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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
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.
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.
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.
Using Multithreading 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.; Bailey, David H. (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 question phase of FE applications on 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 on EARTH-SP2, an implementation of EARTH on the IBM SP2, with different load balancing strategies that are built into the runtime system.
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.
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.
Delanaye, M.; Essers, J.A.
1997-04-01
This paper presents a new finite volume cell-centered scheme for solving the two-dimensional Euler equations. The technique for computing the advective derivatives is based on a high-order Gauss quadrature and an original quadratic reconstruction of the conservative variables for each control volume. A very sensitive detector identifying discontinuity regions switches the scheme to a TVD scheme, and ensures the monotonicity of the solution. The code uses unstructured meshes whose cells are polygons with any number of edges. A mesh adaptation based on cell division is performed in order to increase the resolution of shocks. The accuracy, insensitivity to grid distortions, and shock capturing properties of the scheme are demonstrated for different cascade flow computations.
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.
A simple adaptive mesh generator for 2-D finite element calculations
Fernandez, F.A.; Yong, Y.C.; Ettinger, R.D. )
1993-03-01
A strategy for adaptive mesh generation is proposed. The method consists of the use of a suitably defined density function', which can either be defined by the user or be calculated from a previous approximate solution, to guide the generation of a new mesh. This new mesh is built starting from a minimal number of triangular elements which are then in several sweeps, repeatedly refined according to the density function. The Delaunay algorithm is used in each stage to keep the shape of the triangles as equilateral as possible.
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.
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.
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
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.
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.
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.
Parallel automated adaptive procedures for unstructured meshes
NASA Technical Reports Server (NTRS)
Shephard, M. S.; Flaherty, J. E.; Decougny, H. L.; Ozturan, C.; Bottasso, C. L.; Beall, M. W.
1995-01-01
Consideration is given to the techniques required to support adaptive analysis of automatically generated unstructured meshes on distributed memory MIMD parallel computers. The key areas of new development are focused on the support of effective parallel computations when the structure of the numerical discretization, the mesh, is evolving, and in fact constructed, during the computation. All the procedures presented operate in parallel on already distributed mesh information. Starting from a mesh definition in terms of a topological hierarchy, techniques to support the distribution, redistribution and communication among the mesh entities over the processors is given, and algorithms to dynamically balance processor workload based on the migration of mesh entities are given. A procedure to automatically generate meshes in parallel, starting from CAD geometric models, is given. Parallel procedures to enrich the mesh through local mesh modifications are also given. Finally, the combination of these techniques to produce a parallel automated finite element analysis procedure for rotorcraft aerodynamics calculations is discussed and demonstrated.
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.
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
FEATURE-BASED MULTIBLOCK FINITE ELEMENT MESH GENERATION
Shivanna, Kiran H.; Tadepalli, Srinivas C.; Grosland, Nicole M.
2010-01-01
Hexahedral finite element mesh development for anatomic structures and biomedical implants can be cumbersome. Moreover, using traditional meshing techniques, detailed features may be inadequately captured. In this paper, we describe methodologies to handle multi-feature datasets (i.e., feature edges and surfaces). Coupling multi-feature information with multiblock meshing techniques has enabled anatomic structures, as well as orthopaedic implants, to be readily meshed. Moreover, the projection process, node and element set creation are automated, thus reducing the user interaction during model development. To improve the mesh quality, Laplacian- and optimization-based mesh improvement algorithms have been adapted to the multi-feature datasets. PMID:21076650
NASA Astrophysics Data System (ADS)
Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.
2016-03-01
Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.
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
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
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.
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.
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
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.
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.
Adaptive Skin Meshes Coarsening for Biomolecular Simulation.
Shi, Xinwei; Koehl, Patrice
2011-06-01
In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137
Adaptive Skin Meshes Coarsening for Biomolecular Simulation
Shi, Xinwei; Koehl, Patrice
2011-01-01
In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137
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
Parallel adaptive mesh refinement within the PUMAA3D Project
NASA Technical Reports Server (NTRS)
Freitag, Lori; Jones, Mark; Plassmann, Paul
1995-01-01
To enable the solution of large-scale applications on distributed memory architectures, we are designing and implementing parallel algorithms for the fundamental tasks of unstructured mesh computation. In this paper, we discuss efficient algorithms developed for two of these tasks: parallel adaptive mesh refinement and mesh partitioning. The algorithms are discussed in the context of two-dimensional finite element solution on triangular meshes, but are suitable for use with a variety of element types and with h- or p-refinement. Results demonstrating the scalability and efficiency of the refinement algorithm and the quality of the mesh partitioning are presented for several test problems on the Intel DELTA.
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Adaptive and Quality Quadrilateral/Hexahedral Meshing from Volumetric Data⋆
Zhang, Yongjie; Bajaj, Chandrajit
2009-01-01
This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, a relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations. PMID:19750180
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.
The finite cell method for polygonal meshes: poly-FCM
NASA Astrophysics Data System (ADS)
Duczek, Sascha; Gabbert, Ulrich
2016-06-01
In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.
A finite-element mesh generator based on growing neural networks.
Triantafyllidis, D G; Labridis, D P
2002-01-01
A mesh generator for the production of high-quality finite-element meshes is being proposed. The mesh generator uses an artificial neural network, which grows during the training process in order to adapt itself to a prespecified probability distribution. The initial mesh is a constrained Delaunay triangulation of the domain to be triangulated. Two new algorithms to accelerate the location of the best matching unit are introduced. The mesh generator has been found able to produce meshes of high quality in a number of classic cases examined and is highly suited for problems where the mesh density vector can be calculated in advance. PMID:18244543
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.
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.
Progress in integrated analysis with adaptive unstructured meshing
NASA Technical Reports Server (NTRS)
Dechaumphai, Pramote
1992-01-01
Design of lightweight structures and thermal protection systems for hypersonic vehicles depend on accurate prediction of aerothermal loads, structural temperatures and their gradients, and structural deformations and stresses. Concentration is on an alternative meshing technique which generates an entirely new adaptive unstructured mesh based on the solution obtained from the earlier mesh. The technique combined with the finite element method has been shown to significantly improve the efficiency and accuracy of the fluid, thermal, and structural analyses. Current capability of the adaptive unstructured meshing technique for the integrated fluid-thermal-structural analysis is described first. The technique was extended to transient thermal analysis of structures with time-dependent adaptive meshing to capture the detailed temperature response with a minimum number of unknowns and computational cost. Both linear and higher-order finite elements are implemented to demonstrate the generality of the technique and to investigate their solution accuracy. Currently, the adaptive meshing technique is being developed for plane structures that can be modeled with membrane elements and built-up structures modeled with membrane and bending elements. The capability of the technique to these different disciplinary problems is demonstrated by several examples.
NASA Technical Reports Server (NTRS)
Vemaganti, Gururaja R.; Wieting, Allan R.
1990-01-01
A higher-order streamline upwinding Petrov-Galerkin finite element method is employed for high speed viscous flow analysis using structured and unstructured meshes. For a Mach 8.03 shock interference problem, successive mesh adaptation was performed using an adaptive remeshing method. Results from the finite element algorithm compare well with both experimental data and results from an upwind cell-centered method. Finite element results for a Mach 14.1 flow over a 24 degree compression corner compare well with experimental data and two other numerical algorithms for both structured and unstructured meshes.
A hierarchical structure for automatic meshing and adaptive FEM analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Saxena, Mukul; Perucchio, Renato
1987-01-01
A new algorithm for generating automatically, from solid models of mechanical parts, finite element meshes that are organized as spatially addressable quaternary trees (for 2-D work) or octal trees (for 3-D work) is discussed. Because such meshes are inherently hierarchical as well as spatially addressable, they permit efficient substructuring techniques to be used for both global analysis and incremental remeshing and reanalysis. The global and incremental techniques are summarized and some results from an experimental closed loop 2-D system in which meshing, analysis, error evaluation, and remeshing and reanalysis are done automatically and adaptively are presented. The implementation of 3-D work is briefly discussed.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1995-01-01
In recent work we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered on Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM), is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence.
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.
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.
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).
Determination of an Initial Mesh Density for Finite Element Computations via Data Mining
Kanapady, R; Bathina, S K; Tamma, K K; Kamath, C; Kumar, V
2001-07-23
Numerical analysis software packages which employ a coarse first mesh or an inadequate initial mesh need to undergo a cumbersome and time consuming mesh refinement studies to obtain solutions with acceptable accuracy. Hence, it is critical for numerical methods such as finite element analysis to be able to determine a good initial mesh density for the subsequent finite element computations or as an input to a subsequent adaptive mesh generator. This paper explores the use of data mining techniques for obtaining an initial approximate finite element density that avoids significant trial and error to start finite element computations. As an illustration of proof of concept, a square plate which is simply supported at its edges and is subjected to a concentrated load is employed for the test case. Although simplistic, the present study provides insight into addressing the above considerations.
Diffusive mesh relaxation in ALE finite element numerical simulations
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
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.
Gravitational Collapse With Distributed Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Liebling, Steven; Lehner, Luis; Motl, Patrick; Neilsen, David; Rahman, Tanvir; Reula, Oscar
2006-04-01
Gravitational collapse is studied using distributed adaptive mesh refinement (AMR). The AMR infrastructure includes a novel treatment of adaptive boundaries which allows for high orders of accuracy. Results of the collapse of Brill waves to black holes are presented. Combining both vertex centered and cell centered fields in the same evolution is discussed.
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.
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.
One-node coarse-mesh finite difference algorithm for fine-mesh finite difference operator
Shin, H.C.; Kim, Y.H.; Kim, Y.B.
1999-07-01
This paper is concerned with speeding up the convergence of the fine-mesh finite difference (FMFD) method for the neutron diffusion problem. The basic idea of the new algorithm originates from the two-node coarse-mesh finite difference (CMFD) schemes for nodal methods, where the low-order CMFD operator is iteratively corrected through a global-local iteration so that the final solution of the CMFD problem is equivalent to the high-order nodal solution. Unlike conventional CMFD methods, the new CMFD algorithm is based on one-node local problems, and the high-order solution over the local problem is determined by using the FMFD operator. Nonlinear coupling of CMFD and FMFD operators was previously studied by Aragones and Ahnert. But, in their work, the coarse-mesh operator is corrected by the so-called flux discontinuity factors, and the local problem is defined differently in the sense of boundary conditions and the core dissection scheme.
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
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.
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.
Adaption of unstructured meshes using node movement
Carpenter, J.G.; McRae, V.D.S.
1996-12-31
The adaption algorithm of Benson and McRae is modified for application to unstructured grids. The weight function generation was modified for application to unstructured grids and movement was limited to prevent cross over. A NACA 0012 airfoil is used as a test case to evaluate the modified algorithm when applied to unstructured grids and compared to results obtained by Warren. An adaptive mesh solution for the Sudhoo and Hall four element airfoil is included as a demonstration case.
Finite element simulation of impact response of wire mesh screens
NASA Astrophysics Data System (ADS)
Wang, Caizheng; Shankar, Krishna; Fien, Alan
2015-09-01
In this paper, the response of wire mesh screens to low velocity impact with blunt objects is investigated using finite element (FE) simulation. The woven wire mesh is modelled with homogeneous shell elements with equivalent smeared mechanical properties. The mechanical behaviour of the woven wire mesh was determined experimentally with tensile tests on steel wire mesh coupons to generate the data for the smeared shell material used in the FE. The effects of impacts with a low mass (4 kg) and a large mass (40 kg) providing the same impact energy are studied. The joint between the wire mesh screen and the aluminium frame surrounding it is modelled using contact elements with friction between the corresponding elements. Damage to the screen of different types compromising its structural integrity, such as mesh separation and pulling out from the surrounding frame is modelled. The FE simulation is validated with results of impact tests conducted on woven steel wire screen meshes.
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.
Unstructured Adaptive Meshes: Bad for Your Memory?
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Feng, Hui-Yu; VanderWijngaart, Rob
2003-01-01
This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.
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.
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.
Floating shock fitting via Lagrangian adaptive meshes
NASA Technical Reports Server (NTRS)
Vanrosendale, John
1994-01-01
In recent works we have formulated a new approach to compressible flow simulation, combining the advantages of shock-fitting and shock-capturing. Using a cell-centered Roe scheme discretization on unstructured meshes, we warp the mesh while marching to steady state, so that mesh edges align with shocks and other discontinuities. This new algorithm, the Shock-fitting Lagrangian Adaptive Method (SLAM) is, in effect, a reliable shock-capturing algorithm which yields shock-fitted accuracy at convergence. Shock-capturing algorithms like this, which warp the mesh to yield shock-fitted accuracy, are new and relatively untried. However, their potential is clear. In the context of sonic booms, accurate calculation of near-field sonic boom signatures is critical to the design of the High Speed Civil Transport (HSCT). SLAM should allow computation of accurate N-wave pressure signatures on comparatively coarse meshes, significantly enhancing our ability to design low-boom configurations for high-speed aircraft.
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.
Mesh refinement in finite element analysis by minimization of the stiffness matrix trace
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.
1989-01-01
Most finite element packages provide means to generate meshes automatically. However, the user is usually confronted with the problem of not knowing whether the mesh generated is appropriate for the problem at hand. Since the accuracy of the finite element results is mesh dependent, mesh selection forms a very important step in the analysis. Indeed, in accurate analyses, meshes need to be refined or rezoned until the solution converges to a value so that the error is below a predetermined tolerance. A-posteriori methods use error indicators, developed by using the theory of interpolation and approximation theory, for mesh refinements. Some use other criterions, such as strain energy density variation and stress contours for example, to obtain near optimal meshes. Although these methods are adaptive, they are expensive. Alternatively, a priori methods, until now available, use geometrical parameters, for example, element aspect ratio. Therefore, they are not adaptive by nature. An adaptive a-priori method is developed. The criterion is that the minimization of the trace of the stiffness matrix with respect to the nodal coordinates, leads to a minimization of the potential energy, and as a consequence provide a good starting mesh. In a few examples the method is shown to provide the optimal mesh. The method is also shown to be relatively simple and amenable to development of computer algorithms. When the procedure is used in conjunction with a-posteriori methods of grid refinement, it is shown that fewer refinement iterations and fewer degrees of freedom are required for convergence as opposed to when the procedure is not used. The mesh obtained is shown to have uniform distribution of stiffness among the nodes and elements which, as a consequence, leads to uniform error distribution. Thus the mesh obtained meets the optimality criterion of uniform error distribution.
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 Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
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.
Compressible Flows on Adaptive and Unstrucured Meshes with FLUIDITY
NASA Astrophysics Data System (ADS)
Nelson, R.; Piggott, M.; Wilson, C.; Kramer, S.
2011-09-01
Fluidity is an open source, general purpose, multi-phase CFD code capable of solving numerically the Navier-Stokes and accompanying field equations on arbitrary unstructured finite element meshes in one, two and three dimensions. It uses a moving finite element/control volume method which allows arbitrary movement of the mesh in time dependent problems. It has a wide range of finite element/control volume element choices including mixed formulations. Here, continuous Galerkin (CG) and control volumes (CV) solutions of the compressible Navier-Stokes (N-S) equations are presented for the stratified tests cases of the rising thermal bubble and inertia gravity waves. Results show good agreement with previously published literature and novel result presented here is the ability to dynamically adapt the mesh to increase resolution in the region of interest, thus reducing the number of degrees of freedom in the problem without decreasing the accuracy of the result. Finally, results from the case of a fully three dimensional rising thermal bubble are presented.
Anisotropic Mesh Adaptivity for FE-simulation of cardiovascular flow
NASA Astrophysics Data System (ADS)
Mueller, Jens; Sahni, Onkar; Jansen, Kenneth E.; Shephard, Mark S.; Taylor, Charles A.
2004-11-01
In this study we present an adaptive anisotropic finite element method and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the weak SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretized by linear finite elements, both for the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptavity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical pipe and then to a pig artery with a stenosis bypassed by a graft. The efficiency of the method is measured in terms of computational savings when we compute the wall shear stresses, a quantity identified to be important to understanding arterial disease.
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.
Dynamic mesh adaption for triangular and tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1993-01-01
The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
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.
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.
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.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-11-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
Rapid mesh generation for finite element analysis of investment castings
Lober, R.R.; Bohnhoff, W.J.; Meyers, R.J.
1992-01-01
FASTCAST is a Sandia National Laboratories program to produce investment cast prototypical hardware faster by integrating experimental and computational technologies into the casting process. FASTCAST uses the finite element method to characterize the metal flow and solidification processes to reduce uncertainty in the mold design. For the casting process to benefit from finite element analysis, analysis results must be available in a very short time frame. By focusing on the bottleneck of finite element model creation, automated mesh generation can drastically reduce the time span between geometry definition (design) and accurate analysis results. The increased availability of analysis results will diminish the need for trial and error approaches to acquiring production worthy mold and gating systems for investment casting. The CUBIT meshing tool kit is being developed to address the need for rapid mesh generation. CUBIT is being designed to effectively automate the generation of quadrilateral and hexahedral elements. It is a solid-modeler based, two- and three-dimensional preprocessor that prepares solid models for finite element analysis. CUBIT contains several meshing algorithms including two- and three-dimensional mapping, two- and three-dimensional paving (patented), and a general two and one-half dimensional sweeper based upon the plastering algorithm. This paper describes progress in the development of the CUBIT meshing toolkit.
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.
Shephard, M.S.; Dey, S.; Georges, M.K.
1995-12-31
Specific issues associated with the automatic generation of finite element meshes for curved geometric domains axe considered. A review of the definition of when a triangulation is a valid mesh, a geometric triangulation, for curved geometric domains is given. Consideration is then given to the additional operations necessary to maintain the validity of a mesh when curved finite elements are employed. A procedure to control the mesh gradations based on the curvature of the geometric model faces is also given.
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.
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.
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.
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.
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.
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.
A moving mesh finite difference method for equilibrium radiation diffusion equations
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
A moving mesh finite difference method for equilibrium radiation diffusion equations
NASA Astrophysics Data System (ADS)
Yang, Xiaobo; Huang, Weizhang; Qiu, Jianxian
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor-corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
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.
Finite element meshing approached as a global minimization process
WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.; LEUNG,VITUS J.
2000-03-01
The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested
Finite element mesh refinement criteria for stress analysis
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.
1990-01-01
This paper discusses procedures for finite-element mesh selection and refinement. The objective is to improve accuracy. The procedures are based on (1) the minimization of the stiffness matrix race (optimizing node location); (2) the use of h-version refinement (rezoning, element size reduction, and increasing the number of elements); and (3) the use of p-version refinement (increasing the order of polynomial approximation of the elements). A step-by-step procedure of mesh selection, improvement, and refinement is presented. The criteria for 'goodness' of a mesh are based on strain energy, displacement, and stress values at selected critical points of a structure. An analysis of an aircraft lug problem is presented as an example.
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.
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.
Vortex-dominated conical-flow computations using unstructured adaptively-refined meshes
NASA Technical Reports Server (NTRS)
Batina, John T.
1989-01-01
A conical Euler/Navier-Stokes algorithm is presented for the computation of vortex-dominated flows. The flow solver involves a multistage Runge-Kutta time stepping scheme which uses a finite-volume spatial discretization on an unstructured grid made up of triangles. The algorithm also employs an adaptive mesh refinement procedure which enriches the mesh locally to more accurately resolve the vortical flow features. Results are presented for several highly-swept delta wing and circular cone cases at high angles of attack and at supersonic freestream flow conditions. Accurate solutions were obtained more efficiently when adaptive mesh refinement was used in contrast with refining the grid globally. The paper presents descriptions of the conical Euler/Navier-Stokes flow solver and adaptive mesh refinement procedures along with results which demonstrate the capability.
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.
Adaptive mesh fluid simulations on GPU
NASA Astrophysics Data System (ADS)
Wang, Peng; Abel, Tom; Kaehler, Ralf
2010-10-01
We describe an implementation of compressible inviscid fluid solvers with block-structured adaptive mesh refinement on Graphics Processing Units using NVIDIA's CUDA. We show that a class of high resolution shock capturing schemes can be mapped naturally on this architecture. Using the method of lines approach with the second order total variation diminishing Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an overall speedup of approximately 10 times faster execution on one graphics card as compared to a single core on the host computer. We attain this speedup in uniform grid runs as well as in problems with deep AMR hierarchies. Our framework can readily be applied to more general systems of conservation laws and extended to higher order shock capturing schemes. This is shown directly by an implementation of a magneto-hydrodynamic solver and comparing its performance to the pure hydrodynamic case. Finally, we also combined our CUDA parallel scheme with MPI to make the code run on GPU clusters. Close to ideal speedup is observed on up to four GPUs.
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.
Algebraic turbulence modeling for unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1990-01-01
An algebraic turbulence model based on the Baldwin-Lomax model, has been implemented for use on unstructured grids. The implementation is based on the use of local background structured turbulence meshes. At each time-step, flow variables are interpolated from the unstructured mesh onto the background structured meshes, the turbulence model is executed on these meshes, and the resulting eddy viscosity values are interpolated back to the unstructured mesh. Modifications to the algebraic model were required to enable the treatment of more complicated flows, such as confluent boundary layers and wakes. The model is used in conjuction with an efficient unstructured multigrid finite-element Navier-Stokes solver in order to compute compressible turbulent flows on fully unstructured meshes. Solutions about single and multiple element airfoils are obtained and compared with experimental data.
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.
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.
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.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Joo, H.; Nichols, W.R.
1994-05-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.
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.
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.
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
The adaptive GRP scheme for compressible fluid flows over unstructured meshes
NASA Astrophysics Data System (ADS)
Li, Jiequan; Zhang, Yongjin
2013-06-01
Unstructured mesh methods have attracted much attention in CFD community due to the flexibility for dealing with complex geometries and the ability to easily incorporate adaptive (moving) mesh strategies. When the finite volume framework is applied, a reliable solver is crucial for the construction of numerical fluxes, for which the generalized Riemann problem (GRP) scheme undertakes such a task in the sense of second order accuracy. Combining these techniques yields a second order accurate adaptive generalized Riemann problem (AGRP) scheme for two dimensional compressible fluid flows over unstructured triangular meshes. Besides the generation of meshes, the main process of this combination consists of two ingredients: Fluid dynamical evolution and mesh redistribution. The fluid dynamical evolution ingredient serves to evolve the compressible fluid flows on a fixed nonuniform triangular mesh with the direct Eulerian GRP solver. The role of the mesh redistribution is to redistribute mesh points on which a conservative interpolation formula is adopted to calculate the cell-averages for the conservative variables, and the gradients of primitive variables are reconstructed using the least squares method. Several examples are taken from various contexts to demonstrate the performance of such a program.
Method and apparatus for connecting finite element meshes and performing simulations therewith
Dohrmann, Clark R.; Key, Samuel W.; Heinstein, Martin W.
2003-05-06
The present invention provides a method of connecting dissimilar finite element meshes. A first mesh, designated the master mesh, and a second mesh, designated the slave mesh, each have interface surfaces proximal the other. Each interface surface has a corresponding interface mesh comprising a plurality of interface nodes. Each slave interface node is assigned new coordinates locating the interface node on the interface surface of the master mesh. The slave interface surface is further redefined to be the projection of the slave interface mesh onto the master interface surface.
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.
Finite element error estimation and adaptivity based on projected stresses
Jung, J.
1990-08-01
This report investigates the behavior of a family of finite element error estimators based on projected stresses, i.e., continuous stresses that are a least squared error fit to the conventional Gauss point stresses. An error estimate based on element force equilibrium appears to be quite effective. Examples of adaptive mesh refinement for a one-dimensional problem are presented. Plans for two-dimensional adaptivity are discussed. 12 refs., 82 figs.
Adaptive mesh and algorithm refinement using direct simulation Monte Carlo
Garcia, A.L.; Bell, J.B.; Crutchfield, W.Y.; Alder, B.J.
1999-09-01
Adaptive mesh and algorithm refinement (AMAR) embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement (AMR) hierarchy. The coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of AMR. Direct simulation Monte Carlo (DSMC) is used as the particle algorithm embedded within a Godunov-type compressible Navier-Stokes solver. Several examples are presented and compared with purely continuum calculations.
Anisotropic adaptive mesh generation in two dimensions for CFD
Borouchaki, H.; Castro-Diaz, M.J.; George, P.L.; Hecht, F.; Mohammadi, B.
