mesh, and runtime adaptation of the mesh. Management of this inherent complexity begins with a conceptual analysis and modeling of this domain of intended use; i.e., development of a domain model. The Sierra Toolkit computational mesh software library is designed and implemented based upon this domain model. Software developers using, maintaining, or extending the Sierra Toolkit computational mesh library must be familiar with the concepts/domain model presented in this report.
NASA Technical Reports Server (NTRS)
Litvin, Faydor L.; Tsay, Chung-Biau
1987-01-01
The authors have proposed a method for the generation of circular arc helical gears which is based on the application of standard equipment, worked out all aspects of the geometry of the gears, proposed methods for the computer aided simulation of conditions of meshing and bearing contact, investigated the influence of manufacturing and assembly errors, and proposed methods for the adjustment of gears to these errors. The results of computer aided solutions are illustrated with computer graphics.
Masterlark, Timothy; Lu, Zhiming; Rykhus, Russ
2006-01-01
Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992-1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 ??C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE=2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE=0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 ?? 107 m3) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500-800 ??C. ?? 2005 Elsevier B.V. All rights reserved.
NASA Astrophysics Data System (ADS)
Masterlark, Timothy; Lu, Zhong; Rykhus, Russell
2006-02-01
Interferometric synthetic aperture radar (InSAR) imagery documents the consistent subsidence, during the interval 1992-1999, of a pyroclastic flow deposit (PFD) emplaced during the 1986 eruption of Augustine Volcano, Alaska. We construct finite element models (FEMs) that simulate thermoelastic contraction of the PFD to account for the observed subsidence. Three-dimensional problem domains of the FEMs include a thermoelastic PFD embedded in an elastic substrate. The thickness of the PFD is initially determined from the difference between post- and pre-eruption digital elevation models (DEMs). The initial excess temperature of the PFD at the time of deposition, 640 °C, is estimated from FEM predictions and an InSAR image via standard least-squares inverse methods. Although the FEM predicts the major features of the observed transient deformation, systematic prediction errors (RMSE = 2.2 cm) are most likely associated with errors in the a priori PFD thickness distribution estimated from the DEM differences. We combine an InSAR image, FEMs, and an adaptive mesh algorithm to iteratively optimize the geometry of the PFD with respect to a minimized misfit between the predicted thermoelastic deformation and observed deformation. Prediction errors from an FEM, which includes an optimized PFD geometry and the initial excess PFD temperature estimated from the least-squares analysis, are sub-millimeter (RMSE = 0.3 mm). The average thickness (9.3 m), maximum thickness (126 m), and volume (2.1 × 10 7 m 3) of the PFD, estimated using the adaptive mesh algorithm, are about twice as large as the respective estimations for the a priori PFD geometry. Sensitivity analyses suggest unrealistic PFD thickness distributions are required for initial excess PFD temperatures outside of the range 500-800 °C.
Pervasive generation of oppositely oriented spacers during CRISPR adaptation
Shmakov, Sergey; Savitskaya, Ekaterina; Semenova, Ekaterina; Logacheva, Maria D.; Datsenko, Kirill A.; Severinov, Konstantin
2014-01-01
During the process of prokaryotic CRISPR adaptation, a copy of a segment of foreign deoxyribonucleic acid referred to as protospacer is added to the CRISPR cassette and becomes a spacer. When a protospacer contains a neighboring target interference motif, the specific small CRISPR ribonucleic acid (crRNA) transcribed from expanded CRISPR cassette can protect a prokaryotic cell from virus infection or plasmid transformation and conjugation. We show that in Escherichia coli, a vast majority of plasmid protospacers generate spacers integrated in CRISPR cassette in two opposing orientations, leading to frequent appearance of complementary spacer pairs in a population of cells that underwent CRISPR adaptation. When a protospacer contains a spacer acquisition motif AAG, spacer orientation that generates functional protective crRNA is strongly preferred. All other protospacers give rise to spacers oriented in both ways at comparable frequencies. This phenomenon increases the repertoire of available spacers and should make it more likely that a protective crRNA is formed as a result of CRISPR adaptation. PMID:24728991
Method of modifying a volume mesh using sheet extraction
Borden, Michael J.; Shepherd, Jason F.