1996-12-31
This paper describes the extension of the classical Delaunay method in the case where anisotropic meshes are required such as in CFD when the modelized physic is strongly directional. The way in which such a mesh generation method can be incorporated in an adaptative loop of CFD as well as the case of multicriterium adaptation are discussed. Several concrete application examples are provided to illustrate the capabilities of the proposed method.
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.
A fast approach for accurate content-adaptive mesh generation.
Yang, Yongyi; Wernick, Miles N; Brankov, Jovan G
2003-01-01
Mesh modeling is an important problem with many applications in image processing. A key issue in mesh modeling is how to generate a mesh structure that well represents an image by adapting to its content. We propose a new approach to mesh generation, which is based on a theoretical result derived on the error bound of a mesh representation. In the proposed method, the classical Floyd-Steinberg error-diffusion algorithm is employed to place mesh nodes in the image domain so that their spatial density varies according to the local image content. Delaunay triangulation is next applied to connect the mesh nodes. The result of this approach is that fine mesh elements are placed automatically in regions of the image containing high-frequency features while coarse mesh elements are used to represent smooth areas. The proposed algorithm is noniterative, fast, and easy to implement. Numerical results demonstrate that, at very low computational cost, the proposed approach can produce mesh representations that are more accurate than those produced by several existing methods. Moreover, it is demonstrated that the proposed algorithm performs well with images of various kinds, even in the presence of noise. PMID:18237961
Effects of Mesh Irregularities on Accuracy of Finite-Volume Discretization Schemes
NASA Technical Reports Server (NTRS)
Diskin, Boris; Thomas, James L.
2012-01-01
The effects of mesh irregularities on accuracy of unstructured node-centered finite-volume discretizations are considered. The focus is on an edge-based approach that uses unweighted least-squares gradient reconstruction with a quadratic fit. For inviscid fluxes, the discretization is nominally third order accurate on general triangular meshes. For viscous fluxes, the scheme is an average-least-squares formulation that is nominally second order accurate and contrasted with a common Green-Gauss discretization scheme. Gradient errors, truncation errors, and discretization errors are separately studied according to a previously introduced comprehensive methodology. The methodology considers three classes of grids: isotropic grids in a rectangular geometry, anisotropic grids typical of adapted grids, and anisotropic grids over a curved surface typical of advancing layer grids. The meshes within the classes range from regular to extremely irregular including meshes with random perturbation of nodes. Recommendations are made concerning the discretization schemes that are expected to be least sensitive to mesh irregularities in applications to turbulent flows in complex geometries.
Adaptive Finite Element Methods for Continuum Damage Modeling
NASA Technical Reports Server (NTRS)
Min, J. B.; Tworzydlo, W. W.; Xiques, K. E.
1995-01-01
The paper presents an application of adaptive finite element methods to the modeling of low-cycle continuum damage and life prediction of high-temperature components. The major objective is to provide automated and accurate modeling of damaged zones through adaptive mesh refinement and adaptive time-stepping methods. The damage modeling methodology is implemented in an usual way by embedding damage evolution in the transient nonlinear solution of elasto-viscoplastic deformation problems. This nonlinear boundary-value problem is discretized by adaptive finite element methods. The automated h-adaptive mesh refinements are driven by error indicators, based on selected principal variables in the problem (stresses, non-elastic strains, damage, etc.). In the time domain, adaptive time-stepping is used, combined with a predictor-corrector time marching algorithm. The time selection is controlled by required time accuracy. In order to take into account strong temperature dependency of material parameters, the nonlinear structural solution a coupled with thermal analyses (one-way coupling). Several test examples illustrate the importance and benefits of adaptive mesh refinements in accurate prediction of damage levels and failure time.
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
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
A Numerical Study of Mesh Adaptivity in Multiphase Flows with Non-Newtonian Fluids
NASA Astrophysics Data System (ADS)
Percival, James; Pavlidis, Dimitrios; Xie, Zhihua; Alberini, Federico; Simmons, Mark; Pain, Christopher; Matar, Omar
2014-11-01
We present an investigation into the computational efficiency benefits of dynamic mesh adaptivity in the numerical simulation of transient multiphase fluid flow problems involving Non-Newtonian fluids. Such fluids appear in a range of industrial applications, from printing inks to toothpastes and introduce new challenges for mesh adaptivity due to the additional ``memory'' of viscoelastic fluids. Nevertheless, the multiscale nature of these flows implies huge potential benefits for a successful implementation. The study is performed using the open source package Fluidity, which couples an unstructured mesh control volume finite element solver for the multiphase Navier-Stokes equations to a dynamic anisotropic mesh adaptivity algorithm, based on estimated solution interpolation error criteria, and conservative mesh-to-mesh interpolation routine. The code is applied to problems involving rheologies ranging from simple Newtonian to shear-thinning to viscoelastic materials and verified against experimental data for various industrial and microfluidic flows. This work was undertaken as part of the EPSRC MEMPHIS programme grant EP/K003976/1.
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.
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.
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.
3D unstructured mesh discontinuous finite element hydro
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J.
1995-07-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.
Parallel adaptation of general three-dimensional hybrid meshes
NASA Astrophysics Data System (ADS)
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.
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.
Design of an essentially non-oscillatory reconstruction procedure in finite-element type meshes
NASA Technical Reports Server (NTRS)
Abgrall, Remi
1992-01-01
An essentially non oscillatory reconstruction for functions defined on finite element type meshes is designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitary meshes and the reconstruction of a function from its averages in the control volumes surrounding the nodes of the mesh. Concerning the first problem, the behavior of the highest coefficients of two polynomial interpolations of a function that may admit discontinuities of locally regular curves is studied: the Lagrange interpolation and an approximation such that the mean of the polynomial on any control volume is equal to that of the function to be approximated. This enables the best stencil for the approximation to be chosen. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, two methods were studied: one based on an adaptation of the so called reconstruction via deconvolution method to irregular meshes and one that lies on the approximation on the mean as defined above. The first method is conservative up to a quadrature formula and the second one is exactly conservative. The two methods have the expected order of accuracy, but the second one is much less expensive than the first one. Some numerical examples are given which demonstrate the efficiency of the reconstruction.
NASA Astrophysics Data System (ADS)
Zehner, Björn; Börner, Jana H.; Görz, Ines; Spitzer, Klaus
2015-06-01
Subsurface processing numerical simulations require accurate discretization of the modeling domain such that the geological units are represented correctly. Unstructured tetrahedral grids are particularly flexible in adapting to the shape of geo-bodies and are used in many finite element codes. In order to generate a tetrahedral mesh on a 3D geological model, the tetrahedrons have to belong completely to one geological unit and have to describe geological boundaries by connected facets of tetrahedrons. This is especially complicated at the contact points between several units and for irregular sharp-shaped bodies, especially in case of faulted zones. This study develops, tests and validates three workflows to generate a good tetrahedral mesh from a geological basis model. The tessellation of the model needs (i) to be of good quality to guarantee a stable calculation, (ii) to include certain nodes to apply boundary conditions for the numerical solution, and (iii) support local mesh refinement. As a test case we use the simulation of a transient electromagnetic measurement above a salt diapir. We can show that the suggested workflows lead to a tessellation of the structure on which the simulation can be run robustly. All workflows show advantages and disadvantages with respect to the workload, the control the user has over the resulting mesh and the skills in software handling that are required.
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 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.
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Astrophysics Data System (ADS)
Smith, Wayne A.; Blake, Kenneth R.
1992-11-01
This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.
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.
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.
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. PMID:24483578
Kinetic solvers with adaptive mesh in phase space
NASA Astrophysics Data System (ADS)
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.
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.
PARAMESH V4.1: Parallel Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
MacNeice, Peter; Olson, Kevin M.; Mobarry, Clark; de Fainchtein, Rosalinda; Packer, Charles
2011-06-01
PARAMESH is a package of Fortran 90 subroutines 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 (AMR). 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 builds a hierarchy of sub-grids to cover the computational domain, with spatial resolution varying to satisfy the demands of the application. These sub-grid blocks form the nodes of a tree data-structure (quad-tree in 2D or oct-tree in 3D). Each grid block has a logically cartesian mesh. The package supports 1, 2 and 3D models. PARAMESH is released under the NASA-wide Open-Source software license.
The parallelization of an advancing-front, all-quadrilateral meshing algorithm for adaptive analysis
Lober, R.R.; Tautges, T.J.; Cairncross, R.A.
1995-11-01
The ability to perform effective adaptive analysis has become a critical issue in the area of physical simulation. Of the multiple technologies required to realize a parallel adaptive analysis capability, automatic mesh generation is an enabling technology, filling a critical need in the appropriate discretization of a problem domain. The paving algorithm`s unique ability to generate a function-following quadrilateral grid is a substantial advantage in Sandia`s pursuit of a modified h-method adaptive capability. This characteristic combined with a strong transitioning ability allow the paving algorithm to place elements where an error function indicates more mesh resolution is needed. Although the original paving algorithm is highly serial, a two stage approach has been designed to parallelize the algorithm but also retain the nice qualities of the serial algorithm. The authors approach also allows the subdomain decomposition used by the meshing code to be shared with the finite element physics code, eliminating the need for data transfer across the processors between the analysis and remeshing steps. In addition, the meshed subdomains are adjusted with a dynamic load balancer to improve the original decomposition and maintain load efficiency each time the mesh has been regenerated. This initial parallel implementation assumes an approach of restarting the physics problem from time zero at each interaction, with a refined mesh adapting to the previous iterations objective function. The remeshing tools are being developed to enable real time remeshing and geometry regeneration. Progress on the redesign of the paving algorithm for parallel operation is discussed including extensions allowing adaptive control and geometry regeneration.
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.
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.
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.
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.
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.
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.
FEMHD: An adaptive finite element method for MHD and edge modelling
Strauss, H.R.
1995-07-01
This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.
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.
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.
The design of a parallel adaptive paving all-quadrilateral meshing algorithm
Tautges, T.J.; Lober, R.R.; Vaughan, C.
1995-08-01
Adaptive finite element analysis demands a great deal of computational resources, and as such is most appropriately solved in a massively parallel computer environment. This analysis will require other parallel algorithms before it can fully utilize MP computers, one of which is parallel adaptive meshing. A version of the paving algorithm is being designed which operates in parallel but which also retains the robustness and other desirable features present in the serial algorithm. Adaptive paving in a production mode is demonstrated using a Babuska-Rheinboldt error estimator on a classic linearly elastic plate problem. The design of the parallel paving algorithm is described, and is based on the decomposition of a surface into {open_quotes}virtual{close_quotes} surfaces. The topology of the virtual surface boundaries is defined using mesh entities (mesh nodes and edges) so as to allow movement of these boundaries with smoothing and other operations. This arrangement allows the use of the standard paving algorithm on subdomain interiors, after the negotiation of the boundary mesh.
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
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.
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.
Tangle-Free Finite Element Mesh Motion for Ablation Problems
NASA Technical Reports Server (NTRS)
Droba, Justin
2016-01-01
In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.
Improvement of finite element meshes - Heat transfer in an infinite cylinder
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.
1989-01-01
An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffnes matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.
Improvement in finite element meshes: Heat transfer in an infinite cylinder
NASA Technical Reports Server (NTRS)
Kittur, Madan G.; Huston, Ronald L.; Oswald, Fred B.
1988-01-01
An extension of a structural finite element mesh improvement technique to heat conduction analysis is presented. The mesh improvement concept was originally presented by Prager in studying tapered, axially loaded bars. It was further shown that an improved mesh can be obtained by minimizing the trace of the stiffness matrix. These procedures are extended and applied to the analysis of heat conduction in an infinitely long hollow circular cylinder.
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.
Generating meshes for finite-difference analysis using a solid modeler
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.
Tangle-Free Finite Element Mesh Motion for Ablation Problems
NASA Technical Reports Server (NTRS)
Droba, Justin
2016-01-01
Mesh motion is the process by which a computational domain is updated in time to reflect physical changes in the material the domain represents. Such a technique is needed in the study of the thermal response of ablative materials, which erode when strong heating is applied to the boundary. Traditionally, the thermal solver is coupled with a linear elastic or biharmonic system whose sole purpose is to update mesh node locations in response to altering boundary heating. Simple mesh motion algorithms rely on boundary surface normals. In such schemes, evolution in time will eventually cause the mesh to intersect and "tangle" with itself, causing failure. Furthermore, such schemes are greatly limited in the problems geometries on which they will be successful. This paper presents a comprehensive and sophisticated scheme that tailors the directions of motion based on context. By choosing directions for each node smartly, the inevitable tangle can be completely avoided and mesh motion on complex geometries can be modeled accurately.
Finite element based electrostatic-structural coupled analysis with automated mesh morphing
OWEN,STEVEN J.; ZHULIN,V.I.; OSTERGAARD,D.F.
2000-02-29
A co-simulation tool based on finite element principles has been developed to solve coupled electrostatic-structural problems. An automated mesh morphing algorithm has been employed to update the field mesh after structural deformation. The co-simulation tool has been successfully applied to the hysteric behavior of a MEMS switch.
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.
Sampling and surface reconstruction with adaptive-size meshes
NASA Astrophysics Data System (ADS)
Huang, Wen-Chen; Goldgof, Dmitry B.
1992-03-01
This paper presents a new approach to sampling and surface reconstruction which uses the physically based models. We introduce adaptive-size meshes which automatically update the size of the meshes as the distance between the nodes changes. We have implemented the adaptive-size algorithm to the following three applications: (1) Sampling of the intensity data. (2) Surface reconstruction of the range data. (3) Surface reconstruction of the 3-D computed tomography left ventricle data. The LV data was acquired by the 3-D computed tomography (CT) scanner. It was provided by Dr. Eric Hoffman at University of Pennsylvania Medical school and consists of 16 volumetric (128 X 128 X 118) images taken through the heart cycle.
Particle systems for adaptive, isotropic meshing of CAD models
Levine, Joshua A.; Whitaker, Ross T.
2012-01-01
We present a particle-based approach for generating adaptive triangular surface and tetrahedral volume meshes from computer-aided design models. Input shapes are treated as a collection of smooth, parametric surface patches that can meet non-smoothly on boundaries. Our approach uses a hierarchical sampling scheme that places particles on features in order of increasing dimensionality. These particles reach a good distribution by minimizing an energy computed in 3D world space, with movements occurring in the parametric space of each surface patch. Rather than using a pre-computed measure of feature size, our system automatically adapts to both curvature as well as a notion of topological separation. It also enforces a measure of smoothness on these constraints to construct a sizing field that acts as a proxy to piecewise-smooth feature size. We evaluate our technique with comparisons against other popular triangular meshing techniques for this domain. PMID:23162181
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.
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
Iterative methods for elliptic finite element equations on general meshes
NASA Technical Reports Server (NTRS)
Nicolaides, R. A.; Choudhury, Shenaz
1986-01-01
Iterative methods for arbitrary mesh discretizations of elliptic partial differential equations are surveyed. The methods discussed are preconditioned conjugate gradients, algebraic multigrid, deflated conjugate gradients, an element-by-element techniques, and domain decomposition. Computational results are included.
ROAMing terrain (Real-time Optimally Adapting Meshes)
Duchaineau, M.; Wolinsky, M.; Sigeti, D.E.; Miller, M.C.; Aldrich, C.; Mineev, M.
1997-07-01
Terrain visualization is a difficult problem for applications requiring accurate images of large datasets at high frame rates, such as flight simulation and ground-based aircraft testing using synthetic sensor stimulation. On current graphics hardware, the problem is to maintain dynamic, view-dependent triangle meshes and texture maps that produce good images at the required frame rate. We present an algorithm for constructing triangle meshes that optimizes flexible view-dependent error metrics, produces guaranteed error bounds, achieves specified triangle counts directly, and uses frame-to-frame coherence to operate at high frame rates for thousands of triangles per frame. Our method, dubbed Real-time Optimally Adapting Meshes (ROAM), uses two priority queues to drive split and merge operations that maintain continuous triangulations built from pre-processed bintree triangles. We introduce two additional performance optimizations: incremental triangle stripping and priority-computation deferral lists. ROAM execution time is proportionate to the number of triangle changes per frame, which is typically a few percent of the output mesh size, hence ROAM performance is insensitive to the resolution and extent of the input terrain. Dynamic terrain and simple vertex morphing are supported.
Finite difference methods with non-uniform meshes for nonlinear fractional differential equations
NASA Astrophysics Data System (ADS)
Li, Changpin; Yi, Qian; Chen, An
2016-07-01
In this article, finite difference methods with non-uniform meshes for solving nonlinear fractional differential equations are presented, where the non-equidistant stepsize is non-decreasing. The rectangle formula and trapezoid formula are proposed based on the non-uniform meshes. Combining the above two methods, we then establish the predictor-corrector scheme. The error and stability analysis are carefully investigated. At last, numerical examples are carried out to verify the theoretical analysis. Besides, the comparisons between non-uniform and uniform meshes are given, where the non-uniform meshes show the better performance when dealing with the less smooth problems.
A Method for Connecting Dissimilar Finite Element Meshes in Three Dimensions
Dohrmann, C.R.; Heinstein, M.W.; Key, S.W.
1998-11-12
A method is presented for connecting dissimilar finite element meshes in three dimensions. The method combines the concept of master and slave surfaces with the uniform strain approach for surface, corrections finite elements- By modifyhg the are made to element formulations boundaries of elements on the slave such that first-order patch tests are passed. The method can be used to connect meshes which use different element types. In addition, master and slave surfaces can be designated independently of relative mesh resolutions. Example problems in three-dimensional linear elasticity are presented.
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.
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)
Toward parallel, adaptive mesh refinement for chemically reacting flow simulations
Devine, K.D.; Shadid, J.N.; Salinger, A.G. Hutchinson, S.A.; Hennigan, G.L.
1997-12-01
Adaptive numerical methods offer greater efficiency than traditional numerical methods by concentrating computational effort in regions of the problem domain where the solution is difficult to obtain. In this paper, the authors describe progress toward adding mesh refinement to MPSalsa, a computer program developed at Sandia National laboratories to solve coupled three-dimensional fluid flow and detailed reaction chemistry systems for modeling chemically reacting flow on large-scale parallel computers. Data structures that support refinement and dynamic load-balancing are discussed. Results using uniform refinement with mesh sequencing to improve convergence to steady-state solutions are also presented. Three examples are presented: a lid driven cavity, a thermal convection flow, and a tilted chemical vapor deposition reactor.
A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS
NASA Technical Reports Server (NTRS)
Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.
1993-01-01
Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).
A Lagrangian-Eulerian finite element method with adaptive gridding for advection-dispersion problems
Ijiri, Y.; Karasaki, K.
1994-02-01
In the present paper, a Lagrangian-Eulerian finite element method with adaptive gridding for solving advection-dispersion equations is described. The code creates new grid points in the vicinity of sharp fronts at every time step in order to reduce numerical dispersion. The code yields quite accurate solutions for a wide range of mesh Peclet numbers and for mesh Courant numbers well in excess of 1.
Earthquake Rupture Dynamics using Adaptive Mesh Refinement and High-Order Accurate Numerical Methods
NASA Astrophysics Data System (ADS)
Kozdon, J. E.; Wilcox, L.
2013-12-01
Our goal is to develop scalable and adaptive (spatial and temporal) numerical methods for coupled, multiphysics problems using high-order accurate numerical methods. To do so, we are developing an opensource, parallel library known as bfam (available at http://bfam.in). The first application to be developed on top of bfam is an earthquake rupture dynamics solver using high-order discontinuous Galerkin methods and summation-by-parts finite difference methods. In earthquake rupture dynamics, wave propagation in the Earth's crust is coupled to frictional sliding on fault interfaces. This coupling is two-way, required the simultaneous simulation of both processes. The use of laboratory-measured friction parameters requires near-fault resolution that is 4-5 orders of magnitude higher than that needed to resolve the frequencies of interest in the volume. This, along with earlier simulations using a low-order, finite volume based adaptive mesh refinement framework, suggest that adaptive mesh refinement is ideally suited for this problem. The use of high-order methods is motivated by the high level of resolution required off the fault in earlier the low-order finite volume simulations; we believe this need for resolution is a result of the excessive numerical dissipation of low-order methods. In bfam spatial adaptivity is handled using the p4est library and temporal adaptivity will be accomplished through local time stepping. In this presentation we will present the guiding principles behind the library as well as verification of code against the Southern California Earthquake Center dynamic rupture code validation test problems.
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].
Simulation of nonpoint source contamination based on adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Kourakos, G.; Harter, T.
2014-12-01
Contamination of groundwater aquifers from nonpoint sources is a worldwide problem. Typical agricultural groundwater basins receive contamination from a large array (in the order of ~10^5-6) of spatially and temporally heterogeneous sources such as fields, crops, dairies etc, while the received contaminants emerge at significantly uncertain time lags to a large array of discharge surfaces such as public supply, domestic and irrigation wells and streams. To support decision making in such complex regimes several approaches have been developed, which can be grouped into 3 categories: i) Index methods, ii)regression methods and iii) physically based methods. Among the three, physically based methods are considered more accurate, but at the cost of computational demand. In this work we present a physically based simulation framework which exploits the latest hardware and software developments to simulate large (>>1,000 km2) groundwater basins. First we simulate groundwater flow using a sufficiently detailed mesh to capture the spatial heterogeneity. To achieve optimal mesh quality we combine adaptive mesh refinement with the nonlinear solution for unconfined flow. Starting from a coarse grid the mesh is refined iteratively in the parts of the domain where the flow heterogeneity appears higher resulting in optimal grid. Secondly we simulate the nonpoint source pollution based on the detailed velocity field computed from the previous step. In our approach we use the streamline model where the 3D transport problem is decomposed into multiple 1D transport problems. The proposed framework is applied to simulate nonpoint source pollution in the Central Valley aquifer system, California.
Finite element meshing of ANSYS (trademark) solid models
NASA Technical Reports Server (NTRS)
Kelley, F. S.
1987-01-01
A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.
NASA Astrophysics Data System (ADS)
Dancette, S.; Browet, A.; Martin, G.; Willemet, M.; Delannay, L.
2016-06-01
A new procedure for microstructure-based finite element modeling of polycrystalline aggregates is presented. The proposed method relies (i) on an efficient graph-based community detection algorithm for crystallographic data segmentation and feature contour extraction and (ii) on the generation of selectively refined meshes conforming to grain boundaries. It constitutes a versatile and close to automatic environment for meshing complex microstructures. The procedure is illustrated with polycrystal microstructures characterized by orientation imaging microscopy. Hot deformation of a Duplex stainless steel is investigated based on ex-situ EBSD measurements performed on the same region of interest before and after deformation. A finite element mesh representing the initial microstructure is generated and then used in a crystal plasticity simulation of the plane strain compression. Simulation results and experiments are in relatively good agreement, confirming a large potential for such directly coupled experimental and modeling analyses, which is facilitated by the present image-based meshing procedure.
NASA Astrophysics Data System (ADS)
O'Hara, P.; Hollkamp, J.; Duarte, C. A.; Eason, T.
2016-01-01
This paper presents a two-scale extension of the generalized finite element method (GFEM) which allows for static fracture analyses as well as fatigue crack propagation simulations on fixed, coarse hexahedral meshes. The approach is based on the use of specifically-tailored enrichment functions computed on-the-fly through the use of a fine-scale boundary value problem (BVP) defined in the neighborhood of existing mechanically-short cracks. The fine-scale BVP utilizes tetrahedral elements, and thus offers the potential for the use of a highly adapted fine-scale mesh in the regions of crack fronts capable of generating accurate enrichment functions for use in the coarse-scale hexahedral model. In this manner, automated hp-adaptivity which can be used for accurate fracture analyses, is now available for use on coarse, uniform hexahedral meshes without the requirements of irregular meshes and constrained approximations. The two-scale GFEM approach is verified and compared against alternative approaches for static fracture analyses, as well as mixed-mode fatigue crack propagation simulations. The numerical examples demonstrate the ability of the proposed approach to deliver accurate results even in scenarios involving multiple discontinuities or sharp kinks within a single computational element. The proposed approach is also applied to a representative panel model similar in design and complexity to that which may be used in the aerospace community.
Multiscale Simulation of Microcrack Based on a New Adaptive Finite Element Method
NASA Astrophysics Data System (ADS)
Xu, Yun; Chen, Jun; Chen, Dong Quan; Sun, Jin Shan
In this paper, a new adaptive finite element (FE) framework based on the variational multiscale method is proposed and applied to simulate the dynamic behaviors of metal under loadings. First, the extended bridging scale method is used to couple molecular dynamics and FE. Then, macro damages evolvements of those micro defects are simulated by the adaptive FE method. Some auxiliary strategies, such as the conservative mesh remapping, failure mechanism and mesh splitting technique are also included in the adaptive FE computation. Efficiency of our method is validated by numerical experiments.
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.
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.
Coupling finite element and integral equation solutions using decoupled boundary meshes
NASA Technical Reports Server (NTRS)
Cwik, Tom
1992-01-01
A method is outlined for calculating scattered fields from inhomogeneous penetrable objects using a coupled finite element-integral equation solution. The finite element equation can efficiently model fields in penetrable and inhomogeneous regions, while the integral equation exactly models fields on the finite element mesh boundary and in the exterior region. By decoupling the interior finite element and exterior integral equation meshes, considerable flexibility is found in both the number of field expansion points as well as their density. Only the nonmetal portions of the object need be modeled using a finite element expansion; exterior perfect conducting surfaces are modeled using an integral equation with a single unknown field since E(tan) is identically zero on these surfaces. Numerical convergence, accuracy, and stability at interior resonant frequencies are studied in detail.
Examples of finite element mesh generation using SDRC IDEAS
NASA Technical Reports Server (NTRS)
Zapp, John; Volakis, John L.
1990-01-01
IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.
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 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.
Visualization of Octree Adaptive Mesh Refinement (AMR) in Astrophysical Simulations
NASA Astrophysics Data System (ADS)
Labadens, M.; Chapon, D.; Pomaréde, D.; Teyssier, R.
2012-09-01
Computer simulations are important in current cosmological research. Those simulations run in parallel on thousands of processors, and produce huge amount of data. Adaptive mesh refinement is used to reduce the computing cost while keeping good numerical accuracy in regions of interest. RAMSES is a cosmological code developed by the Commissariat à l'énergie atomique et aux énergies alternatives (English: Atomic Energy and Alternative Energies Commission) which uses Octree adaptive mesh refinement. Compared to grid based AMR, the Octree AMR has the advantage to fit very precisely the adaptive resolution of the grid to the local problem complexity. However, this specific octree data type need some specific software to be visualized, as generic visualization tools works on Cartesian grid data type. This is why the PYMSES software has been also developed by our team. It relies on the python scripting language to ensure a modular and easy access to explore those specific data. In order to take advantage of the High Performance Computer which runs the RAMSES simulation, it also uses MPI and multiprocessing to run some parallel code. We would like to present with more details our PYMSES software with some performance benchmarks. PYMSES has currently two visualization techniques which work directly on the AMR. The first one is a splatting technique, and the second one is a custom ray tracing technique. Both have their own advantages and drawbacks. We have also compared two parallel programming techniques with the python multiprocessing library versus the use of MPI run. The load balancing strategy has to be smartly defined in order to achieve a good speed up in our computation. Results obtained with this software are illustrated in the context of a massive, 9000-processor parallel simulation of a Milky Way-like galaxy.
A comparative study of an ABC and an artificial absorber for truncating finite element meshes
NASA Technical Reports Server (NTRS)
Oezdemir, T.; Volakis, John L.
1993-01-01
The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.
Finite octree meshing through topologically driven geometric operators
NASA Technical Reports Server (NTRS)
Grice, Kurt R.
1987-01-01
The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.
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
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.
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.
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.
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.
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.
Numerical modelling of tsunami generation by deformable submarine slides using mesh adaptivity
NASA Astrophysics Data System (ADS)
Smith, Rebecca; Parkinson, Samuel; Hill, Jon; Collins, Gareth; Piggott, Matthew
2014-05-01
Tsunamis generated by submarine slides are often under considered in comparison to earthquake generated tsunami, despite several recent examples. Tsunamigenic slides have generated waves that have caused significant damage and loss of life, for example the 1998 Papua New Guinea submarine mass failure resulted in a tsunami that devastated coastal villages and killed over 2,100 people. Numerical simulations of submarine slide generated waves can help us understand the nature of the waves that are generated, and identify the important factors in determining wave characteristics. There have not been many studies of tsunami generation by deformable submarine slides, largely because of the complexities and computational expense involved in modelling these large scale events. At large, real world, scales modelling of tsunami waves by the generation of slides is computationally challenging. Fluidity is an open source finite element code that is ideally suited to tackle this type of problem as it uses unstructured, adaptive meshes, which help to reduce the computational expense without losing accuracy in the results. Adaptive meshes change topology and resolution based on the current simulation state and as such can focus or reduce resolution when and where it is required. The model also allows a number of different numerical approaches to be taken to simulate the same problem within the same numerical framework. In this example we use multi-material approach, with both two materials (slide and water) and three materials (slide, water and air), alongside a density-driven sediment model approach. We will present results of validating Fluidity against benchmarks from experimental and other numerical studies, at different scales, for deformable underwater slides, and consider the utility of mesh adaptivity. We show good agreement to both laboratory results and other numerical models, both with a fixed mesh and a dynamically adaptive mesh, tracking important features of the
NASA Astrophysics Data System (ADS)
Yang, Bin; Xu, Canhua; Dai, Meng; Fu, Feng; Dong, Xiuzhen
2013-07-01
For electrical impedance tomography (EIT) of brain, the use of anatomically accurate and patient-specific finite element (FE) mesh has been shown to confer significant improvements in the quality of image reconstruction. But, given the lack of a rapid method to achieve the accurate anatomic geometry of the head, the generation of patient-specifc mesh is time-comsuming. In this paper, a modified fuzzy c-means algorithm based on non-local means method is performed to implement the segmentation of different layers in the head based on head CT images. This algorithm showed a better effect, especially an accurate recognition of the ventricles and a suitable performance dealing with noise. And the FE mesh established according to the segmentation results is validated in computational simulation. So a rapid practicable method can be provided for the generation of patient-specific FE mesh of the human head that is suitable for brain EIT.
Charged particle tracking through electrostatic wire meshes using the finite element method
NASA Astrophysics Data System (ADS)
Devlin, L. J.; Karamyshev, O.; Welsch, C. P.
2016-06-01
Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.
Accurate, finite-volume methods for three dimensional magneto-hydrodynamics on Lagrangian meshes
Rousculp, C.L.; Barnes, D.C.
1999-07-01
Recently developed algorithms for ideal and resistive, 3D MHD calculations on Lagrangian hexahedral meshes have been generalized to work with a lagrangian mesh composed of arbitrary polyhedral cells. this allows for mesh refinement during a calculation to prevent the well known problem of tangling in a Lagrangian mesh. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {sm_bullet} {delta}1, is centered on all faces edges of this extended mesh. Thus, {triangledown} {sm_bullet} B = 0 is maintained to round-off error. For ideal flow, (E = v x B), vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion, (E = {minus}{eta}J), is treated with a support operator method, to obtain an energy conservative, symmetric method on an arbitrary polyhedral mesh. The equation of motion is time-step-split. First, the ideal term is treated explicitly. Next, the diffusion is solved implicitly with a preconditioned conjugate gradient method. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.
Finite Elements approach for Density Functional Theory calculations on locally refined meshes
Fattebert, J; Hornung, R D; Wissink, A M
2006-03-27
We present a quadratic Finite Elements approach to discretize the Kohn-Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.
Finite Element approach for Density Functional Theory calculations on locally refined meshes
Fattebert, J; Hornung, R D; Wissink, A M
2007-02-23
We present a quadratic Finite Element approach to discretize the Kohn-Sham equations on structured non-uniform meshes. A multigrid FAC preconditioner is proposed to iteratively solve the equations by an accelerated steepest descent scheme. The method was implemented using SAMRAI, a parallel software infrastructure for general AMR applications. Examples of applications to small nanoclusters calculations are presented.
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.
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.
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.
Multigrid waveform relaxation on spatial finite element meshes
Janssen, J.; Vandewalle, S.
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
Lin, Paul Tinphone; Jameson, Antony, 1934-; Baker, Timothy J.; Martinelli, Luigi
2005-01-01
An implicit multigrid-driven algorithm for two-dimensional incompressible laminar viscous flows has been coupled with a solution adaptation method and a mesh movement method for boundary movement. Time-dependent calculations are performed implicitly by regarding each time step as a steady-state problem in pseudo-time. The method of artificial compressibility is used to solve the flow equations. The solution mesh adaptation method performs local mesh refinement using an incremental Delaunay algorithm and mesh coarsening by means of edge collapse. Mesh movement is achieved by modeling the computational domain as an elastic solid and solving the equilibrium equations for the stress field. The solution adaptation method has been validated by comparison with experimental results and other computational results for low Reynolds number flow over a shedding circular cylinder. Preliminary validation of the mesh movement method has been demonstrated by a comparison with experimental results of an oscillating airfoil and with computational results for an oscillating cylinder.
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
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
Using Rock SEM Image to Create Pore-scale Finite Element Calculation Mesh
NASA Astrophysics Data System (ADS)
Jianjun, Liu; Lijun, Lin; Youjun, Ji
Micro-scale numerical simulation were often used to study the deformation, flow or heat transfer mechanism of material, among the simulation, one important step is to get simulation mesh. Taking rock as an example, this paper illustrated a method of creating pore-scale finite element calculation mesh from rock Scanning Electron Microscope (SEM) image with image processing toolbox of MATLAB, Algolab Raster to Vector Conversion Toolkit and COMSOL Multiphysics software. It established a more accurate numerical model of the microscopic pore structure of rock. Simulation results demonstrate that the method is efficiency in the application of image processing and the study of microscopic pore structure.
Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure
NASA Technical Reports Server (NTRS)
Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.
1992-01-01
Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.
On the Interconnection of Incompatible Solid Finite Element Meshes Using Multipoint Constraints
NASA Technical Reports Server (NTRS)
Fox, G. L.
1985-01-01
Incompatible meshes, i.e., meshes that physically must have a common boundary, but do not necessarily have coincident grid points, can arise in the course of a finite element analysis. For example, two substructures may have been developed at different times for different purposes and it becomes necessary to interconnect the two models. A technique that uses only multipoint constraints, i.e., MPC cards (or MPCS cards in substructuring), is presented. Since the method uses only MPC's, the procedure may apply at any stage in an analysis; no prior planning or special data is necessary.
NASA Astrophysics Data System (ADS)
Lian, Y.-Y.; Hsu, K.-H.; Shao, Y.-L.; Lee, Y.-M.; Jeng, Y.-W.; Wu, J.-S.
2006-12-01
The development of a parallel three-dimensional (3-D) adaptive mesh refinement (PAMR) scheme for an unstructured tetrahedral mesh using dynamic domain decomposition on a memory-distributed machine is presented in detail. A memory-saving cell-based data structure is designed such that the resulting mesh information can be readily utilized in both node- or cell-based numerical methods. The general procedures include isotropic refinement from one parent cell into eight child cells and then followed by anisotropic refinement which effectively removes hanging nodes. A simple but effective mesh-quality control mechanism is employed to preserve the mesh quality. The resulting parallel performance of this PAMR is found to scale approximately as N for N⩽32. Two test cases, including a particle method (parallel DSMC solver for rarefied gas dynamics) and an equation-based method (parallel Poisson-Boltzmann equation solver for electrostatic field), are used to demonstrate the generality of the PAMR module. It is argued that this PAMR scheme can be applied in any numerical method if the unstructured tetrahedral mesh is adopted.
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.
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
NASA Technical Reports Server (NTRS)
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
Xia, Kelin; Zhan, Meng; Wan, Decheng; Wei, Guo-Wei
2012-02-01
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 L(2) 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
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
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)
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.
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.
Constrained-transport Magnetohydrodynamics with Adaptive Mesh Refinement in CHARM
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Martin, Daniel F.
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.
AMR++: Object-oriented design for adaptive mesh refinement
Quinlan, D.
1998-12-01
The development of object-oriented libraries for scientific computing is complicated by the wide range of applications that are targeted and the complexity and wide range of numerical methods that are used. A problem is to design a library that can be customized to handle a wide range of target applications and increasingly complex numerical methods while maintaining a sufficiently useful library for simple problems. These problems have been classically at odds with one another and have compromised the design of many object-oriented library solutions. In this paper the authors detail the mechanisms used within AMR**, and object-oriented library for Adaptive Mesh Refinement (AMR), to provide the level of extensibility that is required to make AMR++ easily customizable for the more obscure applications while remaining small and simple for less complex applications. The goal has been to have a complex applications. The goal has been to have a complexity that matches the complexity of the target application. These mechanisms are general and extend to other libraries as well.
The response of cranial biomechanical finite element models to variations in mesh density.
Bright, Jen A; Rayfield, Emily J
2011-04-01
Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT-based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time-consuming. To assess how mesh convergence influences results, 18 increasingly refined CT-based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low-strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain "hot-spots" notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place. PMID:21370496
Mesh management methods in finite element simulations of orthodontic tooth movement.
Mengoni, M; Ponthot, J-P; Boman, R
2016-02-01
In finite element simulations of orthodontic tooth movement, one of the challenges is to represent long term tooth movement. Large deformation of the periodontal ligament and large tooth displacement due to bone remodelling lead to large distortions of the finite element mesh when a Lagrangian formalism is used. We propose in this work to use an Arbitrary Lagrangian Eulerian (ALE) formalism to delay remeshing operations. A large tooth displacement is obtained including effect of remodelling without the need of remeshing steps but keeping a good-quality mesh. Very large deformations in soft tissues such as the periodontal ligament is obtained using a combination of the ALE formalism used continuously and a remeshing algorithm used when needed. This work demonstrates that the ALE formalism is a very efficient way to delay remeshing operations. PMID:26671785
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
NASA Astrophysics Data System (ADS)
Pathak, Harshavardhana S.; Shukla, Ratnesh K.
2016-08-01
A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The method achieves dynamic adaptation through a combination of time-dependent mesh node clustering in regions characterized by strong solution gradients and an optimal selection of the order of accuracy and the associated reconstruction stencil in a conservative finite-volume framework. This combined approach maximizes spatial resolution in discontinuous regions that require low-order approximations for oscillation-free shock capturing. Over smooth regions, high-order discretization through finite-volume WENO schemes minimizes numerical dissipation and provides excellent resolution of intricate flow features. The method including the moving mesh equations and the compressible flow solver is formulated entirely on a transformed time-independent computational domain discretized using a simple uniform Cartesian mesh. Approximations for the metric terms that enforce discrete geometric conservation law while preserving the fourth-order accuracy of the two-point Gaussian quadrature rule are developed. Spurious Cartesian grid induced shock instabilities such as carbuncles that feature in a local one-dimensional contact capturing treatment along the cell face normals are effectively eliminated through upwind flux calculation using a rotated Hartex-Lax-van Leer contact resolving (HLLC) approximate Riemann solver for the Euler equations in generalized coordinates. Numerical experiments with the fifth and ninth-order WENO reconstructions at the two-point Gaussian quadrature nodes, over a range of challenging test cases, indicate that the redistributed mesh effectively adapts to the dynamic flow gradients thereby improving the solution accuracy substantially even when the initial starting mesh is non-adaptive. The high adaptivity combined with the fifth and especially the ninth-order WENO reconstruction allows remarkably sharp capture of
Design of an essentially non-oscillatory reconstruction procedure on finite-element type meshes
NASA Technical Reports Server (NTRS)
Abgrall, R.
1991-01-01
An essentially non-oscillatory reconstruction for functions defined on finite-element type meshes was designed. Two related problems are studied: the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a function from its average in the control volumes surrounding the nodes of the mesh. Concerning the first problem, we have studied the behavior of the highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the best stencil for the interpolation. The choice of the smallest possible number of stencils is addressed. Concerning the reconstruction problem, because of the very nature of the mesh, the only method that may work is the so called reconstruction via deconvolution method. Unfortunately, it is well suited only for regular meshes as we show, but we also show how to overcome this difficulty. The global method has the expected order of accuracy but is conservative up to a high order quadrature formula only. Some numerical examples are given which demonstrate the efficiency of the method.
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. PMID:26577253
Accurate, finite-volume methods for 3D MHD on unstructured Lagrangian meshes
Barnes, D.C.; Rousculp, C.L.
1998-10-01
Previous 2D methods for magnetohydrodynamics (MHD) have contributed both to development of core code capability and to physics applications relevant to AGEX pulsed-power experiments. This strategy is being extended to 3D by development of a modular extension of an ASCI code. Extension to 3D not only increases complexity by problem size, but also introduces new physics, such as magnetic helicity transport. The authors have developed a method which incorporates all known conservation properties into the difference scheme on a Lagrangian unstructured mesh. Because the method does not depend on the mesh structure, mesh refinement is possible during a calculation to prevent the well known problem of mesh tangling. Arbitrary polyhedral cells are decomposed into tetrahedrons. The action of the magnetic vector potential, A {center_dot} {delta}l, is centered on the edges of this extended mesh. For ideal flow, this maintains {del} {center_dot} B = 0 to round-off error. Vertex forces are derived by the variation of magnetic energy with respect to vertex positions, F = {minus}{partial_derivative}W{sub B}/{partial_derivative}r. This assures symmetry as well as magnetic flux, momentum, and energy conservation. The method is local so that parallelization by domain decomposition is natural for large meshes. In addition, a simple, ideal-gas, finite pressure term has been included. The resistive diffusion part is calculated using the support operator method, to obtain an energy conservative, symmetric method on an arbitrary mesh. Implicit time difference equations are solved by preconditioned, conjugate gradient methods. Results of convergence tests are presented. Initial results of an annular Z-pinch implosion problem illustrate the application of these methods to multi-material problems.
A New Approach to Parallel Dynamic Partitioning for Adaptive Unstructured Meshes
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.
1999-01-01
Classical mesh partitioning algorithms were designed for rather static situations, and their straightforward application in a dynamical framework may lead to unsatisfactory results, e.g., excessive data migration among processors. Furthermore, special attention should be paid to their amenability to parallelization. In this paper, a novel parallel method for the dynamic partitioning of adaptive unstructured meshes is described. It is based on a linear representation of the mesh using self-avoiding walks.
MAPVAR - A Computer Program to Transfer Solution Data Between Finite Element Meshes
Wellman, G.W.
1999-03-01
MAPVAR, as was the case with its precursor programs, MERLIN and MERLIN II, is designed to transfer solution results from one finite element mesh to another. MAPVAR draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR are described. User instructions are presented. Example problems are included to demonstrate the operation of the code and the effects of various input options.
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 adaptation on unstructured grids is a powerful tool for efficiently computing unsteady problems to resolve solution features of interest. Unfortunately, this causes load inbalances among processors on a parallel machine. This paper described 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 coast 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 percent of the mesh is randomly adapted. For large scale scientific computations, our load balancing strategy gives an almost sixfold reduction in solver execution times over non-balanced loads. Furthermore, our heuristic remappier yields processor assignments that are less than 3 percent of the optimal solutions, but requires only 1 percent of the computational time.
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 new spectral finite volume method for elastic wave modelling on unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.
2016-04-01
In this paper, we consider a new spectral finite volume method for the elastic wave equations. Our new finite volume method is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order finite volume method and the spectral finite volume method. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles, and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an over-determined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2D problems, but the same methodology can be applied to 3D.
Mimetic finite difference method for the stokes problem on polygonal meshes
Lipnikov, K; Beirao Da Veiga, L; Gyrya, V; Manzini, G
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
Yaqi Wang; Jean C. Ragusa
2011-10-01
Diffusion synthetic acceleration (DSA) schemes compatible with adaptive mesh refinement (AMR) grids are derived for the SN transport equations discretized using high-order discontinuous finite elements. These schemes are directly obtained from the discretized transport equations by assuming a linear dependence in angle of the angular flux along with an exact Fick's law and, therefore, are categorized as partially consistent. These schemes are akin to the symmetric interior penalty technique applied to elliptic problems and are all based on a second-order discontinuous finite element discretization of a diffusion equation (as opposed to a mixed or P1 formulation). Therefore, they only have the scalar flux as unknowns. A Fourier analysis has been carried out to determine the convergence properties of the three proposed DSA schemes for various cell optical thicknesses and aspect ratios. Out of the three DSA schemes derived, the modified interior penalty (MIP) scheme is stable and effective for realistic problems, even with distorted elements, but loses effectiveness for some highly heterogeneous configurations. The MIP scheme is also symmetric positive definite and can be solved efficiently with a preconditioned conjugate gradient method. Its implementation in an AMR SN transport code has been performed for both source iteration and GMRes-based transport solves, with polynomial orders up to 4. Numerical results are provided and show good agreement with the Fourier analysis results. Results on AMR grids demonstrate that the cost of DSA can be kept low on locally refined meshes.
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.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
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.
The PLUTO Code for Adaptive Mesh Computations in Astrophysical Fluid Dynamics
NASA Astrophysics Data System (ADS)
Mignone, A.; Zanni, C.; Tzeferacos, P.; van Straalen, B.; Colella, P.; Bodo, G.
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.
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.
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.
Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow
NASA Astrophysics Data System (ADS)
Wood, William Alfred, III
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. The scalar test cases include advected shear, circular advection, non-linear advection with coalescing shock and expansion fans, and advection-diffusion. For all scalar cases the fluctuation splitting scheme is more accurate, and the primary mechanism for the improved fluctuation splitting performance is shown to be the reduced production of artificial dissipation relative to DMFDSFV. The most significant scalar result is for combined advection-diffusion, where the present fluctuation splitting scheme is able to resolve the physical dissipation from the artificial dissipation on a much coarser mesh than DMFDSFV is able to, allowing order-of-magnitude reductions in solution time. Among the inviscid test cases the converging supersonic streams problem is notable in that the fluctuation splitting scheme exhibits superconvergent third-order spatial accuracy. For the inviscid cases of a supersonic diamond airfoil, supersonic slender cone, and incompressible circular bump the fluctuation splitting drag coefficient errors are typically half the DMFDSFV drag errors. However, for the incompressible inviscid sphere the fluctuation splitting drag error is larger than for DMFDSFV. A Blasius flat plate viscous validation case reveals a more accurate v-velocity profile for fluctuation splitting, and the reduced artificial dissipation
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.
New methods and astrophysical applications of adaptive mesh fluid simulations
NASA Astrophysics Data System (ADS)
Wang, Peng
The formation of stars, galaxies and supermassive black holes are among the most interesting unsolved problems in astrophysics. Those problems are highly nonlinear and involve enormous dynamical ranges. Thus numerical simulations with spatial adaptivity are crucial in understanding those processes. In this thesis, we discuss the development and application of adaptive mesh refinement (AMR) multi-physics fluid codes to simulate those nonlinear structure formation problems. To simulate the formation of star clusters, we have developed an AMR magnetohydrodynamics (MHD) code, coupled with radiative cooling. We have also developed novel algorithms for sink particle creation, accretion, merging and outflows, all of which are coupled with the fluid algorithms using operator splitting. With this code, we have been able to perform the first AMR-MHD simulation of star cluster formation for several dynamical times, including sink particle and protostellar outflow feedbacks. The results demonstrated that protostellar outflows can drive supersonic turbulence in dense clumps and explain the observed slow and inefficient star formation. We also suggest that global collapse rate is the most important factor in controlling massive star accretion rate. In the topics of galaxy formation, we discuss the results of three projects. In the first project, using cosmological AMR hydrodynamics simulations, we found that isolated massive star still forms in cosmic string wakes even though the mega-parsec scale structure has been perturbed significantly by the cosmic strings. In the second project, we calculated the dynamical heating rate in galaxy formation. We found that by balancing our heating rate with the atomic cooling rate, it gives a critical halo mass which agrees with the result of numerical simulations. This demonstrates that the effect of dynamical heating should be put into semi-analytical works in the future. In the third project, using our AMR-MHD code coupled with radiative
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
A Parallel Ocean Model With Adaptive Mesh Refinement Capability For Global Ocean Prediction
Herrnstein, A
2005-09-08
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{sub 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
Knupp, P.M.