2007-02-20
A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet extraction. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of determining a sheet of hexahedral mesh elements, generating nodes for merging, and merging the nodes to delete the sheet of hexahedral mesh elements and modify the volume mesh.
Edge-based a posteriori error estimators for generation of d-dimensional quasi-optimal meshes
Lipnikov, Konstantin; Agouzal, Abdellatif; Vassilevski, Yuri
2009-01-01
We present a new method of metric recovery for minimization of L{sub p}-norms of the interpolation error or its gradient. The method uses edge-based a posteriori error estimates. The method is analyzed for conformal simplicial meshes in spaces of arbitrary dimension d.
User Manual for the PROTEUS Mesh Tools
Smith, Micheal A.; Shemon, Emily R.
2015-06-01
This report describes the various mesh tools that are provided with the PROTEUS code giving both descriptions of the input and output. In many cases the examples are provided with a regression test of the mesh tools. The most important mesh tools for any user to consider using are the MT_MeshToMesh.x and the MT_RadialLattice.x codes. The former allows the conversion between most mesh types handled by PROTEUS while the second allows the merging of multiple (assembly) meshes into a radial structured grid. Note that the mesh generation process is recursive in nature and that each input specific for a given mesh tool (such as .axial or .merge) can be used as “mesh” input for any of the mesh tools discussed in this manual.
Guzik, S; McCorquodale, P; Colella, P
2011-12-16
A fourth-order accurate finite-volume method is presented for solving time-dependent hyperbolic systems of conservation laws on mapped grids that are adaptively refined in space and time. Novel considerations for formulating the semi-discrete system of equations in computational space combined with detailed mechanisms for accommodating the adapting grids ensure that conservation is maintained and that the divergence of a constant vector field is always zero (freestream-preservation property). Advancement in time is achieved with a fourth-order Runge-Kutta method.
NASA Astrophysics Data System (ADS)
Miyawaki, Shinjiro; Tawhai, Merryn H.; Hoffman, Eric A.; Lin, Ching-Long
2013-11-01
The authors propose a method to automatically generate three-dimensional subject-specific airway geometries and meshes for computational fluid dynamics (CFD) studies of aerosol delivery in the human lungs. The proposed method automatically expands computed tomography (CT)-based airway skeleton to generate the centerline (CL)-based model, and then fits it to the CT-segmented geometry to generate the hybrid CL-CT-based model. To produce a turbulent laryngeal jet known to affect aerosol transport, we developed a physiologically-consistent laryngeal model that can be attached to the trachea of the above models. We used Gmsh to automatically generate the mesh for the above models. To assess the quality of the models, we compared the regional aerosol distributions in a human lung predicted by the hybrid model and the manually generated CT-based model. The aerosol distribution predicted by the hybrid model was consistent with the prediction by the CT-based model. We applied the hybrid model to 8 healthy and 16 severe asthmatic subjects, and average geometric error was 3.8% of the branch radius. The proposed method can be potentially applied to the branch-by-branch analyses of a large population of healthy and diseased lungs. NIH Grants R01-HL-094315 and S10-RR-022421, CT data provided by SARP, and computer time provided by XSEDE.
Salo, Zoryana; Beek, Maarten; Wright, David; Whyne, Cari Marisa
2015-04-13
Current methods for the development of pelvic finite element (FE) models generally are based upon specimen specific computed tomography (CT) data. This approach has traditionally required segmentation of CT data sets, which is time consuming and necessitates high levels of user intervention due to the complex pelvic anatomy. The purpose of this research was to develop and assess CT landmark-based semi-automated mesh morphing and mapping techniques to aid the generation and mechanical analysis of specimen-specific FE models of the pelvis without the need for segmentation. A specimen-specific pelvic FE model (source) was created using traditional segmentation methods and morphed onto a CT scan of a different (target) pelvis using a landmark-based method. The morphed model was then refined through mesh mapping by moving the nodes to the bone boundary. A second target model was created using traditional segmentation techniques. CT intensity based material properties were assigned to the morphed/mapped model and to the traditionally segmented target models. Models were analyzed to evaluate their geometric concurrency and strain patterns. Strains generated in a double-leg stance configuration were compared to experimental strain gauge data generated from the same target cadaver pelvis. CT landmark-based morphing and mapping techniques were efficiently applied to create a geometrically multifaceted specimen-specific pelvic FE model, which was similar to the traditionally segmented target model and better replicated the experimental strain results (R(2)=0.873). This study has shown that mesh morphing and mapping represents an efficient validated approach for pelvic FE model generation without the need for segmentation.