1999-01-18
Structured mesh quality optimization methods are extended to optimization of unstructured triangular, quadrilateral, and mixed finite element meshes. N"ew interpretations of well-known nodally-bssed objective functions are made possible using matrices and matrix norms. The matrix perspective also suggests several new objective functions. Particularly significant is the interpretation of the Oddy metric and the Smoothness objective functions in terms of the condition number of the metric tensor and Jacobian matrix, respectively. Objective functions are grouped according to dimensionality to form weighted combinations. A simple unconstrained local optimum is computed using a modiiied N-ewton iteration. The optimization approach was implemented in the CUBIT mesh generation code and tested on several problems. Results were compared against several standard element-based quaIity measures to demonstrate that good mesh quality can be achieved with nodally-based objective functions.
NASA Astrophysics Data System (ADS)
Davies, D. R.; Davies, J. H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2007-05-01
An adaptive finite element procedure is presented for improving the quality of solutions to convection-dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation-based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well-established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid-based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.
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
Zonal multigrid solution of compressible flow problems on unstructured and adaptive meshes
NASA Technical Reports Server (NTRS)
Mavriplis, Dimitri J.
1989-01-01
The simultaneous use of adaptive meshing techniques with a multigrid strategy for solving the 2-D Euler equations in the context of unstructured meshes is studied. To obtain optimal efficiency, methods capable of computing locally improved solutions without recourse to global recalculations are pursued. A method for locally refining an existing unstructured mesh, without regenerating a new global mesh is employed, and the domain is automatically partitioned into refined and unrefined regions. Two multigrid strategies are developed. In the first, time-stepping is performed on a global fine mesh covering the entire domain, and convergence acceleration is achieved through the use of zonal coarse grid accelerator meshes, which lie under the adaptively refined regions of the global fine mesh. Both schemes are shown to produce similar convergence rates to each other, and also with respect to a previously developed global multigrid algorithm, which performs time-stepping throughout the entire domain, on each mesh level. However, the present schemes exhibit higher computational efficiency due to the smaller number of operations on each level.
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.
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.
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.
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.
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.
CRASH: A Block-adaptive-mesh Code for Radiative Shock Hydrodynamics—Implementation and Verification
NASA Astrophysics Data System (ADS)
van der Holst, B.; Tóth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Karni, S.; Fryxell, B.; Drake, R. P.
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.
CRASH: A Block-Adaptive-Mesh Code for Radiative Shock Hydrodynamics
NASA Astrophysics Data System (ADS)
van der Holst, B.; Toth, G.; Sokolov, I. V.; Powell, K. G.; Holloway, J. P.; Myra, E. S.; Stout, Q.; Adams, M. L.; Morel, J. E.; Drake, R. P.
2011-01-01
We describe the CRASH (Center for Radiative Shock Hydrodynamics) code, a block adaptive mesh code for multi-material radiation hydrodynamics. The implementation solves the radiation diffusion model with the gray or multigroup method and uses a flux limited diffusion approximation to recover the free-streaming limit. The electrons and ions are allowed to have different temperatures and we include a 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) solve the hydrodynamic equations with shock-capturing schemes, (2) a linear advection of the radiation in frequency-logarithm space, and (3) an implicit solve 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 CRASH code is an extension of the Block-Adaptive Tree Solarwind Roe Upwind Scheme (BATS-R-US) code with this new radiation transfer and heat conduction library and equation-of-state and multigroup opacity solvers. Both CRASH and BATS-R-US are part of the publicly available Space Weather Modeling Framework (SWMF).
Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations
NASA Astrophysics Data System (ADS)
Ahmed, Mohd.; Singh, Devinder
2016-05-01
In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.
Stress Recovery Based h-Adaptive Finite Element Simulation of Sheet Forming Operations
NASA Astrophysics Data System (ADS)
Ahmed, Mohd.; Singh, Devinder
2016-07-01
In the present work, stress recovery techniques based adaptive finite element analysis of sheet forming operations is presented. An adaptive two dimensional finite element computer code allows the analysis of sheet forming operations and results in distribution of adaptively refined mesh, effective strain, and punch load, stress and strain rate tensor in the domain that has been developed. The recovery scheme for determining more accurate stress field is based on the least squares fitting of the computed stresses in an element patch surrounding and including a particular node. The solution error is estimated on the basis of an energy norm. It is shown with the help of an illustrative example of axi-symmetric stretching of a metal blank by a hemispherical punch that the adaptive analysis may be usefully employed to predict accurately deformation process, the seats of large deformations and locations of possible instability.
A staggered mesh finite difference scheme for the computation of hypersonic Euler flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1991-01-01
A shock capturing finite difference method for systems of hyperbolic conservation laws is presented which avoids the need to solve Riemann problems while being competitive in performance with other current methods. A staggered spatial mesh is employed, so that complicated nonlinear waves generated at cell interfaces are averaged over cell interiors at the next time level. The full method combines to form a conservative version of the modified method of characteristics. The advantages of the method are discussed, and numerical results are presented for the two-dimensional double ellipse problem.
Ismagilov, Timur Z.
2015-02-01
This paper presents a second order finite volume scheme for numerical solution of Maxwell's equations with discontinuous dielectric permittivity and magnetic permeability on unstructured meshes. The scheme is based on Godunov scheme and employs approaches of Van Leer and Lax–Wendroff to increase the order of approximation. To keep the second order of approximation near dielectric permittivity and magnetic permeability discontinuities a novel technique for gradient calculation and limitation is applied near discontinuities. Results of test computations for problems with linear and curvilinear discontinuities confirm second order of approximation. The scheme was applied to modelling propagation of electromagnetic waves inside photonic crystal waveguides with a bend.
NASA Astrophysics Data System (ADS)
Northrup, Scott A.
A new parallel implicit adaptive mesh refinement (AMR) algorithm is developed for the prediction of unsteady behaviour of laminar flames. The scheme is applied to the solution of the system of partial-differential equations governing time-dependent, two- and three-dimensional, compressible laminar flows for reactive thermally perfect gaseous mixtures. A high-resolution finite-volume spatial discretization procedure is used to solve the conservation form of these equations on body-fitted multi-block hexahedral meshes. A local preconditioning technique is used to remove numerical stiffness and maintain solution accuracy for low-Mach-number, nearly incompressible flows. A flexible block-based octree data structure has been developed and is used to facilitate automatic solution-directed mesh adaptation according to physics-based refinement criteria. The data structure also enables an efficient and scalable parallel implementation via domain decomposition. The parallel implicit formulation makes use of a dual-time-stepping like approach with an implicit second-order backward discretization of the physical time, in which a Jacobian-free inexact Newton method with a preconditioned generalized minimal residual (GMRES) algorithm is used to solve the system of nonlinear algebraic equations arising from the temporal and spatial discretization procedures. An additive Schwarz global preconditioner is used in conjunction with block incomplete LU type local preconditioners for each sub-domain. The Schwarz preconditioning and block-based data structure readily allow efficient and scalable parallel implementations of the implicit AMR approach on distributed-memory multi-processor architectures. The scheme was applied to solutions of steady and unsteady laminar diffusion and premixed methane-air combustion and was found to accurately predict key flame characteristics. For a premixed flame under terrestrial gravity, the scheme accurately predicted the frequency of the natural
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.
ZONE - a finite element mesh generator. [2-D, for CDC 7600
Burger, M.J.
1980-03-12
The ZONE computer program is a finite element mesh generator that produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated for slide lines and to describe pressure boundary conditions. The mesh that is generated can be used as input to any two dimensional as well as any axisymmetrical structure program. The following points are taken up: program concept and characteristics; regions; layers; meridians (offset, circular arc, ellipse); rays; common characterstics - rays and meridians, ZONE input description; output files; examples; and program availability. Also generated is the input to the program PLOT. 15 figures. (RWR)
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
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
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility. PMID:16383571
A new spectral finite volume method for elastic wave modelling on unstructured meshes
NASA Astrophysics Data System (ADS)
Zhang, Wensheng; Zhuang, Yuan; Chung, Eric T.
2016-07-01
In this paper, we consider a new spectral finite volume method (FVM) for the elastic wave equations. Our new FVM is based on a piecewise constant approximation on a fine mesh and a high-order polynomial reconstruction on a coarser mesh. Our new method is constructed based on two existing techniques, the high-order FVM and the spectral FVM. In fact, we will construct a new method to take advantage of both methods. More precisely, our method has two distinctive features. The first one is that the local polynomial reconstructions are performed on the coarse triangles and the reconstruction matrices for all the coarse triangles are the same. This fact enhances the parallelization of our algorithm. We will present a parallel implementation of our method and show excellent efficiency results. The second one is that, by using a suitable number of finer triangles with a coarse triangle, we obtain an overdetermined reconstruction system, which can enhance the robustness of the reconstruction process. To derive our scheme, standard finite volume technique is applied to each fine triangle, and the high-order reconstructed polynomials, computed on coarse triangles, are used to compute numerical fluxes. We will present numerical results to show the performance of our method. Our method is presented for 2-D problems, but the same methodology can be applied to 3-D.
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
Conditional entropy maximization for PET image reconstruction using adaptive mesh model.
Zhu, Hongqing; Shu, Huazhong; Zhou, Jian; Dai, Xiubin; Luo, Limin
2007-04-01
Iterative image reconstruction algorithms have been widely used in the field of positron emission tomography (PET). However, such algorithms are sensitive to noise artifacts so that the reconstruction begins to degrade when the number of iterations is high. In this paper, we propose a new algorithm to reconstruct an image from the PET emission projection data by using the conditional entropy maximization and the adaptive mesh model. In a traditional tomography reconstruction method, the reconstructed image is directly computed in the pixel domain. Unlike this kind of methods, the proposed approach is performed by estimating the nodal values from the observed projection data in a mesh domain. In our method, the initial Delaunay triangulation mesh is generated from a set of randomly selected pixel points, and it is then modified according to the pixel intensity value of the estimated image at each iteration step in which the conditional entropy maximization is used. The advantage of using the adaptive mesh model for image reconstruction is that it provides a natural spatially adaptive smoothness mechanism. In experiments using the synthetic and clinical data, it is found that the proposed algorithm is more robust to noise compared to the common pixel-based MLEM algorithm and mesh-based MLEM with a fixed mesh structure. PMID:17368841
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.
Tsunami modelling with adaptively refined finite volume methods
LeVeque, R.J.; George, D.L.; Berger, M.J.
2011-01-01
Numerical modelling of transoceanic tsunami propagation, together with the detailed modelling of inundation of small-scale coastal regions, poses a number of algorithmic challenges. The depth-averaged shallow water equations can be used to reduce this to a time-dependent problem in two space dimensions, but even so it is crucial to use adaptive mesh refinement in order to efficiently handle the vast differences in spatial scales. This must be done in a 'wellbalanced' manner that accurately captures very small perturbations to the steady state of the ocean at rest. Inundation can be modelled by allowing cells to dynamically change from dry to wet, but this must also be done carefully near refinement boundaries. We discuss these issues in the context of Riemann-solver-based finite volume methods for tsunami modelling. Several examples are presented using the GeoClaw software, and sample codes are available to accompany the paper. The techniques discussed also apply to a variety of other geophysical flows. ?? 2011 Cambridge University Press.
Solution-adaptive finite element method in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1993-01-01
Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.
McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; Colella, Phillip
2015-09-04
We present a high-order finite-volume approach for solving the shallow-water equations on the sphere, using multiblock grids on the cubed-sphere. This approach combines a Runge--Kutta time discretization with a fourth-order accurate spatial discretization, and includes adaptive mesh refinement and refinement in time. Results of tests show fourth-order convergence for the shallow-water equations as well as for advection in a highly deformational flow. Hierarchical adaptive mesh refinement allows solution error to be achieved that is comparable to that obtained with uniform resolution of the most refined level of the hierarchy, but with many fewer operations.
NASA Astrophysics Data System (ADS)
Grayver, Alexander V.
2015-07-01
This paper presents a distributed magnetotelluric inversion scheme based on adaptive finite-element method (FEM). The key novel aspect of the introduced algorithm is the use of automatic mesh refinement techniques for both forward and inverse modelling. These techniques alleviate tedious and subjective procedure of choosing a suitable model parametrization. To avoid overparametrization, meshes for forward and inverse problems were decoupled. For calculation of accurate electromagnetic (EM) responses, automatic mesh refinement algorithm based on a goal-oriented error estimator has been adopted. For further efficiency gain, EM fields for each frequency were calculated using independent meshes in order to account for substantially different spatial behaviour of the fields over a wide range of frequencies. An automatic approach for efficient initial mesh design in inverse problems based on linearized model resolution matrix was developed. To make this algorithm suitable for large-scale problems, it was proposed to use a low-rank approximation of the linearized model resolution matrix. In order to fill a gap between initial and true model complexities and resolve emerging 3-D structures better, an algorithm for adaptive inverse mesh refinement was derived. Within this algorithm, spatial variations of the imaged parameter are calculated and mesh is refined in the neighborhoods of points with the largest variations. A series of numerical tests were performed to demonstrate the utility of the presented algorithms. Adaptive mesh refinement based on the model resolution estimates provides an efficient tool to derive initial meshes which account for arbitrary survey layouts, data types, frequency content and measurement uncertainties. Furthermore, the algorithm is capable to deliver meshes suitable to resolve features on multiple scales while keeping number of unknowns low. However, such meshes exhibit dependency on an initial model guess. Additionally, it is demonstrated
NASA Astrophysics Data System (ADS)
Wilson, C. R.; Kramer, S. C.; Collins, G. S.
2010-12-01
Linear wave models cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Models based on the nonlinear Navier-Stokes equations can simulate complex landslide-water interactions at realistic scales; however, the computing power required for such a simulation can be prohibitively high for large domains with realistic bathymetries. The variable resolution available with the use of unstructured adaptive meshes allows larger domains to be modeled at the same resolution for a lower computational cost than on structured meshes; they are also better at representing complex geometries and bathymetries. However, unstructured meshes introduce extra numerical challenges requiring the use of novel interface preservation techniques coupled with velocity-pressure discretisations that ensure the conservation and boundedness of all materials in the simulation. In this study we describe some of the challenges encountered extending the finite element, finite volume multiple-material fluid dynamics model Fluidity to large-scale landslide-generated tsunami simulations. In particular, we focus on the ability of the model to preserve the balance between the buoyancy and pressure gradient forces. Failure to discretely satisfy this relationship is shown to result in spurious waves that contaminate any physical tsunami signal. However, ensuring that balance is preserved in a computationally efficient manner imposes extra constraints on the dynamic mesh optimisation process. Incorporating these restrictions allows us to validate our model against multi-scale experimental simulations of landslide generated tsunami (see figure). Experimental (top, taken from Di Risio et. al. 2009, doi:10.1029/2008JC004858) and equivalent numerical simulation (bottom) of a subaerial landslide impacting into water. In the experiment the 80cm long landslide produces waves of amplitude 1-2cm around a 9m diameter island in a 50x
Operator splitting and adaptive mesh refinement for the Luo-Rudy I model
NASA Astrophysics Data System (ADS)
Trangenstein, John A.; Kim, Chisup
2004-05-01
We apply second-order operator splitting to the Luo-Rudy I model for electrical wave propagation in the heart. The purpose of the operator splitting is to separate the nonlinear but local reaction computations from the linear but globally coupled diffusion computations. This approach allows us to use local nonlinear iterations for the stiff nonlinear reactions and to solve global linear systems for the implicit treatment of diffusion. For computational efficiency, we use dynamically adaptive mesh refinement (AMR), involving hierarchies of unions of grid patches on distinct levels of refinement. The linear system for the discretization of the diffusion on the composite AMR grid is formulated via standard conforming finite elements on unions grid patches within a level of refinement and aligned mortar elements along interfaces between levels of refinement. The linear systems are solved iteratively by preconditioned conjugate gradients. Our preconditioner uses multiplicative domain decomposition between levels of refinement; the smoother involves algebraic additive domain decomposition between patches within a level of refinement, and Gauss-Seidel iteration within grid patches. Numerical results are presented in 1D and 2D, including spiral waves.
NASA Astrophysics Data System (ADS)
Teyssier, Romain; Fromang, Sébastien; Dormy, Emmanuel
2006-10-01
We propose to extend the well-known MUSCL-Hancock scheme for Euler equations to the induction equation modeling the magnetic field evolution in kinematic dynamo problems. The scheme is based on an integral form of the underlying conservation law which, in our formulation, results in a “finite-surface” scheme for the induction equation. This naturally leads to the well-known “constrained transport” method, with additional continuity requirement on the magnetic field representation. The second ingredient in the MUSCL scheme is the predictor step that ensures second order accuracy both in space and time. We explore specific constraints that the mathematical properties of the induction equations place on this predictor step, showing that three possible variants can be considered. We show that the most aggressive formulations (referred to as C-MUSCL and U-MUSCL) reach the same level of accuracy as the other one (referred to as Runge Kutta), at a lower computational cost. More interestingly, these two schemes are compatible with the adaptive mesh refinement (AMR) framework. It has been implemented in the AMR code RAMSES. It offers a novel and efficient implementation of a second order scheme for the induction equation. We have tested it by solving two kinematic dynamo problems in the low diffusion limit. The construction of this scheme for the induction equation constitutes a step towards solving the full MHD set of equations using an extension of our current methodology.
Lee, D. W.; Joo, H. G.
2013-07-01
The methods and performance of a three-dimensional S{sub n} transport code employing the Discontinuous Finite Element Method (DFEM) and the Coarse Mesh Finite Difference (CMFD) formulation are presented. The mesh generator GMSH and a post processing visualization tool Visit are combined with the code for flexible geometry processing and versatile visualization. The CMFD method for DFEM Sn applications is formulated and the performance of the CMFD acceleration of eigenvalue calculations is demonstrated for a simple set of neutron transport problems. (authors)
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.
NASA Astrophysics Data System (ADS)
Tang, Qiuyan; Wang, Jing; Lv, Pin; Sun, Quan
2015-10-01
Propagation simulation method and choosing mesh grid are both very important to get the correct propagation results in wave optics simulation. A new angular spectrum propagation method with alterable mesh grid based on the traditional angular spectrum method and the direct FFT method is introduced. With this method, the sampling space after propagation is not limited to propagation methods no more, but freely alterable. However, choosing mesh grid on target board influences the validity of simulation results directly. So an adaptive mesh choosing method based on wave characteristics is proposed with the introduced propagation method. We can calculate appropriate mesh grids on target board to get satisfying results. And for complex initial wave field or propagation through inhomogeneous media, we can also calculate and set the mesh grid rationally according to above method. Finally, though comparing with theoretical results, it's shown that the simulation result with the proposed method coinciding with theory. And by comparing with the traditional angular spectrum method and the direct FFT method, it's known that the proposed method is able to adapt to a wider range of Fresnel number conditions. That is to say, the method can simulate propagation results efficiently and correctly with propagation distance of almost zero to infinity. So it can provide better support for more wave propagation applications such as atmospheric optics, laser propagation and so on.
Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration
NASA Astrophysics Data System (ADS)
Zhang, Y.; Key, K.; Ovall, J.; Holst, M.
2014-12-01
We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented
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.
NASA Astrophysics Data System (ADS)
Burman, E.; Jacot, A.; Picasso, M.
2004-03-01
A multiphase-field model for the description of coalescence in a binary alloy is solved numerically using adaptive finite elements with high aspect ratio. The unknown of the multiphase-field model are the three phase fields (solid phase 1, solid phase 2, and liquid phase), a Lagrange multiplier and the concentration field. An Euler implicit scheme is used for time discretization, together with continuous, piecewise linear finite elements. At each time step, a linear system corresponding to the three phases plus the Lagrange multiplier has to be solved. Then, the linear system pertaining to concentration is solved. An adaptive finite element algorithm is proposed. In order to reduce the number of mesh vertices, the generated meshes contain elements with high aspect ratio. The refinement and coarsening criteria are based on an error indicator which has already been justified theoretically for simpler problems. Numerical results on two test cases show the efficiency of the method.
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.
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.
A knowledge-based approach to the adaptive finite element analysis
Haghighi, K.; Kang, E.
1995-12-31
An automatic and knowledge-based finite element mesh generator (INTELMESH), which makes extensive use of interactive computer graphics techniques, has been developed. INTELMESH is designed for planar domains and axisymmetric 3-D structures of elasticity and heat transfer subjected to mechanical and thermal loading. It intelligently identifies the critical regions/points in the problem domain and utilizes the new concepts of substructuring and wave propagation to choose the proper mesh size for them. INTELMESH generates well-shaped triangular elements by applying triangulation and Laplacian smoothing procedures. The adaptive analysis involves the initial finite element analysis and an efficient a-posteriori error analysis and estimation. Once a problem is defined, the system automatically builds a finite element model and analyzes the problem through an automatic iterative process until the error reaches a desired level. It has been shown that the proposed approach which initiates the process with an a-priori, and near optimum mesh of the object, converges to the desired accuracy in less time and at less cost.
Multiphase flow through porous media: an adaptive control volume finite element formulation
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.
2012-12-01
Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.
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.
2011-01-01
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. PMID:21646711
Kothe, D.B.; Turner, J.A.; Mosso, S.J.; Ferrell, R.C.
1997-03-01
We discuss selected aspects of a new parallel three-dimensional (3-D) computational tool for the unstructured mesh simulation of Los Alamos National Laboratory (LANL) casting processes. This tool, known as {bold Telluride}, draws upon on robust, high resolution finite volume solutions of metal alloy mass, momentum, and enthalpy conservation equations to model the filling, cooling, and solidification of LANL castings. We briefly describe the current {bold Telluride} physical models and solution methods, then detail our parallelization strategy as implemented with Fortran 90 (F90). This strategy has yielded straightforward and efficient parallelization on distributed and shared memory architectures, aided in large part by new parallel libraries {bold JTpack9O} for Krylov-subspace iterative solution methods and {bold PGSLib} for efficient gather/scatter operations. We illustrate our methodology and current capabilities with source code examples and parallel efficiency results for a LANL casting simulation.
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.
Modeling, mesh generation, and adaptive numerical methods for partial differential equations
Babuska, I.; Henshaw, W.D.; Oliger, J.E.; Flaherty, J.E.; Hopcroft, J.E.; Tezduyar, T.
1995-12-31
Mesh generation is one of the most time consuming aspects of computational solutions of problems involving partial differential equations. It is, furthermore, no longer acceptable to compute solutions without proper verification that specified accuracy criteria are being satisfied. Mesh generation must be related to the solution through computable estimates of discretization errors. Thus, an iterative process of alternate mesh and solution generation evolves in an adaptive manner with the end result that the solution is computed to prescribed specifications in an optimal, or at least efficient, manner. While mesh generation and adaptive strategies are becoming available, major computational challenges remain. One, in particular, involves moving boundaries and interfaces, such as free-surface flows and fluid-structure interactions. A 3-week program was held from July 5 to July 23, 1993 with 173 participants and 66 keynote, invited, and contributed presentations. This volume represents written versions of 21 of these lectures. These proceedings are organized roughly in order of their presentation at the workshop. Thus, the initial papers are concerned with geometry and mesh generation and discuss the representation of physical objects and surfaces on a computer and techniques to use this data to generate, principally, unstructured meshes of tetrahedral or hexahedral elements. The remainder of the papers cover adaptive strategies, error estimation, and applications. Several submissions deal with high-order p- and hp-refinement methods where mesh refinement/coarsening (h-refinement) is combined with local variation of method order (p-refinement). Combinations of mathematically verified and physically motivated approaches to error estimation are represented. Applications center on fluid mechanics. Selected papers are indexed separately for inclusion in the Energy Science and Technology Database.
Implementation of a mesh adaptive scheme based on an element-level error indicator
NASA Technical Reports Server (NTRS)
Keating, Scott; Felippa, Carlos A.; Militello, Carmelo
1993-01-01
We investigate the formulation and application of element-level error indicators based on parametrized variational principles. The qualifier 'element-level' means that no information from adjacent elements is used for error estimation. This property is ideally suited to drive adaptive mesh refinement on parallel computers where access to neighboring elements resident on different processors may incur significant computational overhead. Furthermore, such indicators are not affected by physical jumps at junctures or interfaces. An element-level indicator has been derived from the higher-order element energy and applied to r and h mesh adaptation of meshes in plates and shell structures. We report on our initial experiments with a cylindrical shell that intersects with fist plates forming a simplified 'wing-body intersection' benchmark problem.
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. 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.
NASA Astrophysics Data System (ADS)
Dimitrov, Yuri M.; Vulkov, Lubin G.
2015-11-01
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are discussed.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Zhang, Qian-Jiang; Dai, Shi-Kun; Chen, Long-Wei; Qiang, Jian-Ke; Li, Kun; Zhao, Dong-Dong
2016-06-01
To deal with the problem of low computational precision at the nodes near the source and satisfy the requirements for computational efficiency in inversion imaging and finite-element numerical simulations of the direct current method, we propose a new mesh refinement and recoarsement method for a two-dimensional point source. We introduce the mesh refinement and mesh recoarsement into the traditional structured mesh subdivision. By refining the horizontal grids, the singularity owing to the point source is minimized and the topography is simulated. By recoarsening the horizontal grids, the number of grid cells is reduced significantly and computational efficiency is improved. Model tests show that the proposed method solves the singularity problem and reduces the number of grid cells by 80% compared to the uniform grid refinement.
NASA Astrophysics Data System (ADS)
Ghattas, O.; Burstedde, C.; Stadler, G.; Wilcox, L. C.; Tu, T.; Issac, T.; Gurnis, M.; Alisic, L.; Tan, E.; Zhong, S.
2009-12-01
Many problems in solid earth geophysics are characterized by dynamics occurring on a wide range of length and time scales, placing the solution of the governing partial differential equations (PDEs) for such problems among the grand challenges of computational geophysics. One approach to overcoming the tyranny of scales is adaptive mesh refinement (AMR), which locally and dynamically adapts the mesh to resolve spatio-temporal scales and features of interest. For example, we are interested in modeling global mantle convection with nonlinear rheology and kilometer-scale resolution at faulted plate boundaries. Another problem of interest is modeling the dynamics of polar ice sheets with fine resolution in the vicinity of stick-slip transitions. Geophysical inverse problems characterized by a wide range of medium properties can also benefit from AMR as the earth model is updated. While AMR promises to help overcome the challenges inherent in modeling multiscale problems, the benefits are difficult to achieve in practice, particularly on petascale computers that are essential for frontier problems. Due to the complex dynamic data structures and communication patterns, and frequent data exchange and redistribution, scaling dynamic AMR to tens of thousands of processors has long been considered a challenge. Another difficulty is extending parallel AMR techniques to high-order-accurate, complex-geometry-conforming finite element methods that are favored for many classes of solid earth geophysical problems. Here, we present the ALPS (Adaptive Large-scale Parallel Simulations) framework for parallel adaptive solution of PDEs. ALPS includes the octor and p4est libraries for parallel dynamic mesh adaptivity on single-octree-based and forest-of-octree-based geometries, respectively, and the mangll library for arbitrary-order hexahedral continuous and discontinuous finite/spectral element discretizations on general multi-octree geometries. ALPS has been shown to scale well
The geometry of r-adaptive meshes generated using optimal transport methods
NASA Astrophysics Data System (ADS)
Budd, C. J.; Russell, R. D.; Walsh, E.
2015-02-01
The principles of mesh equidistribution and alignment play a fundamental role in the design of adaptive methods, and a metric tensor and mesh metric are useful theoretical tools for understanding a method's level of mesh alignment, or anisotropy. We consider a mesh redistribution method based on the Monge-Ampère equation which combines equidistribution of a given scalar density function with optimal transport. It does not involve explicit use of a metric tensor, although such a tensor must exist for the method, and an interesting question to ask is whether or not the alignment produced by the metric gives an anisotropic mesh. For model problems with a linear feature and with a radially symmetric feature, we derive the exact form of the metric, which involves expressions for its eigenvalues and eigenvectors. The eigenvectors are shown to be orthogonal and tangential to the feature, and the ratio of the eigenvalues (corresponding to the level of anisotropy) is shown to depend, both locally and globally, on the value of the density function and the amount of curvature. We thereby demonstrate how the optimal transport method produces an anisotropic mesh along a given feature while equidistributing a suitably chosen scalar density function. Numerical results are given to verify these results and to demonstrate how the analysis is useful for problems involving more complex features, including for a non-trivial time dependant nonlinear PDE which evolves narrow and curved reaction fronts.
NASA Astrophysics Data System (ADS)
De Corato, M.; Slot, J. J. M.; Hütter, M.; D'Avino, G.; Maffettone, P. L.; Hulsen, M. A.
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation-dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Time-dependent grid adaptation for meshes of triangles and tetrahedra
NASA Technical Reports Server (NTRS)
Rausch, Russ D.
1993-01-01
This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.
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.
Adaptive finite volume methods for time-dependent P.D.E.S.
Ware, J.; Berzins, M.
1995-12-31
The aim of adaptive methods for time-dependent p.d.e.s is to control the numerical error so that it is less than a user-specified tolerance. This error depends on the spatial discretization method, the spatial mesh, the method of time integration and the timestep. The spatial discretization method and positioning of the spatial mesh points should attempt to ensure that the spatial error is controlled to meet the user`s requirements. It is then desirable to integrate the o.d.e. system in time with sufficient accuracy so that the temporal error does not corrupt the spatial accuracy or the reliability of the spatial error estimates. This paper is concerned with the development of a prototype algorithm of this type, based on a cell-centered triangular finite volume scheme, for two space dimensional convection-dominated problems.
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.
Spatially adaptive bases in wavelet-based coding of semi-regular meshes
NASA Astrophysics Data System (ADS)
Denis, Leon; Florea, Ruxandra; Munteanu, Adrian; Schelkens, Peter
2010-05-01
In this paper we present a wavelet-based coding approach for semi-regular meshes, which spatially adapts the employed wavelet basis in the wavelet transformation of the mesh. The spatially-adaptive nature of the transform requires additional information to be stored in the bit-stream in order to allow the reconstruction of the transformed mesh at the decoder side. In order to limit this overhead, the mesh is first segmented into regions of approximately equal size. For each spatial region, a predictor is selected in a rate-distortion optimal manner by using a Lagrangian rate-distortion optimization technique. When compared against the classical wavelet transform employing the butterfly subdivision filter, experiments reveal that the proposed spatially-adaptive wavelet transform significantly decreases the energy of the wavelet coefficients for all subbands. Preliminary results show also that employing the proposed transform for the lowest-resolution subband systematically yields improved compression performance at low-to-medium bit-rates. For the Venus and Rabbit test models the compression improvements add up to 1.47 dB and 0.95 dB, respectively.
Fast animation of lightning using an adaptive mesh.
Kim, Theodore; Lin, Ming C
2007-01-01
We present a fast method for simulating, animating, and rendering lightning using adaptive grids. The "dielectric breakdown model" is an elegant algorithm for electrical pattern formation that we extend to enable animation of lightning. The simulation can be slow, particularly in 3D, because it involves solving a large Poisson problem. Losasso et al. recently proposed an octree data structure for simulating water and smoke, and we show that this discretization can be applied to the problem of lightning simulation as well. However, implementing the incomplete Cholesky conjugate gradient (ICCG) solver for this problem can be daunting, so we provide an extensive discussion of implementation issues. ICCG solvers can usually be accelerated using "Eisenstat's trick," but the trick cannot be directly applied to the adaptive case. Fortunately, we show that an "almost incomplete Cholesky" factorization can be computed so that Eisenstat's trick can still be used. We then present a fast rendering method based on convolution that is competitive with Monte Carlo ray tracing but orders of magnitude faster, and we also show how to further improve the visual results using jittering. PMID:17218754
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.
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.
Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations
NASA Technical Reports Server (NTRS)
Rausch, Russ D.; Batina, John T.; Yang, Henry T. Y.
1993-01-01
Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. A detailed description of the enrichment and coarsening procedures are presented and comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply.
NASA Astrophysics Data System (ADS)
Ravindran, Prashaanth
The unstable nature of detonation waves is a result of the critical relationship between the hydrodynamic shock and the chemical reactions sustaining the shock. A perturbative analysis of the critical point is quite challenging due to the multiple spatio-temporal scales involved along with the non-linear nature of the shock-reaction mechanism. The author's research attempts to provide detailed resolution of the instabilities at the shock front. Another key aspect of the present research is to develop an understanding of the causality between the non-linear dynamics of the front and the eventual breakdown of the sub-structures. An accurate numerical simulation of detonation waves requires a very efficient solution of the Euler equations in conservation form with detailed, non-equilibrium chemistry. The difference in the flow and reaction length scales results in very stiff source terms, requiring the problem to be solved with adaptive mesh refinement. For this purpose, Berger-Colella's block-structured adaptive mesh refinement (AMR) strategy has been developed and applied to time-explicit finite volume methods. The block-structured technique uses a hierarchy of parent-child sub-grids, integrated recursively over time. One novel approach to partition the problem within a large supercomputer was the use of modified Peano-Hilbert space filling curves. The AMR framework was merged with CLAWPACK, a package providing finite volume numerical methods tailored for wave-propagation problems. The stiffness problem is bypassed by using a 1st order Godunov or a 2nd order Strang splitting technique, where the flow variables and source terms are integrated independently. A linearly explicit fourth-order Runge-Kutta integrator is used for the flow, and an ODE solver was used to overcome the numerical stiffness. Second-order spatial resolution is obtained by using a second-order Roe-HLL scheme with the inclusion of numerical viscosity to stabilize the solution near the discontinuity
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Motamarri, P.; Nowak, M.R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
NASA Astrophysics Data System (ADS)
Motamarri, P.; Nowak, M. R.; Leiter, K.; Knap, J.; Gavini, V.
2013-11-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100-200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings-of the order of 1000-fold-relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn-Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using
Adaptive finite difference for seismic wavefield modelling in acoustic media.
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang's optimised finite difference scheme. PMID:27491333
Adaptive finite difference for seismic wavefield modelling in acoustic media
NASA Astrophysics Data System (ADS)
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-08-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme.
Adaptive finite difference for seismic wavefield modelling in acoustic media
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-01-01
Efficient numerical seismic wavefield modelling is a key component of modern seismic imaging techniques, such as reverse-time migration and full-waveform inversion. Finite difference methods are perhaps the most widely used numerical approach for forward modelling, and here we introduce a novel scheme for implementing finite difference by introducing a time-to-space wavelet mapping. Finite difference coefficients are then computed by minimising the difference between the spatial derivatives of the mapped wavelet and the finite difference operator over all propagation angles. Since the coefficients vary adaptively with different velocities and source wavelet bandwidths, the method is capable to maximise the accuracy of the finite difference operator. Numerical examples demonstrate that this method is superior to standard finite difference methods, while comparable to Zhang’s optimised finite difference scheme. PMID:27491333
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.
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 Astrophysics Data System (ADS)
Schaal, Kevin; Bauer, Andreas; Chandrashekar, Praveen; Pakmor, Rüdiger; Klingenberg, Christian; Springel, Volker
2015-11-01
Solving the Euler equations of ideal hydrodynamics as accurately and efficiently as possible is a key requirement in many astrophysical simulations. It is therefore important to continuously advance the numerical methods implemented in current astrophysical codes, especially also in light of evolving computer technology, which favours certain computational approaches over others. Here we introduce the new adaptive mesh refinement (AMR) code TENET, which employs a high-order discontinuous Galerkin (DG) scheme for hydrodynamics. The Euler equations in this method are solved in a weak formulation with a polynomial basis by means of explicit Runge-Kutta time integration and Gauss-Legendre quadrature. This approach offers significant advantages over commonly employed second-order finite-volume (FV) solvers. In particular, the higher order capability renders it computationally more efficient, in the sense that the same precision can be obtained at significantly less computational cost. Also, the DG scheme inherently conserves angular momentum in regions where no limiting takes place, and it typically produces much smaller numerical diffusion and advection errors than an FV approach. A further advantage lies in a more natural handling of AMR refinement boundaries, where a fall-back to first order can be avoided. Finally, DG requires no wide stencils at high order, and offers an improved data locality and a focus on local computations, which is favourable for current and upcoming highly parallel supercomputers. We describe the formulation and implementation details of our new code, and demonstrate its performance and accuracy with a set of two- and three-dimensional test problems. The results confirm that DG schemes have a high potential for astrophysical applications.
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.
Development of an adaptive hp-version finite element method for computational optimal control
NASA Technical Reports Server (NTRS)
Hodges, Dewey H.; Warner, Michael S.
1994-01-01
In this research effort, the usefulness of hp-version finite elements and adaptive solution-refinement techniques in generating numerical solutions to optimal control problems has been investigated. Under NAG-939, a general FORTRAN code was developed which approximated solutions to optimal control problems with control constraints and state constraints. Within that methodology, to get high-order accuracy in solutions, the finite element mesh would have to be refined repeatedly through bisection of the entire mesh in a given phase. In the current research effort, the order of the shape functions in each element has been made a variable, giving more flexibility in error reduction and smoothing. Similarly, individual elements can each be subdivided into many pieces, depending on the local error indicator, while other parts of the mesh remain coarsely discretized. The problem remains to reduce and smooth the error while still keeping computational effort reasonable enough to calculate time histories in a short enough time for on-board applications.
NASA Astrophysics Data System (ADS)
Yang, Dikun; Oldenburg, Douglas W.; Haber, Eldad
2014-03-01
Airborne electromagnetic (AEM) methods are highly efficient tools for assessing the Earth's conductivity structures in a large area at low cost. However, the configuration of AEM measurements, which typically have widely distributed transmitter-receiver pairs, makes the rigorous modelling and interpretation extremely time-consuming in 3-D. Excessive overcomputing can occur when working on a large mesh covering the entire survey area and inverting all soundings in the data set. We propose two improvements. The first is to use a locally optimized mesh for each AEM sounding for the forward modelling and calculation of sensitivity. This dedicated local mesh is small with fine cells near the sounding location and coarse cells far away in accordance with EM diffusion and the geometric decay of the signals. Once the forward problem is solved on the local meshes, the sensitivity for the inversion on the global mesh is available through quick interpolation. Using local meshes for AEM forward modelling avoids unnecessary computing on fine cells on a global mesh that are far away from the sounding location. Since local meshes are highly independent, the forward modelling can be efficiently parallelized over an array of processors. The second improvement is random and dynamic down-sampling of the soundings. Each inversion iteration only uses a random subset of the soundings, and the subset is reselected for every iteration. The number of soundings in the random subset, determined by an adaptive algorithm, is tied to the degree of model regularization. This minimizes the overcomputing caused by working with redundant soundings. Our methods are compared against conventional methods and tested with a synthetic example. We also invert a field data set that was previously considered to be too large to be practically inverted in 3-D. These examples show that our methodology can dramatically reduce the processing time of 3-D inversion to a practical level without losing resolution
NASA Astrophysics Data System (ADS)
Castro-Mateos, Isaac; Pozo, Jose M.; Lazary, Aron; Frangi, Alejandro F.
2016-03-01
Computational medicine aims at developing patient-specific models to help physicians in the diagnosis and treatment selection for patients. The spine, and other skeletal structures, is an articulated object, composed of rigid bones (vertebrae) and non-rigid parts (intervertebral discs (IVD), ligaments and muscles). These components are usually extracted from different image modalities, involving patient repositioning. In the case of the spine, these models require the segmentation of IVDs from MR and vertebrae from CT. In the literature, there exists a vast selection of segmentations methods, but there is a lack of approaches to align the vertebrae and IVDs. This paper presents a method to create patient-specific finite element meshes for biomechanical simulations, integrating rigid and non-rigid parts of articulated objects. First, the different parts are aligned in a complete surface model. Vertebrae extracted from CT are rigidly repositioned in between the IVDs, initially using the IVDs location and then refining the alignment using the MR image with a rigid active shape model algorithm. Finally, a mesh morphing algorithm, based on B-splines, is employed to map a template finite-element (volumetric) mesh to the patient-specific surface mesh. This morphing reduces possible misalignments and guarantees the convexity of the model elements. Results show that the accuracy of the method to align vertebrae into MR, together with IVDs, is similar to that of the human observers. Thus, this method is a step forward towards the automation of patient-specific finite element models for biomechanical simulations.
NASA Astrophysics Data System (ADS)
Shishkin, G. I.
2013-04-01
For a singularly perturbed parabolic convection-diffusion equation, the conditioning and stability of finite difference schemes on uniform meshes are analyzed. It is shown that a convergent standard monotone finite difference scheme on a uniform mesh is not ɛ-uniformly well conditioned or ɛ-uniformly stable to perturbations of the data of the grid problem (here, ɛ is a perturbation parameter, ɛ ∈ (0, 1]). An alternative finite difference scheme is proposed, namely, a scheme in which the discrete solution is decomposed into regular and singular components that solve grid subproblems considered on uniform meshes. It is shown that this solution decomposition scheme converges ɛ-uniformly in the maximum norm at an O( N -1ln N + N {0/-1}) rate, where N + 1 and N 0 + 1 are the numbers of grid nodes in x and t, respectively. This scheme is ɛ-uniformly well conditioned and ɛ-uniformly stable to perturbations of the data of the grid problem. The condition number of the solution decomposition scheme is of order O(δ-2lnδ-1 + δ{0/-1}); i.e., up to a logarithmic factor, it is the same as that of a classical scheme on uniform meshes in the case of a regular problem. Here, δ = N -1ln N and δ0 = N {0/-1} are the accuracies of the discrete solution in x and t, respectively.
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.
Parallel Implementation and Scaling of an Adaptive Mesh Discrete Ordinates Algorithm for Transport
Howell, L H
2004-11-29
Block-structured adaptive mesh refinement (AMR) uses a mesh structure built up out of locally-uniform rectangular grids. In the BoxLib parallel framework used by the Raptor code, each processor operates on one or more of these grids at each refinement level. The decomposition of the mesh into grids and the distribution of these grids among processors may change every few timesteps as a calculation proceeds. Finer grids use smaller timesteps than coarser grids, requiring additional work to keep the system synchronized and ensure conservation between different refinement levels. In a paper for NECDC 2002 I presented preliminary results on implementation of parallel transport sweeps on the AMR mesh, conjugate gradient acceleration, accuracy of the AMR solution, and scalar speedup of the AMR algorithm compared to a uniform fully-refined mesh. This paper continues with a more in-depth examination of the parallel scaling properties of the scheme, both in single-level and multi-level calculations. Both sweeping and setup costs are considered. The algorithm scales with acceptable performance to several hundred processors. Trends suggest, however, that this is the limit for efficient calculations with traditional transport sweeps, and that modifications to the sweep algorithm will be increasingly needed as job sizes in the thousands of processors become common.
Adaptive finite-element method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
NASA Astrophysics Data System (ADS)
Emamzadeh, Seyed Shahab; Ahmadi, Mohammad Taghi; Mohammadi, Soheil; Biglarkhani, Masoud
2015-07-01
In this paper, an investigation into the propagation of far field explosion waves in water and their effects on nearby structures are carried out. For the far field structure, the motion of the fluid surrounding the structure may be assumed small, allowing linearization of the governing fluid equations. A complete analysis of the problem must involve simultaneous solution of the dynamic response of the structure and the propagation of explosion wave in the surrounding fluid. In this study, a dynamic adaptive finite element procedure is proposed. Its application to the solution of a 2D fluid-structure interaction is investigated in the time domain. The research includes: a) calculation of the far-field scatter wave due to underwater explosion including solution of the time-depended acoustic wave equation, b) fluid-structure interaction analysis using coupled Euler-Lagrangian approach, and c) adaptive finite element procedures employing error estimates, and re-meshing. The temporal mesh adaptation is achieved by local regeneration of the grid using a time-dependent error indicator based on curvature of pressure function. As a result, the overall response is better predicted by a moving mesh than an equivalent uniform mesh. In addition, the cost of computation for large problems is reduced while the accuracy is improved.
Adaptive explicit and implicit finite element methods for transient thermal analysis
NASA Technical Reports Server (NTRS)
Probert, E. J.; Hassan, O.; Morgan, K.; Peraire, J.
1992-01-01
The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
Crane, N K; Parsons, I D; Hjelmstad, K D
2002-03-21
Adaptive mesh refinement selectively subdivides the elements of a coarse user supplied mesh to produce a fine mesh with reduced discretization error. Effective use of adaptive mesh refinement coupled with an a posteriori error estimator can produce a mesh that solves a problem to a given discretization error using far fewer elements than uniform refinement. A geometric multigrid solver uses increasingly finer discretizations of the same geometry to produce a very fast and numerically scalable solution to a set of linear equations. Adaptive mesh refinement is a natural method for creating the different meshes required by the multigrid solver. This paper describes the implementation of a scalable adaptive multigrid method on a distributed memory parallel computer. Results are presented that demonstrate the parallel performance of the methodology by solving a linear elastic rocket fuel deformation problem on an SGI Origin 3000. Two challenges must be met when implementing adaptive multigrid algorithms on massively parallel computing platforms. First, although the fine mesh for which the solution is desired may be large and scaled to the number of processors, the multigrid algorithm must also operate on much smaller fixed-size data sets on the coarse levels. Second, the mesh must be repartitioned as it is adapted to maintain good load balancing. In an adaptive multigrid algorithm, separate mesh levels may require separate partitioning, further complicating the load balance problem. This paper shows that, when the proper optimizations are made, parallel adaptive multigrid algorithms perform well on machines with several hundreds of processors.
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.
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.
NASA Astrophysics Data System (ADS)
Danaila, Ionut; Moglan, Raluca; Hecht, Frédéric; Le Masson, Stéphane
2014-10-01
We present a new numerical system using finite elements with mesh adaptivity for the simulation of solid-liquid phase change systems. In the liquid phase, the natural convection flow is simulated by solving the incompressible Navier-Stokes equations with Boussinesq approximation. A variable viscosity model allows the velocity to progressively vanish in the solid phase, through an intermediate mushy region. The phase change is modeled by introducing an implicit enthalpy source term in the heat equation. The final system of equations describing the liquid-solid system by a single domain approach is solved using a Newton iterative algorithm. The space discretization is based on a P2-P1 Taylor-Hood finite elements and mesh adaptivity by metric control is used to accurately track the solid-liquid interface or the density inversion interface for water flows. The numerical method is validated against classical benchmarks that progressively add strong non-linearities in the system of equations: natural convection of air, natural convection of water, melting of a phase-change material and water freezing. Very good agreement with experimental data is obtained for each test case, proving the capability of the method to deal with both melting and solidification problems with convection. The presented numerical method is easy to implement using FreeFem++ software using a syntax close to the mathematical formulation.
Directionally adaptive finite element method for multidimensional Euler and Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Tan, Zhiqiang; Varghese, Philip L.
1993-01-01
A directionally adaptive finite element method for multidimensional compressible flows is presented. Quadrilateral and hexahedral elements are used because they have several advantages over triangular and tetrahedral elements. Unlike traditional methods that use quadrilateral/hexahedral elements, our method allows an element to be divided in each of the three directions in 3D and two directions in 2D. Some restrictions on mesh structure are found to be necessary, especially in 3D. The refining and coarsening procedures, and the treatment of constraints are given. A new implementation of upwind schemes in the constrained finite element system is presented. Some example problems, including a Mach 10 shock interaction with the walls of a 2D channel, a 2D viscous compression corner flow, and inviscid and viscous 3D flows in square channels, are also shown.
AMESH A mesh creating program for the integral finite differencemethod: A User's Manual
Haukwa, Charles
1998-08-31
Amesh program generates discrete grids for numerical modeling of flow and transport problems in which the formulation is based on integral finite difference method (IFDM). For example, the output of Amesh can be used directly as (part of) the input to TOUGH2 or TOUGH numerical Simulator (Pruess, 1987, 1990, Pruess, et al., 1996). The code Amesh can generate 1D, 2D or 3D numerical grids for a given set of locations, i.e. the centers of each discrete sub-domain. In the 2D aerial plane the Voronoi tessellation method is used (Voronoi, 1908; Ahuja, 1982; Aurehammer, 1991; Fortune, 1987, 1988, 1993). In this method we can create a mesh of elements, within model domain, where the interfaces between neighbor elements are the perpendicular bisectors of the line connecting the element centers. The interface distances are simply the medians of the line connecting the centers. To create the 3D grid, the vertical direction interface areas are always treated as horizontal projections of the 2D areal plane. In the lateral direction the interface areas are always vertical projections. In both cases the direction of gravity vector is given by the cosine of angle formed by the line joining the element centers and the vertical. From the list of element locations (center points), the program determines element volumes, and the connection information, i.e. areas, connection distances and the angle. The default input file is ''in''. The output files are ''eleme'' are ''conne'' and ''segmt''. The files ''eleme'' and ''come'' contain all the data required to describe a TOUGH2 input and together they describe the input TOUGH2 input file called ''MESH'', for the specified domain. The file ''segmt'' can be used to plot the geometrical shape of each element in each layer of the input domain. The input data into Amesh does not have to be ordered. AMESH uses a fast quaternary sorting algorithm (Fortune, 1988; Watson 1985) to sort and compute the adjacency relationships between nodes in the 2D
NASA Astrophysics Data System (ADS)
Horritt, M. S.; Bates, P. D.; Mattinson, M. J.