Genetic adaptation to captivity can occur in a single generation.
Christie, Mark R; Marine, Melanie L; French, Rod A; Blouin, Michael S
2012-01-01
Captive breeding programs are widely used for the conservation and restoration of threatened and endangered species. Nevertheless, captive-born individuals frequently have reduced fitness when reintroduced into the wild. The mechanism for these fitness declines has remained elusive, but hypotheses include environmental effects of captive rearing, inbreeding among close relatives, relaxed natural selection, and unintentional domestication selection (adaptation to captivity). We used a multigenerational pedigree analysis to demonstrate that domestication selection can explain the precipitous decline in fitness observed in hatchery steelhead released into the Hood River in Oregon. After returning from the ocean, wild-born and first-generation hatchery fish were used as broodstock in the hatchery, and their offspring were released into the wild as smolts. First-generation hatchery fish had nearly double the lifetime reproductive success (measured as the number of returning adult offspring) when spawned in captivity compared with wild fish spawned under identical conditions, which is a clear demonstration of adaptation to captivity. We also documented a tradeoff among the wild-born broodstock: Those with the greatest fitness in a captive environment produced offspring that performed the worst in the wild. Specifically, captive-born individuals with five (the median) or more returning siblings (i.e., offspring of successful broodstock) averaged 0.62 returning offspring in the wild, whereas captive-born individuals with less than five siblings averaged 2.05 returning offspring in the wild. These results demonstrate that a single generation in captivity can result in a substantial response to selection on traits that are beneficial in captivity but severely maladaptive in the wild.
Tangle-Free Mesh Motion for Ablation Simulations
NASA Technical Reports Server (NTRS)
Droba, Justin
2016-01-01
Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and
Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR
NASA Technical Reports Server (NTRS)
Marcum, David L.
2007-01-01
An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.
Generating Adaptive Behaviour within a Memory-Prediction Framework
Rawlinson, David; Kowadlo, Gideon
2012-01-01
The Memory-Prediction Framework (MPF) and its Hierarchical-Temporal Memory implementation (HTM) have been widely applied to unsupervised learning problems, for both classification and prediction. To date, there has been no attempt to incorporate MPF/HTM in reinforcement learning or other adaptive systems; that is, to use knowledge embodied within the hierarchy to control a system, or to generate behaviour for an agent. This problem is interesting because the human neocortex is believed to play a vital role in the generation of behaviour, and the MPF is a model of the human neocortex. We propose some simple and biologically-plausible enhancements to the Memory-Prediction Framework. These cause it to explore and interact with an external world, while trying to maximize a continuous, time-varying reward function. All behaviour is generated and controlled within the MPF hierarchy. The hierarchy develops from a random initial configuration by interaction with the world and reinforcement learning only. Among other demonstrations, we show that a 2-node hierarchy can learn to successfully play “rocks, paper, scissors” against a predictable opponent. PMID:22272231
A novel adaptive Cuckoo search for optimal query plan generation.
Gomathi, Ramalingam; Sharmila, Dhandapani
2014-01-01
The emergence of multiple web pages day by day leads to the development of the semantic web technology. A World Wide Web Consortium (W3C) standard for storing semantic web data is the resource description framework (RDF). To enhance the efficiency in the execution time for querying large RDF graphs, the evolving metaheuristic algorithms become an alternate to the traditional query optimization methods. This paper focuses on the problem of query optimization of semantic web data. An efficient algorithm called adaptive Cuckoo search (ACS) for querying and generating optimal query plan for large RDF graphs is designed in this research. Experiments were conducted on different datasets with varying number of predicates. The experimental results have exposed that the proposed approach has provided significant results in terms of query execution time. The extent to which the algorithm is efficient is tested and the results are documented. PMID:25215330
A novel adaptive Cuckoo search for optimal query plan generation.