2006-09-01
SummaryThe effects of mesh resolution and topographic data quality on the predictions of a 2D finite volume model of channel flow are investigated. 25 cm resolution side scan sonar swath bathymetry of a 7 km reach of the river Thames, UK, provides topography for a series of finite volume models with resolutions ranging from 2.5 to 50 m. Results from the coarser meshes are compared with the 2.5 m simulation which is used as a benchmark. The model shows greater sensitivity to mesh resolution than topographic sampling. Sensitivity to mesh resolution is attributed to two effects of roughly equal magnitude. Small elements are able to represent hydraulic features such as recirculation zones, and a more accurate representation of the domain boundary helps to drive these flow features. In practical terms, a models at a resolution of 20 and 50 m require 50 m cross-sections, whereas the 10 m model predictions are improved by using all the bathymetry data.
Experience with automatic, dynamic load balancing and adaptive finite element computation
Wheat, S.R.; Devine, K.D.; Maccabe, A.B.
1993-10-01
Distributed memory, Massively Parallel (MP), MIMD technology has enabled the development of applications requiring computational resources previously unobtainable. Structural mechanics and fluid dynamics applications, for example, are often solved by finite element methods (FEMs) requiring, millions of degrees of freedom to accurately simulate physical phenomenon. Adaptive methods, which automatically refine or coarsen meshes and vary the order of accuracy of the numerical solution, offer greater robustness and computational efficiency than traditional FEMs by reducing the amount of computation required away from physical structures such as shock waves and boundary layers. On MP computers, FEMs frequently result in distributed processor load imbalances. To overcome load imbalance, many MP FEMs use static load balancing as a preprocessor to the finite element calculation. Adaptive methods complicate the load imbalance problem since the work per element is not uniform across the solution domain and changes as the computation proceeds. Therefore, dynamic load balancing is required to maintain global load balance. We describe a dynamic, fine-grained, element-based data migration system that maintains global load balance and is effective in the presence of changing work loads. Global load balance is achieved by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. The method utilizes an automatic element management system library to which a programmer integrates the application`s computational description. The library`s flexibility supports a large class of finite element and finite difference based applications.
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.
NASA Astrophysics Data System (ADS)
Yan, Bo; Li, Yuguo; Liu, Ying
2016-07-01
In this paper, we present an adaptive finite element (FE) algorithm for direct current (DC) resistivity modeling in 2-D generally anisotropic conductivity structures. Our algorithm is implemented on an unstructured triangular mesh that readily accommodates complex structures such as topography and dipping layers and so on. We implement a self-adaptive, goal-oriented grid refinement algorithm in which the finite element analysis is performed on a sequence of refined grids. The grid refinement process is guided by an a posteriori error estimator. The problem is formulated in terms of total potentials where mixed boundary conditions are incorporated. This type of boundary condition is superior to the Dirichlet type of conditions and improves numerical accuracy considerably according to model calculations. We have verified the adaptive finite element algorithm using a two-layered earth with azimuthal anisotropy. The FE algorithm with incorporation of mixed boundary conditions achieves high accuracy. The relative error between the numerical and analytical solutions is less than 1% except in the vicinity of the current source location, where the relative error is up to 2.4%. A 2-D anisotropic model is used to demonstrate the effects of anisotropy upon the apparent resistivity in DC soundings.
Impact of space-time mesh adaptation on solute transport modeling in porous media
NASA Astrophysics Data System (ADS)
Esfandiar, Bahman; Porta, Giovanni; Perotto, Simona; Guadagnini, Alberto
2015-02-01
We implement a space-time grid adaptation procedure to efficiently improve the accuracy of numerical simulations of solute transport in porous media in the context of model parameter estimation. We focus on the Advection Dispersion Equation (ADE) for the interpretation of nonreactive transport experiments in laboratory-scale heterogeneous porous media. When compared to a numerical approximation based on a fixed space-time discretization, our approach is grounded on a joint automatic selection of the spatial grid and the time step to capture the main (space-time) system dynamics. Spatial mesh adaptation is driven by an anisotropic recovery-based error estimator which enables us to properly select the size, shape, and orientation of the mesh elements. Adaptation of the time step is performed through an ad hoc local reconstruction of the temporal derivative of the solution via a recovery-based approach. The impact of the proposed adaptation strategy on the ability to provide reliable estimates of the key parameters of an ADE model is assessed on the basis of experimental solute breakthrough data measured following tracer injection in a nonuniform porous system. Model calibration is performed in a Maximum Likelihood (ML) framework upon relying on the representation of the ADE solution through a generalized Polynomial Chaos Expansion (gPCE). Our results show that the proposed anisotropic space-time grid adaptation leads to ML parameter estimates and to model results of markedly improved quality when compared to classical inversion approaches based on a uniform space-time discretization.
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.
NASA Technical Reports Server (NTRS)
Bibel, George; Lewicki, David G. (Technical Monitor)
2002-01-01
A procedure was developed to perform tooth contact analysis between a face gear meshing with a spur pinion using finite element analysis. The face gear surface points from a previous analysis were used to create a connected tooth solid model without gaps or overlaps. The face gear surface points were used to create a five tooth face gear Patran model (with rim) using Patran PCL commands. These commands were saved in a series of session files suitable for Patran input. A four tooth spur gear that meshes with the face gear was designed and constructed with Patran PCL commands. These commands were also saved in a session files suitable for Patran input. The orientation of the spur gear required for meshing with the face gear was determined. The required rotations and translations are described and built into the session file for the spur gear. The Abaqus commands for three-dimensional meshing were determined and verified for a simplified model containing one spur tooth and one face gear tooth. The boundary conditions, loads, and weak spring constraints were determined to make the simplified model work. The load steps and load increments to establish contact and obtain a realistic load was determined for the simplified two tooth model. Contact patterns give some insight into required mesh density. Building the two gears in two different local coordinate systems and rotating the local coordinate systems was verified as an easy way to roll the gearset through mesh. Due to limitation of swap space, disk space and time constraints of the summer period, the larger model was not completed.
NASA Astrophysics Data System (ADS)
Balsara, Dinshaw S.; Dumbser, Michael
2015-10-01
Several advances have been reported in the recent literature on divergence-free finite volume schemes for Magnetohydrodynamics (MHD). Almost all of these advances are restricted to structured meshes. To retain full geometric versatility, however, it is also very important to make analogous advances in divergence-free schemes for MHD on unstructured meshes. Such schemes utilize a staggered Yee-type mesh, where all hydrodynamic quantities (mass, momentum and energy density) are cell-centered, while the magnetic fields are face-centered and the electric fields, which are so useful for the time update of the magnetic field, are centered at the edges. Three important advances are brought together in this paper in order to make it possible to have high order accurate finite volume schemes for the MHD equations on unstructured meshes. First, it is shown that a divergence-free WENO reconstruction of the magnetic field can be developed for unstructured meshes in two and three space dimensions using a classical cell-centered WENO algorithm, without the need to do a WENO reconstruction for the magnetic field on the faces. This is achieved via a novel constrained L2-projection operator that is used in each time step as a postprocessor of the cell-centered WENO reconstruction so that the magnetic field becomes locally and globally divergence free. Second, it is shown that recently-developed genuinely multidimensional Riemann solvers (called MuSIC Riemann solvers) can be used on unstructured meshes to obtain a multidimensionally upwinded representation of the electric field at each edge. Third, the above two innovations work well together with a high order accurate one-step ADER time stepping strategy, which requires the divergence-free nonlinear WENO reconstruction procedure to be carried out only once per time step. The resulting divergence-free ADER-WENO schemes with MuSIC Riemann solvers give us an efficient and easily-implemented strategy for divergence-free MHD on
NASA Astrophysics Data System (ADS)
Liu, Hongxu; Jiao, Xiangmin
2016-06-01
ENO (Essentially Non-Oscillatory) and WENO (Weighted Essentially Non-Oscillatory) schemes are widely used high-order schemes for solving partial differential equations (PDEs), especially hyperbolic conservation laws with piecewise smooth solutions. For structured meshes, these techniques can achieve high order accuracy for smooth functions while being non-oscillatory near discontinuities. For unstructured meshes, which are needed for complex geometries, similar schemes are required but they are much more challenging. We propose a new family of non-oscillatory schemes, called WLS-ENO, in the context of solving hyperbolic conservation laws using finite-volume methods over unstructured meshes. WLS-ENO is derived based on Taylor series expansion and solved using a weighted least squares formulation. Unlike other non-oscillatory schemes, the WLS-ENO does not require constructing sub-stencils, and hence it provides a more flexible framework and is less sensitive to mesh quality. We present rigorous analysis of the accuracy and stability of WLS-ENO, and present numerical results in 1-D, 2-D, and 3-D for a number of benchmark problems, and also report some comparisons against WENO.
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.
Numerical modeling of landslide-generated tsunami using adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Wilson, Cian; Collins, Gareth; Desousa Costa, Patrick; Piggott, Matthew
2010-05-01
Landslides impacting into or occurring under water generate waves, which can have devastating environmental consequences. Depending on the characteristics of the landslide the waves can have significant amplitude and potentially propagate over large distances. Linear models of classical earthquake-generated tsunamis cannot reproduce the highly nonlinear generation mechanisms required to accurately predict the consequences of landslide-generated tsunamis. Also, laboratory-scale experimental investigation is limited to simple geometries and short time-scales before wave reflections contaminate the data. Computational fluid dynamics models based on the nonlinear Navier-Stokes equations can simulate landslide-tsunami generation at realistic scales. However, traditional chessboard-like structured meshes introduce superfluous resolution and hence the computing power required for such a simulation can be prohibitively high, especially in three dimensions. Unstructured meshes allow the grid spacing to vary rapidly from high resolution in the vicinity of small scale features to much coarser, lower resolution in other areas. Combining this variable resolution with dynamic mesh adaptivity allows such high resolution zones to follow features like the interface between the landslide and the water whilst minimising the computational costs. Unstructured meshes are also better suited to representing complex geometries and bathymetries allowing more realistic domains to be simulated. Modelling multiple materials, like water, air and a landslide, on an unstructured adaptive mesh poses significant numerical challenges. Novel methods of interface preservation must be considered and coupled to a flow model in such a way that ensures conservation of the different materials. Furthermore this conservation property must be maintained during successive stages of mesh optimisation and interpolation. In this paper we validate a new multi-material adaptive unstructured fluid dynamics model
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.
An adaptive mesh method for phase-field simulation of alloy solidification in three dimensions
NASA Astrophysics Data System (ADS)
Bollada, P. C.; Jimack, P. K.; Mullis, A. M.
2015-06-01
We present our computational method for binary alloy solidification which takes advantage of high performance computing where up to 1024 cores are employed. Much of the simulation at a sufficiently fine resolution is possible on a modern 12 core PC and the 1024 core simulation is only necessary for very mature dendrite and convergence testing where high resolution puts extreme demands on memory. In outline, the method uses implicit time stepping in conjunction with an iterative solver, adaptive meshing and a scheme for dividing the work load across processors. We include three dimensional results for a Lewis number of 100 and a snapshot for a mature dendrite for a Lewis number of 40.
Development of a Godunov method for Maxwell's equations with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Barbas, Alfonso; Velarde, Pedro
2015-11-01
In this paper we present a second order 3D method for Maxwell's equations based on a Godunov scheme with Adaptive Mesh Refinement (AMR). In order to achieve it, we apply a limiter which better preserves extrema and boundary conditions based on a characteristic fields decomposition. Despite being more complex, simplifications in the boundary conditions make the resulting method competitive in computer time consumption and accuracy compared to FDTD. AMR allows us to simulate systems with a sharp step in material properties with negligible rebounds and also large domains with accuracy in small wavelengths.
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.
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
An h-adaptive finite element method for turbulent heat transfer
Carriington, David B
2009-01-01
A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.
Adaptive finite element simulation of flow and transport applications on parallel computers
NASA Astrophysics Data System (ADS)
Kirk, Benjamin Shelton
The subject of this work is the adaptive finite element simulation of problems arising in flow and transport applications on parallel computers. Of particular interest are new contributions to adaptive mesh refinement (AMR) in this parallel high-performance context, including novel work on data structures, treatment of constraints in a parallel setting, generality and extensibility via object-oriented programming, and the design/implementation of a flexible software framework. This technology and software capability then enables more robust, reliable treatment of multiscale--multiphysics problems and specific studies of fine scale interaction such as those in biological chemotaxis (Chapter 4) and high-speed shock physics for compressible flows (Chapter 5). The work begins by presenting an overview of key concepts and data structures employed in AMR simulations. Of particular interest is how these concepts are applied in the physics-independent software framework which is developed here and is the basis for all the numerical simulations performed in this work. This open-source software framework has been adopted by a number of researchers in the U.S. and abroad for use in a wide range of applications. The dynamic nature of adaptive simulations pose particular issues for efficient implementation on distributed-memory parallel architectures. Communication cost, computational load balance, and memory requirements must all be considered when developing adaptive software for this class of machines. Specific extensions to the adaptive data structures to enable implementation on parallel computers is therefore considered in detail. The libMesh framework for performing adaptive finite element simulations on parallel computers is developed to provide a concrete implementation of the above ideas. This physics-independent framework is applied to two distinct flow and transport applications classes in the subsequent application studies to illustrate the flexibility of the
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
NASA Astrophysics Data System (ADS)
Wendling, A.; Daniel, J. L.; Hivet, G.; Vidal-Sallé, E.; Boisse, P.
2015-12-01
Numerical simulation is a powerful tool to predict the mechanical behavior and the feasibility of composite parts. Among the available numerical approaches, as far as woven reinforced composites are concerned, 3D finite element simulation at the mesoscopic scale leads to a good compromise between realism and complexity. At this scale, the fibrous reinforcement is modeled by an interlacement of yarns assumed to be homogeneous that have to be accurately represented. Among the numerous issues induced by these simulations, the first one consists in providing a representative meshed geometrical model of the unit cell at the mesoscopic scale. The second one consists in enabling a fast data input in the finite element software (contacts definition, boundary conditions, elements reorientation, etc.) so as to obtain results within reasonable time. Based on parameterized 3D CAD modeling tool of unit-cells of dry fabrics already developed, this paper presents an efficient strategy which permits an automated meshing of the models with 3D hexahedral elements and to accelerate of several orders of magnitude the simulation data input. Finally, the overall modeling strategy is illustrated by examples of finite element simulation of the mechanical behavior of fabrics.
NASA Astrophysics Data System (ADS)
Grosges, T.; Borouchaki, H.; Barchiesi, D.
2010-12-01
We present an improved adaptive mesh process based on Riemannian transformation to control the accuracy in high field gradient representation for diffraction problems. Such an adaptive meshing is applied in representing the electromagnetic intensity around a metallic submicronic spherical particle, which is known to present high gradients in limited zones of space including the interference pattern of the electromagnetic field. We show that, the precision of the field variation being controlled, this improved scheme permits drastically decreasing the computational time as well as the memory requirements by adapting the number and the position of nodes where the electromagnetic field must be computed and represented.
Three-dimensional numerical simulations of falling films using an adaptive unstructured mesh
NASA Astrophysics Data System (ADS)
Pain, Chris; Xie, Zhihua; Matar, Omar
2015-11-01
Falling liquid films have rich wave dynamics, often occurring in many industrial applications, such as condensers, evaporators and chemical reactors. A number of numerical studies featuring falling liquid films are available in the literature; the majority of them, however, have focused on two-dimensional falling films. Far fewer studies have considered three-dimensional falling films, and those that have only studied the flow in a periodic domain. The objective of this study is to investigate flow dynamics of developing three-dimensional falling films using the Navier-Stokes equations coupled with interface capturing approach over extended domains. An adaptive, unstructured mesh modelling framework is employed here to study this problem, which can modify and adapt three-dimensional meshes to better represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. Numerical examples of three-dimensional falling films in a long domain are presented and discussed. EPSRC Programme Grant, MEMPHIS, EP/K0039761/1.
Adaptive Mesh Expansion Model (AMEM) for Liver Segmentation from CT Image
Wang, Xuehu; Yang, Jian; Ai, Danni; Zheng, Yongchang; Tang, Songyuan; Wang, Yongtian
2015-01-01
This study proposes a novel adaptive mesh expansion model (AMEM) for liver segmentation from computed tomography images. The virtual deformable simplex model (DSM) is introduced to represent the mesh, in which the motion of each vertex can be easily manipulated. The balloon, edge, and gradient forces are combined with the binary image to construct the external force of the deformable model, which can rapidly drive the DSM to approach the target liver boundaries. Moreover, tangential and normal forces are combined with the gradient image to control the internal force, such that the DSM degree of smoothness can be precisely controlled. The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver. The proposed method is evaluated on the basis of different criteria applied to 10 clinical data sets. Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms. Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively. PMID:25769030
NASA Astrophysics Data System (ADS)
Fromang, S.; Hennebelle, P.; Teyssier, R.
2006-10-01
Aims. In this paper, we present a new method to perform numerical simulations of astrophysical MHD flows using the Adaptive Mesh Refinement framework and Constrained Transport. Methods: . The algorithm is based on a previous work in which the MUSCL-Hancock scheme was used to evolve the induction equation. In this paper, we detail the extension of this scheme to the full MHD equations and discuss its properties. Results: . Through a series of test problems, we illustrate the performances of this new code using two different MHD Riemann solvers (Lax-Friedrich and Roe) and the need of the Adaptive Mesh Refinement capabilities in some cases. Finally, we show its versatility by applying it to two completely different astrophysical situations well studied in the past years: the growth of the magnetorotational instability in the shearing box and the collapse of magnetized cloud cores. Conclusions: . We have implemented a new Godunov scheme to solve the ideal MHD equations in the AMR code RAMSES. We have shown that it results in a powerful tool that can be applied to a great variety of astrophysical problems, ranging from galaxies formation in the early universe to high resolution studies of molecular cloud collapse in our galaxy.
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.
NASA Astrophysics Data System (ADS)
Jia, Jinhong; Wang, Hong
2015-10-01
Numerical methods for fractional differential equations generate full stiffness matrices, which were traditionally solved via Gaussian type direct solvers that require O (N3) of computational work and O (N2) of memory to store where N is the number of spatial grid points in the discretization. We develop a preconditioned fast Krylov subspace iterative method for the efficient and faithful solution of finite volume schemes defined on a locally refined composite mesh for fractional differential equations to resolve boundary layers of the solutions. Numerical results are presented to show the utility of the method.
MHD simulations on an unstructured mesh
Strauss, H.R.; Park, W.; Belova, E.; Fu, G.Y.; Longcope, D.W.; Sugiyama, L.E.
1998-12-31
Two reasons for using an unstructured computational mesh are adaptivity, and alignment with arbitrarily shaped boundaries. Two codes which use finite element discretization on an unstructured mesh are described. FEM3D solves 2D and 3D RMHD using an adaptive grid. MH3D++, which incorporates methods of FEM3D into the MH3D generalized MHD code, can be used with shaped boundaries, which might be 3D.
Yu, Jingjing; He, Xiaowei; Geng, Guohua; Liu, Fang; Jiao, L C
2013-01-01
Quantitative reconstruction of bioluminescent sources from boundary measurements is a challenging ill-posed inverse problem owing to the high degree of absorption and scattering of light through tissue. We present a hybrid multilevel reconstruction scheme by combining the ability of sparse regularization with the advantage of adaptive finite element method. In view of the characteristics of different discretization levels, two different inversion algorithms are employed on the initial coarse mesh and the succeeding ones to strike a balance between stability and efficiency. Numerical experiment results with a digital mouse model demonstrate that the proposed scheme can accurately localize and quantify source distribution while maintaining reconstruction stability and computational economy. The effectiveness of this hybrid reconstruction scheme is further confirmed with in vivo experiments. PMID:23533542
Garcia-Herranz, Nuria; Cabellos, Oscar; Aragones, Jose M.; Ahnert, Carol
2003-05-15
In order to take into account in a more effective and accurate way the intranodal heterogeneities in coarse-mesh finite-difference (CMFD) methods, a new equivalent parameter generation methodology has been developed and tested. This methodology accounts for the dependence of the nodal homogeneized two-group cross sections and nodal coupling factors, with interface flux discontinuity (IFD) factors that account for heterogeneities on the flux-spectrum and burnup intranodal distributions as well as on neighbor effects.The methodology has been implemented in an analytic CMFD method, rigorously obtained for homogeneous nodes with transverse leakage and generalized now for heterogeneous nodes by including IFD heterogeneity factors. When intranodal mesh node heterogeneity vanishes, the heterogeneous solution tends to the analytic homogeneous nodal solution. On the other hand, when intranodal heterogeneity increases, a high accuracy is maintained since the linear and nonlinear feedbacks on equivalent parameters have been shown to be as a very effective way of accounting for heterogeneity effects in two-group multidimensional coarse-mesh diffusion calculations.
NASA Astrophysics Data System (ADS)
Hu, Guanghui; Yi, Nianyu
2016-05-01
In this paper, we present an adaptive finite volume method for steady Euler equations with a non-oscillatory k-exact reconstruction on unstructured mesh. The numerical framework includes a Newton method as an outer iteration to linearize the Euler equations, and a geometrical multigrid method as an inner iteration to solve the derived linear system. A non-oscillatory k-exact reconstruction of the conservative solution in each element is proposed for the high order and non-oscillatory behavior of the numerical solutions. The importance on handling the curved boundary in an appropriate way is also studied with the numerical experiments. The h-adaptive method is introduced to enhance the efficiency of the algorithm. The numerical tests show successfully that the quality solutions can be obtained smoothly with the proposed algorithm, i.e., the expected convergence order of the numerical solution with the mesh refinement can be reached, while the non-oscillation shock structure can be obtained. Furthermore, the mesh adaptive method with the appropriate error indicators can effectively enhance the implementation efficiency of numerical method, while the steady state convergence and numerical accuracy are kept in the meantime.
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.
NASA Technical Reports Server (NTRS)
Ashford, Gregory A.; Powell, Kenneth G.
1995-01-01
A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
NASA Astrophysics Data System (ADS)
Ashford, Gregory A.; Powell, Kenneth G.
1995-10-01
A method for generating high quality unstructured triangular grids for high Reynolds number Navier-Stokes calculations about complex geometries is described. Careful attention is paid in the mesh generation process to resolving efficiently the disparate length scales which arise in these flows. First the surface mesh is constructed in a way which ensures that the geometry is faithfully represented. The volume mesh generation then proceeds in two phases thus allowing the viscous and inviscid regions of the flow to be meshed optimally. A solution-adaptive remeshing procedure which allows the mesh to adapt itself to flow features is also described. The procedure for tracking wakes and refinement criteria appropriate for shock detection are described. Although at present it has only been implemented in two dimensions, the grid generation process has been designed with the extension to three dimensions in mind. An implicit, higher-order, upwind method is also presented for computing compressible turbulent flows on these meshes. Two recently developed one-equation turbulence models have been implemented to simulate the effects of the fluid turbulence. Results for flow about a RAE 2822 airfoil and a Douglas three-element airfoil are presented which clearly show the improved resolution obtainable.
Rate sensitive continuum damage models and mesh dependence in finite element analyses.
Ljustina, Goran; Fagerström, Martin; Larsson, Ragnar
2014-01-01
The experiences from orthogonal machining simulations show that the Johnson-Cook (JC) dynamic failure model exhibits significant element size dependence. Such mesh dependence is a direct consequence of the utilization of local damage models. The current contribution is an investigation of the extent of the possible pathological mesh dependence. A comparison of the resulting JC model behavior combined with two types of damage evolution is considered. The first damage model is the JC dynamic failure model, where the development of the "damage" does not affect the response until the critical state is reached. The second one is a continuum damage model, where the damage variable is affecting the material response continuously during the deformation. Both the plasticity and the damage models are rate dependent, and the damage evolutions for both models are defined as a postprocessing of the effective stress response. The investigation is conducted for a series of 2D shear tests utilizing different FE representations of the plane strain plate with pearlite material properties. The results show for both damage models, using realistic pearlite material parameters, that similar extent of the mesh dependence is obtained and that the possible viscous regularization effects are absent in the current investigation. PMID:25530994
Rate Sensitive Continuum Damage Models and Mesh Dependence in Finite Element Analyses
Fagerström, Martin
2014-01-01
The experiences from orthogonal machining simulations show that the Johnson-Cook (JC) dynamic failure model exhibits significant element size dependence. Such mesh dependence is a direct consequence of the utilization of local damage models. The current contribution is an investigation of the extent of the possible pathological mesh dependence. A comparison of the resulting JC model behavior combined with two types of damage evolution is considered. The first damage model is the JC dynamic failure model, where the development of the “damage” does not affect the response until the critical state is reached. The second one is a continuum damage model, where the damage variable is affecting the material response continuously during the deformation. Both the plasticity and the damage models are rate dependent, and the damage evolutions for both models are defined as a postprocessing of the effective stress response. The investigation is conducted for a series of 2D shear tests utilizing different FE representations of the plane strain plate with pearlite material properties. The results show for both damage models, using realistic pearlite material parameters, that similar extent of the mesh dependence is obtained and that the possible viscous regularization effects are absent in the current investigation. PMID:25530994
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.
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity
NASA Astrophysics Data System (ADS)
Wick, Thomas
2016-03-01
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.
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.
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.
A consistent approach to large eddy simulation using adaptive mesh refinement
Cook, A.W.
1999-09-01
The large eddy simulation of turbulent flows is discussed with particular attention paid to the issue of commutation of differentiation and filtering. Multi-level adaptive mesh refinement is proposed as a means of mostly avoiding commutation errors where increased grid resolution is required to capture key flow features. The strategy is to employ multiple uniform grids in a nested hierarchy using a constant-width filter for each grid. It is shown that commutivity of fine and coarse grid filters must be enforced in order to consistently relate variables at different refinement levels. Methods for treating fine grid boundaries and walls are also discussed. It is shown that errors associated with boundary treatments are small and localized.
AstroBEAR: Adaptive Mesh Refinement Code for Ideal Hydrodynamics & Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Cunningham, Andrew J.; Frank, Adam; Varniere, Peggy; Mitran, Sorin; Jones, Thomas W.
2011-04-01
AstroBEAR is a modular hydrodynamic & magnetohydrodynamic code environment designed for a variety of astrophysical applications. It uses the BEARCLAW package, a multidimensional, Eulerian computational code used to solve hyperbolic systems of equations. AstroBEAR allows adaptive-mesh-refinment (AMR) simulations in 2, 2.5 (i.e., cylindrical), and 3 dimensions, in either cartesian or curvilinear coordinates. Parallel applications are supported through the MPI architecture. AstroBEAR is written in Fortran 90/95 using standard libraries. AstroBEAR supports hydrodynamic (HD) and magnetohydrodynamic (MHD) applications using a variety of spatial and temporal methods. MHD simulations are kept divergence-free via the constrained transport (CT) methods of Balsara & Spicer. Three different equation of state environments are available: ideal gas, gas with differing isentropic γ, and the analytic Thomas-Fermi formulation of A.R. Bell [2]. Current work is being done to develop a more advanced real gas equation of state.
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.
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.
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.
Block structured adaptive mesh and time refinement for hybrid, hyperbolic + N-body systems
NASA Astrophysics Data System (ADS)
Miniati, Francesco; Colella, Phillip
2007-11-01
We present a new numerical algorithm for the solution of coupled collisional and collisionless systems, based on the block structured adaptive mesh and time refinement strategy (AMR). We describe the issues associated with the discretization of the system equations and the synchronization of the numerical solution on the hierarchy of grid levels. We implement a code based on a higher order, conservative and directionally unsplit Godunov’s method for hydrodynamics; a symmetric, time centered modified symplectic scheme for collisionless component; and a multilevel, multigrid relaxation algorithm for the elliptic equation coupling the two components. Numerical results that illustrate the accuracy of the code and the relative merit of various implemented schemes are also presented.
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.
Radiation hydrodynamics including irradiation and adaptive mesh refinement with AZEuS. I. Methods
NASA Astrophysics Data System (ADS)
Ramsey, J. P.; Dullemond, C. P.
2015-02-01
Aims: The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods: We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results: We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
NASA Astrophysics Data System (ADS)
Rosenberg, D.; Pouquet, A.; Mininni, P. D.
2007-08-01
We examine the effect of accuracy of high-order spectral element methods, with or without adaptive mesh refinement (AMR), in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang (OT) vortex made up of a magnetic X-point centred on a stagnation point of the velocity. A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code is applied to simulate this problem. The MHD solver is explicit, and uses the Elsässer formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere in the fluid context (Rosenberg et al 2006 J. Comput. Phys. 215 59-80) the code allows both statically refined and dynamically refined grids. Tests of the algorithm using analytic solutions are described, and comparisons of the OT solutions with pseudo-spectral computations are performed. We demonstrate for moderate Reynolds numbers that the algorithms using both static and refined grids reproduce the pseudo-spectral solutions quite well. We show that low-order truncation—even with a comparable number of global degrees of freedom—fails to correctly model some strong (sup-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.
Parallel, adaptive finite element methods for conservation laws
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.
1994-01-01
We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.
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
Model of adaptive temporal development of structured finite systems
NASA Astrophysics Data System (ADS)
Patera, Jiri; Shaw, Gordon L.; Slansky, Richard; Leng, Xiaodan
1989-07-01
The weight systems of level-zero representations of affine Kac-Moody algebras provide an appropriate kinematical framework for studying structured finite systems with adaptive temporal development. Much of the structure is determined by Lie algebra theory, so it is possible to restrict greatly the connection space and analytic results are possible. The time development of these systems often evolves to cyclic temporal-spatial patterns, depending on the definition of the dynamics. The purpose of this paper is to set up the mathematical formalism for this ``memory in Lie algebras'' class of models. An illustration is used to show the kinds of complex behavior that occur in simple cases.
Adaptive meshless local maximum-entropy finite element method for convection-diffusion problems
NASA Astrophysics Data System (ADS)
Wu, C. T.; Young, D. L.; Hong, H. K.
2014-01-01
In this paper, a meshless local maximum-entropy finite element method (LME-FEM) is proposed to solve 1D Poisson equation and steady state convection-diffusion problems at various Peclet numbers in both 1D and 2D. By using local maximum-entropy (LME) approximation scheme to construct the element shape functions in the formulation of finite element method (FEM), additional nodes can be introduced within element without any mesh refinement to increase the accuracy of numerical approximation of unknown function, which procedure is similar to conventional p-refinement but without increasing the element connectivity to avoid the high conditioning matrix. The resulted LME-FEM preserves several significant characteristics of conventional FEM such as Kronecker-delta property on element vertices, partition of unity of shape function and exact reproduction of constant and linear functions. Furthermore, according to the essential properties of LME approximation scheme, nodes can be introduced in an arbitrary way and the continuity of the shape function along element edge is kept at the same time. No transition element is needed to connect elements of different orders. The property of arbitrary local refinement makes LME-FEM be a numerical method that can adaptively solve the numerical solutions of various problems where troublesome local mesh refinement is in general necessary to obtain reasonable solutions. Several numerical examples with dramatically varying solutions are presented to test the capability of the current method. The numerical results show that LME-FEM can obtain much better and stable solutions than conventional FEM with linear element.
Knupp, P.M.
1999-03-26
Three-dimensional unstructured tetrahedral and hexahedral finite element mesh optimization is studied from a theoretical perspective and by computer experiments to determine what objective functions are most effective in attaining valid, high quality meshes. The approach uses matrices and matrix norms to extend the work in Part I to build suitable 3D objective functions. Because certain matrix norm identities which hold for 2 x 2 matrices do not hold for 3 x 3 matrices. significant differences arise between surface and volume mesh optimization objective functions. It is shown, for example, that the equivalence in two-dimensions of the Smoothness and Condition Number of the Jacobian matrix objective functions does not extend to three dimensions and further. that the equivalence of the Oddy and Condition Number of the Metric Tensor objective functions in two-dimensions also fails to extend to three-dimensions. Matrix norm identities are used to systematically construct dimensionally homogeneous groups of objective functions. The concept of an ideal minimizing matrix is introduced for both hexahedral and tetrahedral elements. Non-dimensional objective functions having barriers are emphasized as the most logical choice for mesh optimization. The performance of a number of objective functions in improving mesh quality was assessed on a suite of realistic test problems, focusing particularly on all-hexahedral ''whisker-weaved'' meshes. Performance is investigated on both structured and unstructured meshes and on both hexahedral and tetrahedral meshes. Although several objective functions are competitive, the condition number objective function is particularly attractive. The objective functions are closely related to mesh quality measures. To illustrate, it is shown that the condition number metric can be viewed as a new tetrahedral element quality measure.
NASA Technical Reports Server (NTRS)
Panthaki, Malcolm J.
1987-01-01
Three general tasks on general-purpose, interactive color graphics postprocessing for three-dimensional computational mechanics were accomplished. First, the existing program (POSTPRO3D) is ported to a high-resolution device. In the course of this transfer, numerous enhancements are implemented in the program. The performance of the hardware was evaluated from the point of view of engineering postprocessing, and the characteristics of future hardware were discussed. Second, interactive graphical tools implemented to facilitate qualitative mesh evaluation from a single analysis. The literature was surveyed and a bibliography compiled. Qualitative mesh sensors were examined, and the use of two-dimensional plots of unaveraged responses on the surface of three-dimensional continua was emphasized in an interactive color raster graphics environment. Finally, a postprocessing environment was designed for state-of-the-art workstation technology. Modularity, personalization of the environment, integration of the engineering design processes, and the development and use of high-level graphics tools are some of the features of the intended environment.
ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION
HOLST, MICHAEL; MCCAMMON, JAMES ANDREW; YU, ZEYUN; ZHOU, YOUNGCHENG; ZHU, YUNRONG
2011-01-01
We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first provably convergent discretization, and also allowed for the development of a provably convergent AFEM. However, in practical implementation, this two-term regularization exhibits numerical instability. Therefore, we examine a variation of this regularization technique which can be shown to be less susceptible to such instability. We establish a priori estimates and other basic results for the continuous regularized problem, as well as for Galerkin finite element approximations. We show that the new approach produces regularized continuous and discrete problems with the same mathematical advantages of the original regularization. We then design an AFEM scheme for the new regularized problem, and show that the resulting AFEM scheme is accurate and reliable, by proving a contraction result for the error. This result, which is one of the first results of this type for nonlinear elliptic problems, is based on using continuous and discrete a priori L∞ estimates to establish quasi-orthogonality. To provide a high-quality geometric model as input to the AFEM algorithm, we also describe a class of feature-preserving adaptive mesh generation algorithms designed specifically for constructing meshes of biomolecular structures, based on the intrinsic local structure tensor of the molecular surface. All of the algorithms described in the article are implemented in the Finite Element Toolkit (FETK), developed and maintained at UCSD. The stability advantages of the new regularization scheme
NASA Astrophysics Data System (ADS)
Ding, H.; Shu, C.; Yeo, K. S.; Xu, D.
2007-01-01
In this paper, the mesh-free least square-based finite difference (MLSFD) method is applied to numerically study the flow field around two circular cylinders arranged in side-by-side and tandem configurations. For each configuration, various geometrical arrangements are considered, in order to reveal the different flow regimes characterized by the gap between the two cylinders. In this work, the flow simulations are carried out in the low Reynolds number range, that is, Re=100 and 200. Instantaneous vorticity contours and streamlines around the two cylinders are used as the visualization aids. Some flow parameters such as Strouhal number, drag and lift coefficients calculated from the solution are provided and quantitatively compared with those provided by other researchers.
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.
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.
An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension
Bolstad, John H.
1982-06-01
Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.
Eulerian adaptive finite-difference method for high-velocity impact and penetration problems
Barton, Philip T.; Deiterding, Ralf; Meiron, Daniel I.; Pullin, Dale I
2013-01-01
Owing to the complex processes involved, faithful prediction of high-velocity impact events demands a simulation method delivering efficient calculations based on comprehensively formulated constitutive models. Such an approach is presented herein, employing a weighted essentially non-oscillatory (WENO) method within an adaptive mesh refinement (AMR) framework for the numerical solution of hyperbolic partial differential equations. Applied widely in computational fluid dynamics, these methods are well suited to the involved locally non-smooth finite deformations, circumventing any requirement for artificial viscosity functions for shock capturing. Application of the methods is facilitated through using a model of solid dynamics based upon hyper-elastic theory comprising kinematic evolution equations for the elastic distortion tensor. The model for finite inelastic deformations is phenomenologically equivalent to Maxwell s model of tangential stress relaxation. Closure relations tailored to the expected high-pressure states are proposed and calibrated for the materials of interest. Sharp interface resolution is achieved by employing level-set functions to track boundary motion, along with a ghost material method to capture the necessary internal boundary conditions for material interactions and stress-free surfaces. The approach is demonstrated for the simulation of high velocity impacts of steel projectiles on aluminium target plates in two and three dimensions.
Software Library for Storing and Retrieving Mesh and Results of Finite Element
1997-07-07
EXOII is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code transfer. An EXOII data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface (API).
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.
Parallel Finite Element Electron-Photon Transport Analysis on 2-D Unstructured Mesh
Drumm, C.R.
1999-01-01
A computer code has been developed to solve the linear Boltzmann transport equation on an unstructured mesh of triangles, from a Pro/E model. An arbitriwy arrangement of distinct material regions is allowed. Energy dependence is handled by solving over an arbitrary number of discrete energy groups. Angular de- pendence is treated by Legendre-polynomial expansion of the particle cross sections and a discrete ordinates treatment of the particle fluence. The resulting linear system is solved in parallel with a preconditioned conjugate-gradients method. The solution method is unique, in that the space-angle dependence is solved si- multaneously, eliminating the need for the usual inner iterations. Electron cross sections are obtained from a Goudsrnit-Saunderson modifed version of the CEPXS code. A one-dimensional version of the code has also been develop@ for testing and development purposes.
DRIESSEN,BRIAN
2000-02-17
In this work, a method is proposed for modifying the standard master-slave stiffness matrix so that linear consistency across the interface of the master and slave meshes is achieved. The existence of such a local stiffness modification is implied by the work of [Dohrmann, et al, to appear]. The present work aims at achieving the same linear consistency through a different method of stiffness modification that is based on simply ensuring zero residual force at the interior interface nodes for all non-zero-stress linear displacement fields and zero residual force at all interface nodes for all rigid-body linear displacement fields. These zero residuals ensure that the local stiffness modification results in an interface that passes the patch test. Numerical examples herein demonstrate that the maximum stress error at the interface goes to zero with the proposed method while it does not for the standard master-slave method.
NASA Astrophysics Data System (ADS)
Blatov, I. A.; Dobrobog, N. V.; Kitaeva, E. V.
2016-07-01
The Galerkin finite element method is applied to nonself-adjoint singularly perturbed boundary value problems on Shishkin meshes. The Galerkin projection method is used to obtain conditionally ɛ-uniform a priori error estimates and to prove the convergence of a sequence of meshes in the case of an unknown boundary layer edge.
Lu, Yujie; Zhu, Banghe; Shen, Haiou; Rasmussen, John C; Wang, Ge; Sevick-Muraca, Eva M
2010-08-21
Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP(N)) approximations. To fully evaluate the performance of the SP(N) approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP(N) can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation. PMID:20671350
Wind Forecasting Based on the HARMONIE Model and Adaptive Finite Elements
NASA Astrophysics Data System (ADS)
Oliver, Albert; Rodríguez, Eduardo; Escobar, José María; Montero, Gustavo; Hortal, Mariano; Calvo, Javier; Cascón, José Manuel; Montenegro, Rafael
2015-01-01
In this paper, we introduce a new method for wind field forecasting over complex terrain. The main idea is to use the predictions of the HARMONIE meso-scale model as the input data for an adaptive finite element mass-consistent wind model. The HARMONIE results (obtained with a maximum resolution of about 1 km) are refined in a local scale (about a few metres). An interface between both models is implemented in such a way that the initial wind field is obtained by a suitable interpolation of the HARMONIE results. Genetic algorithms are used to calibrate some parameters of the local wind field model in accordance to the HARMONIE data. In addition, measured data are considered to improve the reliability of the simulations. An automatic tetrahedral mesh generator, based on the meccano method, is applied to adapt the discretization to complex terrains. The main characteristic of the framework is a minimal user intervention. The final goal is to validate our model in several realistic applications on Gran Canaria island, Spain, with some experimental data obtained by the AEMET in their meteorological stations. The source code of the mass-consistent wind model is available online at http://www.dca.iusiani.ulpgc.es/Wind3D/.
Language Model Combination and Adaptation Using Weighted Finite State Transducers
NASA Technical Reports Server (NTRS)
Liu, X.; Gales, M. J. F.; Hieronymus, J. L.; Woodland, P. C.
2010-01-01
In speech recognition systems language model (LMs) are often constructed by training and combining multiple n-gram models. They can be either used to represent different genres or tasks found in diverse text sources, or capture stochastic properties of different linguistic symbol sequences, for example, syllables and words. Unsupervised LM adaption may also be used to further improve robustness to varying styles or tasks. When using these techniques, extensive software changes are often required. In this paper an alternative and more general approach based on weighted finite state transducers (WFSTs) is investigated for LM combination and adaptation. As it is entirely based on well-defined WFST operations, minimum change to decoding tools is needed. A wide range of LM combination configurations can be flexibly supported. An efficient on-the-fly WFST decoding algorithm is also proposed. Significant error rate gains of 7.3% relative were obtained on a state-of-the-art broadcast audio recognition task using a history dependently adapted multi-level LM modelling both syllable and word sequences
A staggered mesh finite difference scheme for the computation of compressible flows
NASA Technical Reports Server (NTRS)
Sanders, Richard
1992-01-01
A simple high resolution finite difference technique is presented to approximate weak solutions to hyperbolic systems of conservation laws. The method does not rely on Riemann problem solvers and is therefore easy to extend to a wide variety of problems. The overall performance (resolution and CPU requirements) is competitive, with other state-of-the-art techniques offering sharp nonoscillatory shocks and contacts. Theoretical results confirm the reliability of the approach for linear systems and nonlinear scalar equations.
NASA Astrophysics Data System (ADS)
Rastigejev, Y.; Semakin, A. N.
2012-12-01
In this work we present a multilevel Wavelet-based Adaptive Mesh Refinement (WAMR) method for numerical modeling of global atmospheric chemical transport problems. An accurate numerical simulation of such problems presents an enormous challenge. Atmospheric Chemical Transport Models (CTMs) combine chemical reactions with meteorologically predicted atmospheric advection and turbulent mixing. The resulting system of multi-scale advection-reaction-diffusion equations is extremely stiff, nonlinear and involves a large number of chemically interacting species. As a consequence, the need for enormous computational resources for solving these equations imposes severe limitations on the spatial resolution of the CTMs implemented on uniform or quasi-uniform grids. In turn, this relatively crude spatial resolution results in significant numerical diffusion introduced into the system. This numerical diffusion is shown to noticeably distort the pollutant mixing and transport dynamics for typically used grid resolutions. The developed WAMR method for numerical modeling of atmospheric chemical evolution equations presented in this work provides a significant reduction in the computational cost, without upsetting numerical accuracy, therefore it addresses the numerical difficulties described above. WAMR method introduces a fine grid in the regions where sharp transitions occur and cruder grid in the regions of smooth solution behavior. Therefore WAMR results in much more accurate solutions than conventional numerical methods implemented on uniform or quasi-uniform grids. The algorithm allows one to provide error estimates of the solution that are used in conjunction with appropriate threshold criteria to adapt the non-uniform grid. The method has been tested for a variety of problems including numerical simulation of traveling pollution plumes. It was shown that pollution plumes in the remote troposphere can propagate as well-defined layered structures for two weeks or more as
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
Hermeline, F. )
1993-05-01
This paper deals with the approximation of Vlasov-Poisson and Vlasov-Maxwell equations. We present two coupled particle-finite volume methods which use the properties of Delaunay-Voronoi meshes. These methods are applied to benchmark calculations and engineering problems such as simulation of electron injector devices. 42 refs., 13 figs.
3D Boltzmann Simulation of the Io's Plasma Environment with Adaptive Mesh and Particle Refinement
NASA Astrophysics Data System (ADS)
Lipatov, A. S.; Combi, M. R.
2002-12-01
The global dynamics of the ionized and neutral components in the environment of Io plays an important role in the interaction of Jupiter's corotating magnetospheric plasma with Io [Combi et al., 2002; 1998; Kabin et al., 2001]. The stationary simulation of this problem was done in the MHD [Combi et al., 1998; Linker et al, 1998; Kabin et al., 2001] and the electrodynamic [Saur et al., 1999] approaches. In this report, we develop a method of kinetic ion-neutral simulation, which is based on a multiscale adaptive mesh, particle and algorithm refinement. This method employs the fluid description for electrons whereas for ions the drift-kinetic and particle approaches are used. This method takes into account charge-exchange and photoionization processes. The first results of such simulation of the dynamics of ions in the Io's environment are discussed in this report. ~ M R Combi et al., J. Geophys. Res., 103, 9071, 1998. M R Combi, T I Gombosi, K Kabin, Atmospheres in the Solar System: Comparative\\ Aeronomy. Geophys. Monograph Series, 130, 151, 2002. K Kabin et al., Planetary and Space Sci., 49, 337, 2001. J A Linker et al., J. Geophys. Res., 103(E9), 19867, 1998. J Saur et al., J. Geophys. Res., 104, 25105, 1999.
AMR++: A design for parallel object-oriented adaptive mesh refinement
Quinlan, D.
1997-11-01
Adaptive mesh refinement computations are complicated by their dynamic nature. In the serial environment they require substantial infrastructures to support the regridding processes, intergrid operations, and local bookkeeping of positions of grids relative to one another. In the parallel environment the dynamic behavior is more problematic because it requires dynamic distribution support and load balancing. Parallel AMR is further complicated by the substantial task parallelism, in addition to the obvious data parallelism, this task parallelism requires additional infrastructure to support efficiently. The degree of parallelism is typically dependent upon the algorithms in use and the equations being solved. Different algorithms have significant compromises between computation and communication. Substantial research work is often required to define efficient methods and suitable infrastructure. The purpose of this paper is to introduce AMR++ as an object-oriented library which forms a part of the OVERTURE framework, a much larger object-oriented numerical framework developed and supported at Los Alamos National Laboratory and distributed on the Web for the last several years.
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.
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.
EMMA: an adaptive mesh refinement cosmological simulation code with radiative transfer
NASA Astrophysics Data System (ADS)
Aubert, Dominique; Deparis, Nicolas; Ocvirk, Pierre
2015-11-01
EMMA is a cosmological simulation code aimed at investigating the reionization epoch. It handles simultaneously collisionless and gas dynamics, as well as radiative transfer physics using a moment-based description with the M1 approximation. Field quantities are stored and computed on an adaptive three-dimensional mesh and the spatial resolution can be dynamically modified based on physically motivated criteria. Physical processes can be coupled at all spatial and temporal scales. We also introduce a new and optional approximation to handle radiation: the light is transported at the resolution of the non-refined grid and only once the dynamics has been fully updated, whereas thermo-chemical processes are still tracked on the refined elements. Such an approximation reduces the overheads induced by the treatment of radiation physics. A suite of standard tests are presented and passed by EMMA, providing a validation for its future use in studies of the reionization epoch. The code is parallel and is able to use graphics processing units (GPUs) to accelerate hydrodynamics and radiative transfer calculations. Depending on the optimizations and the compilers used to generate the CPU reference, global GPU acceleration factors between ×3.9 and ×16.9 can be obtained. Vectorization and transfer operations currently prevent better GPU performance and we expect that future optimizations and hardware evolution will lead to greater accelerations.
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.