Gomathi, Ramalingam; Sharmila, Dhandapani
2014-01-01
The emergence of multiple web pages day by day leads to the development of the semantic web technology. A World Wide Web Consortium (W3C) standard for storing semantic web data is the resource description framework (RDF). To enhance the efficiency in the execution time for querying large RDF graphs, the evolving metaheuristic algorithms become an alternate to the traditional query optimization methods. This paper focuses on the problem of query optimization of semantic web data. An efficient algorithm called adaptive Cuckoo search (ACS) for querying and generating optimal query plan for large RDF graphs is designed in this research. Experiments were conducted on different datasets with varying number of predicates. The experimental results have exposed that the proposed approach has provided significant results in terms of query execution time. The extent to which the algorithm is efficient is tested and the results are documented.
A Novel Adaptive Cuckoo Search for Optimal Query Plan Generation
Gomathi, Ramalingam; Sharmila, Dhandapani
2014-01-01
The emergence of multiple web pages day by day leads to the development of the semantic web technology. A World Wide Web Consortium (W3C) standard for storing semantic web data is the resource description framework (RDF). To enhance the efficiency in the execution time for querying large RDF graphs, the evolving metaheuristic algorithms become an alternate to the traditional query optimization methods. This paper focuses on the problem of query optimization of semantic web data. An efficient algorithm called adaptive Cuckoo search (ACS) for querying and generating optimal query plan for large RDF graphs is designed in this research. Experiments were conducted on different datasets with varying number of predicates. The experimental results have exposed that the proposed approach has provided significant results in terms of query execution time. The extent to which the algorithm is efficient is tested and the results are documented. PMID:25215330
On Linear Spaces of Polyhedral Meshes.
Poranne, Roi; Chen, Renjie; Gotsman, Craig
2015-05-01
Polyhedral meshes (PM)-meshes having planar faces-have enjoyed a rise in popularity in recent years due to their importance in architectural and industrial design. However, they are also notoriously difficult to generate and manipulate. Previous methods start with a smooth surface and then apply elaborate meshing schemes to create polyhedral meshes approximating the surface. In this paper, we describe a reverse approach: given the topology of a mesh, we explore the space of possible planar meshes having that topology. Our approach is based on a complete characterization of the maximal linear spaces of polyhedral meshes contained in the curved manifold of polyhedral meshes with a given topology. We show that these linear spaces can be described as nullspaces of differential operators, much like harmonic functions are nullspaces of the Laplacian operator. An analysis of this operator provides tools for global and local design of a polyhedral mesh, which fully expose the geometric possibilities and limitations of the given topology.
Gamra: Simple meshing for complex earthquakes
NASA Astrophysics Data System (ADS)
Landry, Walter; Barbot, Sylvain
2016-05-01
The static offsets caused by earthquakes are well described by elastostatic models with a discontinuity in the displacement along the fault. A traditional approach to model this discontinuity is to align the numerical mesh with the fault and solve the equations using finite elements. However, this distorted mesh can be difficult to generate and update. We present a new numerical method, inspired by the Immersed Interface Method (Leveque and Li, 1994), for solving the elastostatic equations with embedded discontinuities. This method has been carefully designed so that it can be used on parallel machines on an adapted finite difference grid. We have implemented this method in Gamra, a new code for earth modeling. We demonstrate the correctness of the method with analytic tests, and we demonstrate its practical performance by solving a realistic earthquake model to extremely high precision.
NASA Technical Reports Server (NTRS)
Raju, I. S.
1992-01-01
A computer program that generates three-dimensional (3D) finite element models for cracked 3D solids was written. This computer program, gensurf, uses minimal input data to generate 3D finite element models for isotropic solids with elliptic or part-elliptic cracks. These models can be used with a 3D finite element program called surf3d. This report documents this mesh generator. In this manual the capabilities, limitations, and organization of gensurf are described. The procedures used to develop 3D finite element models and the input for and the output of gensurf are explained. Several examples are included to illustrate the use of this program. Several input data files are included with this manual so that the users can edit these files to conform to their crack configuration and use them with gensurf.
Li, Pak Shing; Klein, Richard I.; Martin, Daniel F.; McKee, Christopher F. E-mail: klein@astron.berkeley.edu E-mail: cmckee@astro.berkeley.edu
2012-02-01
Performing a stable, long-duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and constrained transport electromotive force averaging schemes that can meet this challenge, and using this strategy, we have developed a new adaptive mesh refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma {beta}{sub 0} of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers (M{sub rms}= 17.3) and smaller plasma beta ({beta}{sub 0} = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
NASA Astrophysics Data System (ADS)
Sides, Scott; Jamroz, Ben; Crockett, Robert; Pletzer, Alexander
2012-02-01
Self-consistent field theory (SCFT) for dense polymer melts has been highly successful in describing complex morphologies in block copolymers. Field-theoretic simulations such as these are able to access large length and time scales that are difficult or impossible for particle-based simulations such as molecular dynamics. The modified diffusion equations that arise as a consequence of the coarse-graining procedure in the SCF theory can be efficiently solved with a pseudo-spectral (PS) method that uses fast-Fourier transforms on uniform Cartesian grids. However, PS methods can be difficult to apply in many block copolymer SCFT simulations (eg. confinement, interface adsorption) in which small spatial regions might require finer resolution than most of the simulation grid. Progress on using new solver algorithms to address these problems will be presented. The Tech-X Chompst project aims at marrying the best of adaptive mesh refinement with linear matrix solver algorithms. The Tech-X code PolySwift++ is an SCFT simulation platform that leverages ongoing development in coupling Chombo, a package for solving PDEs via block-structured AMR calculations and embedded boundaries, with PETSc, a toolkit that includes a large assortment of sparse linear solvers.
NASA Astrophysics Data System (ADS)
Garel, F.; Davies, R.; Goes, S. D.; Davies, J.; Lithgow-Bertelloni, C. R.; Stixrude, L. P.
2012-12-01
Seismic observations show a wide range of slab morphologies within the mantle transition zone. This zone is likely to have been critical in Earth's thermal and chemical evolution, acting as a 'valve' that controls material transfer between the upper and lower mantle. However, the interaction between slabs and this complex region remains poorly understood. The complexity arises from non-linear and multi-scale interactions between several aspects of the mantle system, including mineral phase changes and material rheology. In this study, we will utilize new, multi-scale geodynamic models to determine what controls the seismically observed variability in slab behavior within the mantle transition zone and, hence, the down-going branch of the mantle 'valve'. Our models incorporate the newest mineral physics and theoretical constraints on density, phase proportions and rheology. In addition we exploit novel and unique adaptive grid methodologies to provide the resolution necessary to capture rapid changes in material properties in and around the transition zone. Our early results, which will be presented, illustrate the advantages of the new modelling technique for studying subduction including the effects of changes in material properties and mineral phases.
h-Refinement for simple corner balance scheme of SN transport equation on distorted meshes
NASA Astrophysics Data System (ADS)
Yang, Rong; Yuan, Guangwei
2016-11-01
The transport sweep algorithm is a common method for solving discrete ordinate transport equation, but it breaks down once a concave cell appears in spatial meshes. To deal with this issue a local h-refinement for simple corner balance (SCB) scheme of SN transport equation on arbitrary quadrilateral meshes is presented in this paper by using a new subcell partition. It follows that a hybrid mesh with both triangle and quadrilateral cells is generated, and the geometric quality of these cells improves, especially it is ensured that all cells become convex. Combining with the original SCB scheme, an adaptive transfer algorithm based on the hybrid mesh is constructed. Numerical experiments are presented to verify the utility and accuracy of the new algorithm, especially for some application problems such as radiation transport coupled with Lagrangian hydrodynamic flow. The results show that it performs well on extremely distorted meshes with concave cells, on which the original SCB scheme does not work.