Svyatskiy, Daniil; Shashkov, Mikhail; Kuzmin, D
2008-01-01
A new approach to the design of constrained finite element approximations to second-order elliptic problems is introduced. This approach guarantees that the finite element solution satisfies the discrete maximum principle (DMP). To enforce these monotonicity constrains the sufficient conditions for elements of the stiffness matrix are formulated. An algebraic splitting of the stiffness matrix is employed to separate the contributions of diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L{sub 2} projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.
NASA Astrophysics Data System (ADS)
Parkinson, S. D.; Hill, J.; Piggott, M. D.; Allison, P. A.
2014-05-01
High resolution direct numerical simulations (DNS) are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier-Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE) DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two, and three-dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring mesh performance in capturing the range of dynamics. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. Use of discontinuous discretisations and adaptive unstructured meshing technologies, which reduce the required element count by approximately two orders of magnitude, results in high resolution DNS models of turbidity currents at a fraction of the cost of traditional FE models. The benefits of this technique will enable simulation of turbidity currents in complex and large domains where DNS modelling was previously unachievable.
Highly accurate adaptive finite element schemes for nonlinear hyperbolic problems
NASA Astrophysics Data System (ADS)
Oden, J. T.
1992-08-01
This document is a final report of research activities supported under General Contract DAAL03-89-K-0120 between the Army Research Office and the University of Texas at Austin from July 1, 1989 through June 30, 1992. The project supported several Ph.D. students over the contract period, two of which are scheduled to complete dissertations during the 1992-93 academic year. Research results produced during the course of this effort led to 6 journal articles, 5 research reports, 4 conference papers and presentations, 1 book chapter, and two dissertations (nearing completion). It is felt that several significant advances were made during the course of this project that should have an impact on the field of numerical analysis of wave phenomena. These include the development of high-order, adaptive, hp-finite element methods for elastodynamic calculations and high-order schemes for linear and nonlinear hyperbolic systems. Also, a theory of multi-stage Taylor-Galerkin schemes was developed and implemented in the analysis of several wave propagation problems, and was configured within a general hp-adaptive strategy for these types of problems. Further details on research results and on areas requiring additional study are given in the Appendix.
A parallel geometric multigrid method for finite elements on octree meshes
Sampath, Rahul S; Biros, George
2010-01-01
In this article, we present a parallel geometric multigrid algorithm for solving variable-coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann boundary conditions) using highly nonuniform, octree-based, conforming finite element discretizations. Our octrees are 2:1 balanced, that is, we allow no more than one octree-level difference between octants that share a face, edge, or vertex. We describe a parallel algorithm whose input is an arbitrary 2:1 balanced fine-grid octree and whose output is a set of coarser 2:1 balanced octrees that are used in the multigrid scheme. Also, we derive matrix-free schemes for the discretized finite element operators and the intergrid transfer operations. The overall scheme is second-order accurate for sufficiently smooth right-hand sides and material properties; its complexity for nearly uniform trees is {Omicron}(N/n{sub p} log N/n{sub p}) + {Omicron}(n{sub p} log n{sub p}), where N is the number of octree nodes and n{sub p} is the number of processors. Our implementation uses the Message Passing Interface standard. We present numerical experiments for the Laplace and Navier (linear elasticity) operators that demonstrate the scalability of our method. Our largest run was a highly nonuniform, 8-billion-unknown, elasticity calculation using 32,000 processors on the Teragrid system, 'Ranger,' at the Texas Advanced Computing Center. Our implementation is publically available in the Dendro library, which is built on top of the PETSc library from Argonne National Laboratory.
NASA Technical Reports Server (NTRS)
Kleb, William L.; Williams, Marc H.; Batina, John T.
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.
Toward automatic finite element analysis
NASA Technical Reports Server (NTRS)
Kela, Ajay; Perucchio, Renato; Voelcker, Herbert
1987-01-01
Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.
NASA Astrophysics Data System (ADS)
Becker, P.; Idelsohn, S. R.; Oñate, E.
2015-06-01
This paper describes a strategy to solve multi-fluid and fluid-structure interaction (FSI) problems using Lagrangian particles combined with a fixed finite element (FE) mesh. Our approach is an extension of the fluid-only PFEM-2 (Idelsohn et al., Eng Comput 30(2):2-2, 2013; Idelsohn et al., J Numer Methods Fluids, 2014) which uses explicit integration over the streamlines to improve accuracy. As a result, the convective term does not appear in the set of equations solved on the fixed mesh. Enrichments in the pressure field are used to improve the description of the interface between phases.
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.
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.
Parallel adaptive simplical re-meshing for deforming domain CFD computations
NASA Astrophysics Data System (ADS)
Menon, Sandeep; Mooney, Kyle G.; Stapf, K. G.; Schmidt, David P.
2015-10-01
Deforming domains occur in many fields of computational fluid dynamics (CFD), such as interface tracking, simulation of pumps and engines, and fluid/structure interaction. The deformation of the domain presents a challenge to the integrity of the computational mesh; substantial motion of the domain boundaries requires vertex motion and changes in mesh connectivity. For cases of simple boundary motion or structured meshes, predetermined changes to the mesh structure can be sufficient. However, without a priori knowledge of how the domain will change, a more robust solution is required. The present work offers a parallelized solution for simplical meshes that is well-suited to extremely complex geometry. The mesh continuously evolves without user intervention or the use of target meshes. Varying length scales imposed by evolving boundary curvatures and narrow gaps are resolved with a fast length-scale algorithm. The set of algorithms are incorporated into an object-oriented code structure that permits broad application to a range of CFD problems. The robustness and versatility of the algorithm is demonstrated in several examples, representing motion of internal and external boundaries, where the boundary motion may or may not be known a priori.
Projections of grounding line retreat in West Antarctica carried out with an adaptive mesh model
NASA Astrophysics Data System (ADS)
Cornford, Stephen; Payne, Antony; Martin, Daniel; Le Brocq, Anne
2013-04-01
Present and future sea level rise associated with mass loss from West Antarctica is typically attributed to marine glaciers retreating in response to a warming ocean. Warmer waters melt the floating ice shelves that restrain some, if not all, marine glaciers, and the glaciers themselves respond by speeding up. That leads to thinning and in turn grounding line retreat. Satellite observations indicate that Amundsen Sea Embayment and, in particular, Pine Island Glacier, are undergoing this kind of dynamic change today. Numerical models, however, struggle to reproduce the observed behavior because either high resolution or some other kind special treatment is required at the grounding line. We present 200-year projections of three major glacier systems of West Antarctica: those that drain into the Amundsen Sea , the Filchner-Ronne Ice Shelf and the Ross Ice shelf. We do so using the newly developed BISICLES ice sheet model, which employs adaptive mesh refinement to maintain sub-kilometer resolution close to the grounding line and coarser resolution elsewhere. Ice accumulation and ice shelf melt-rate are derived from a range of models of the Antarctic atmosphere and ocean forced by the SRES A1B and E1 scenarios. We find that a substantial proportion of the grounding line in West Antarctica retreats, however the total sea level rise is less than 50 mm by 2100, and less than 100 mm by 2200. The lion's share of the mass loss is attributed to Pine Island Glacier, while its immediate neighbor Thwaites Glacier does not retreat until the end of the simulations.
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.
Kelley, Mireille E; Miller, Logan E; Urban, Jillian E; Stitzel, Joel D
2015-01-01
The brain-skull interface plays an important role in the strain and pressure response of the brain due to impact. In this study, a finite element (FE) model was developed from a brain atlas, representing an adult brain, by converting each 1mm isotropic voxel into a single element of the same size using a custom code developed in MATLAB. This model includes the brain (combined cerebrum and cerebellum), cerebrospinal fluid (CSF), ventricles, and a rigid skull. A voxel-based approach to develop a FE model causes the outer surface of each part to be stair-stepped, which may affect the stress and strain measurements at interfaces between parts. To improve the interaction between the skull, CSF, and brain surfaces, a previously developed mesh smoothing algorithm based on a Laplacian non-shrinking smoothing algorithm was applied to the FE model. This algorithm not only applies smoothing to the surface of the model, but also to the interfaces between the brain, CSF, and skull, while preserving volume and element quality. Warpage, jacobian, aspect ratio, and skew were evaluated and reveal that >99% of the elements retain good element quality. Future work includes implementation of contact definitions to accurately represent the brain-skull interface and to ultimately better understand and predict head injury. PMID:25996716
NASA Astrophysics Data System (ADS)
Alvarez Laguna, A.; Lani, A.; Deconinck, H.; Mansour, N. N.; Poedts, S.
2016-08-01
We present a Finite Volume scheme for solving Maxwell's equations coupled to magnetized multi-fluid plasma equations for reactive and collisional partially ionized flows on unstructured meshes. The inclusion of the displacement current allows for studying electromagnetic wave propagation in a plasma as well as charge separation effects beyond the standard magnetohydrodynamics (MHD) description, however, it leads to a very stiff system with characteristic velocities ranging from the speed of sound of the fluids up to the speed of light. In order to control the fulfillment of the elliptical constraints of the Maxwell's equations, we use the hyperbolic divergence cleaning method. In this paper, we extend the latter method applying the CIR scheme with scaled numerical diffusion in order to balance those terms with the Maxwell flux vectors. For the fluids, we generalize the AUSM+-up to multiple fluids of different species within the plasma. The fully implicit second-order method is first verified on the Hartmann flow (including comparison with its analytical solution), two ideal MHD cases with strong shocks, namely, Orszag-Tang and the MHD rotor, then validated on a much more challenging case, representing a two-fluid magnetic reconnection under solar chromospheric conditions. For the latter case, a comparison with pioneering results available in literature is provided.
Stresses in faulted tunnel models by photoelasticity and adaptive finite element
Ladkany, S.G.; Huang, Y.
1995-12-01
Research efforts in this area continue to investigate the development of a proper technique to analyze the stresses in the Ghost Dance fault and the effect of the fault on the stability of drifts in the proposed repository. Results from two parallel techniques are being compared to each other - Photoelastic models and Finite Element (FE) models. The Photoelastic plexiglass model (88.89 mm thick & 256.1 mm long and wide) has two adjacent spare openings (57.95 mm long and wide) and a central round opening (57.95 mm diameter) placed at a clear distance approximately equal to its diameter from the square openings. The vertical loading on top of the model is 2269 N (500 lb.). Saw cuts (0.5388 mm wide), representing a fault, are being propagated from the tunnels outward with stress measurements taken at predefined locations, as the saw cuts increase in length. The FE model duplicates exactly the Photoelastic models. The adaptive mesh generation method is used to refine the FE grid at every step of the analysis. This nonlinear interactive computational techniques uses various uses various percent tolerance errors in the convergence of stress values as a measure in ending the iterative process.
Adaptive finite element methods for two-dimensional problems in computational fracture mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1994-01-01
Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.
NASA Astrophysics Data System (ADS)
Sui, Yi; Spelt, Peter D. M.; Ding, Hang
2010-11-01
Diffuse Interface (DI) methods are employed widely for the numerical simulation of two-phase flows, even with moving contact lines. In a DI method, the interface thickness should be as thin as possible to simulate spreading phenomena under realistic flow conditions, so a fine grid is required, beyond the reach of current methods that employ a uniform grid. Here we have integrated a DI method based on a uniform mesh, to a block-based adaptive mesh refinement method, so that only the regions near the interface are resolved by a fine mesh. The performance of the present method is tested by simulations including drop deformation in shear flow, Rayleigh-Taylor instability and drop spreading on a flat surface, et al. The results show that the present method can give accurate results with much smaller computational cost, compared to the original DI method based on a uniform mesh. Based on the present method, simulation of drop spreading is carried out with Cahn number of 0.001 and the contact line region is well resolved. The flow field near the contact line, the contact line speed as well as the apparent contact angle are investigated in detail and compared with previous analytical work.
NASA Astrophysics Data System (ADS)
Zheng, H. W.; Shu, C.; Chew, Y. T.
2008-07-01
In this paper, an object-oriented and quadrilateral-mesh based solution adaptive algorithm for the simulation of compressible multi-fluid flows is presented. The HLLC scheme (Harten, Lax and van Leer approximate Riemann solver with the Contact wave restored) is extended to adaptively solve the compressible multi-fluid flows under complex geometry on unstructured mesh. It is also extended to the second-order of accuracy by using MUSCL extrapolation. The node, edge and cell are arranged in such an object-oriented manner that each of them inherits from a basic object. A home-made double link list is designed to manage these objects so that the inserting of new objects and removing of the existing objects (nodes, edges and cells) are independent of the number of objects and only of the complexity of O( 1). In addition, the cells with different levels are further stored in different lists. This avoids the recursive calculation of solution of mother (non-leaf) cells. Thus, high efficiency is obtained due to these features. Besides, as compared to other cell-edge adaptive methods, the separation of nodes would reduce the memory requirement of redundant nodes, especially in the cases where the level number is large or the space dimension is three. Five two-dimensional examples are used to examine its performance. These examples include vortex evolution problem, interface only problem under structured mesh and unstructured mesh, bubble explosion under the water, bubble-shock interaction, and shock-interface interaction inside the cylindrical vessel. Numerical results indicate that there is no oscillation of pressure and velocity across the interface and it is feasible to apply it to solve compressible multi-fluid flows with large density ratio (1000) and strong shock wave (the pressure ratio is 10,000) interaction with the interface.
H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows
NASA Technical Reports Server (NTRS)
Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.
1993-01-01
The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).
Feature-Sensitive Tetrahedral Mesh Generation with Guaranteed Quality
Wang, Jun; Yu, Zeyun
2012-01-01
Tetrahedral meshes are being extensively used in finite element methods (FEM). This paper proposes an algorithm to generate feature-sensitive and high-quality tetrahedral meshes from an arbitrary surface mesh model. A top-down octree subdivision is conducted on the surface mesh and a set of tetrahedra are constructed using adaptive body-centered cubic (BCC) lattices. Special treatments are given to the tetrahedra near the surface such that the quality of the resulting tetrahedral mesh is provably guaranteed: the smallest dihedral angle is always greater than 5.71°. The meshes generated by our method are not only adaptive from the interior to the boundary, but also feature-sensitive on the surface with denser elements in high-curvature regions where geometric feature most likely reside. A variety of experimental results are presented to demonstrate the effectiveness and robustness of this algorithm. PMID:22328787
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.
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
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.
2008-01-01
Parallel Heterogeneous Dynamic unstructured Mesh (phdMesh) data structure library and integration testing code that performs dynamic load balancing of the data structure and parallel geometric proximity search on a contrived test problem. The phdMesh library is intended to be module within a finite element or finite volume library or code. The integration testing code is intended to provide a compact and highly portable performance evaluation code for parallel computing systems.
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.
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.
Choi, Young Joon; Jorshari, Razzi Movassaghi; Djilali, Ned
2015-03-10
Direct numerical simulations of the flow-nanoparticle interaction in a colloidal suspension are presented using an extended finite element method (XFEM) in which the dynamics of the nanoparticles is solved in a fully-coupled manner with the flow. The method is capable of accurately describing solid-fluid interfaces without the need of boundary-fitted meshes to investigate the dynamics of particles in complex flows. In order to accurately compute the high interparticle shear stresses and pressures while minimizing computing costs, an adaptive meshing technique is incorporated with the fluid-structure interaction algorithm. The particle-particle interaction at the microscopic level is modeled using the Lennard-Jones (LJ) potential and the corresponding potential parameters are determined by a scaling procedure. The study is relevant to the preparation of inks used in the fabrication of catalyst layers for fuel cells. In this paper, we are particularly interested in investigating agglomeration of the nanoparticles under external shear flow in a sliding bi-periodic Lees-Edwards frame. The results indicate that the external shear has a crucial impact on the structure formation of colloidal particles in a suspension.
NASA Technical Reports Server (NTRS)
Balas, M. J.
1985-01-01
Distributed Parameter Systems (DPS), such as systems described by partial differential equations, require infinite-dimensional state space descriptions to correctly model their dynamical behavior. However, any adaptive control algorithm must be finite-dimensional in order to be implemented via on-line digital computers. Finite-dimensional adaptive control of linear DPS requires stability analysis of nonlinear, time-varying, infinite-dimensional systems. The structure of nonadaptive finite-dimensional control of linear DPS is summarized as it relates to the existence of limiting systems for adaptive control. Two candidate schemes for finite-dimensional adaptive control of DPS are described and critical issues in infinite-dimensional stability analysis are discussed, in particular, the invariance principle, center manifold theory, and relationships between input-output and internal stability.
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.
NASA Technical Reports Server (NTRS)
Fasanella, Edwin L.; Jackson, Karen E.; Lyle, Karen H.; Spellman, Regina L.
2006-01-01
A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0-in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at four discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density.
Väänänen, Sami P; Grassi, Lorenzo; Flivik, Gunnar; Jurvelin, Jukka S; Isaksson, Hanna
2015-08-01
Areal bone mineral density (aBMD), as measured by dual-energy X-ray absorptiometry (DXA), predicts hip fracture risk only moderately. Simulation of bone mechanics based on DXA imaging of the proximal femur, may help to improve the prediction accuracy. Therefore, we collected three (1-3) image sets, including CT images and DXA images of 34 proximal cadaver femurs (set 1, including 30 males, 4 females), 35 clinical patient CT images of the hip (set 2, including 27 males, 8 females) and both CT and DXA images of clinical patients (set 3, including 12 female patients). All CT images were segmented manually and landmarks were placed on both femurs and pelvises. Two separate statistical appearance models (SAMs) were built using the CT images of the femurs and pelvises in sets 1 and 2, respectively. The 3D shape of the femur was reconstructed from the DXA image by matching the SAMs with the DXA images. The orientation and modes of variation of the SAMs were adjusted to minimize the sum of the absolute differences between the projection of the SAMs and a DXA image. The mesh quality and the location of the SAMs with respect to the manually placed control points on the DXA image were used as additional constraints. Then, finite element (FE) models were built from the reconstructed shapes. Mean point-to-surface distance between the reconstructed shape and CT image was 1.0 mm for cadaver femurs in set 1 (leave-one-out test) and 1.4 mm for clinical subjects in set 3. The reconstructed volumetric BMD showed a mean absolute difference of 140 and 185 mg/cm(3) for set 1 and set 3 respectively. The generation of the SAM and the limitation of using only one 2D image were found to be the most significant sources of errors in the shape reconstruction. The noise in the DXA images had only small effect on the accuracy of the shape reconstruction. DXA-based FE simulation was able to explain 85% of the CT-predicted strength of the femur in stance loading. The present method can be used to
Computational results for parallel unstructured mesh computations
Jones, M.T.; Plassmann, P.E.
1994-12-31
The majority of finite element models in structural engineering are composed of unstructured meshes. These unstructured meshes are often very large and require significant computational resources; hence they are excellent candidates for massively parallel computation. Parallel solution of the sparse matrices that arise from such meshes has been studied heavily, and many good algorithms have been developed. Unfortunately, many of the other aspects of parallel unstructured mesh computation have gone largely ignored. The authors present a set of algorithms that allow the entire unstructured mesh computation process to execute in parallel -- including adaptive mesh refinement, equation reordering, mesh partitioning, and sparse linear system solution. They briefly describe these algorithms and state results regarding their running-time and performance. They then give results from the 512-processor Intel DELTA for a large-scale structural analysis problem. These results demonstrate that the new algorithms are scalable and efficient. The algorithms are able to achieve up to 2.2 gigaflops for this unstructured mesh problem.
NASA Technical Reports Server (NTRS)
Jackson, Karen E.; Fasanella, Edwin L.; Lyle, Karen H.; Spellman, Regina L.
2004-01-01
A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0- in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA version 960 for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at five discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density. As a final comparison, the model with a fine panel and fine foam mesh was executed with slightly different material properties for the RCC. For this model, the average degraded properties of the RCC were replaced with the maximum degraded properties. Similar comparisons of panel and foam responses were made for the average and maximum degraded models.
Adaptive grid finite element model of the tokamak scrapeoff layer
Kuprat, A.P.; Glasser, A.H.
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
NASA Astrophysics Data System (ADS)
Danilov, A. A.; Salamatova, V. Yu; Vassilevski, Yu V.
2012-12-01
Here, a workflow for high-resolution efficient numerical modeling of bioimpedance measurements is suggested that includes 3D image segmentation, adaptive mesh generation, finite-element discretization, and the analysis of simulation results. Using the adaptive unstructured tetrahedral meshes enables to decrease significantly a number of mesh elements while keeping model accuracy. The numerical results illustrate current, potential, and sensitivity field distributions for a conventional Kubicek-like scheme of bioimpedance measurements using segmented geometric model of human torso based on Visible Human Project data. The whole body VHP man computational mesh is constructed that contains 574 thousand vertices and 3.3 million tetrahedrons.
Evaluation of discretization procedures for transition elements in adaptive mesh refinement
NASA Technical Reports Server (NTRS)
Park, K. C.; Levit, Itzak; Stanley, Gary M.
1991-01-01
Three transition interpolation schemes for use in h-or r-refinement have been analyzed in terms of accuracy, implementation ease and extendability. They include blending-function interpolation, displacement averaging, and strain matching at discrete points along the transition edge lines. The results suggest that the choice of matching depends strongly on the element formulations, (viz. displacement or assumed strain, etc.) and mesh refinement criteria employed, and to a lesser extent the choice of computer architecture (serial vs. parallel) and the equation solution procedures. A recommended pairing of some of the elements with the choice factors is suggested.
Octree based automatic meshing from CSG models
NASA Technical Reports Server (NTRS)
Perucchio, Renato
1987-01-01
Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.
An efficient parallel algorithm for mesh smoothing
Freitag, L.; Plassmann, P.; Jones, M.
1995-12-31
Automatic mesh generation and adaptive refinement methods have proven to be very successful tools for the efficient solution of complex finite element applications. A problem with these methods is that they can produce poorly shaped elements; such elements are undesirable because they introduce numerical difficulties in the solution process. However, the shape of the elements can be improved through the determination of new geometric locations for mesh vertices by using a mesh smoothing algorithm. In this paper the authors present a new parallel algorithm for mesh smoothing that has a fast parallel runtime both in theory and in practice. The authors present an efficient implementation of the algorithm that uses non-smooth optimization techniques to find the new location of each vertex. Finally, they present experimental results obtained on the IBM SP system demonstrating the efficiency of this approach.
Large spatial, temporal, and algorithmic adaptivity for implicit nonlinear finite element analysis
Engelmann, B.E.; Whirley, R.G.
1992-07-30
The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis has been the subject of much research in recent years. Robust algorithms are needed to handle the complex nonlinearities that arise in many implicit finite element applications such as metalforming process simulation. The authors experience indicates that robustness can best be achieved through adaptive solution strategies. In the course of their research, this adaptivity and flexibility has been refined into a production tool through the development of a solution control language called ISLAND. This paper discusses aspects of adaptive solution strategies including iterative procedures to solve the global equations and remeshing techniques to extend the domain of Lagrangian methods. Examples using the newly developed ISLAND language are presented to illustrate the advantages of embedding temporal, algorithmic, and spatial adaptivity in a modem implicit nonlinear finite element analysis code.
NASA Astrophysics Data System (ADS)
Jeshvaghani, Mehdi Shahmirzae; Darijani, Mehrdad
2014-06-01
Forward modeling approach is a major concept in geophysical exploration and also a key factor in the development of inversion algorithms. Finite element method for two-dimensional (2-D) geomagnetic forward modeling is based on numerical solution of the Laplace equation. In this paper we present a fast and accurate adaptive finite element algorithm for forward modeling of 2-D geomagnetic structures. Our method is stable and is reliable to recover 2-D magnetization distribution with complex shapes. It uses an unstructured triangular grid which allows modeling the complex geometry with the presence of topography. The Galerkin's method is used to derive the systems of equations. Then, the conjugate gradient solver with incomplete LU decomposition as the pre-conditioner is used to solve the system of equations. To ensure numerical accuracy, iterative mesh refinement is guided by a posteriori error estimator. We validate our algorithm in simple geometry by analytical technique. The tests on synthetic data illustrate a good performance of the method in mapping the complex geometry of the magnetic sources with topography. The magnetic responses of the model have proved to be different in the presence of topography. Therefore, it is highly recommended to consider the effects of topography on interpretation. Finally, we applied numerical FEM algorithm to real data set providing fine recovery model of the shallow high mineralized crustal setting of Soltanieh region, Iran.
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.
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.
Armstrong, Jerawan C.; Favorite, Jeffrey A.
2012-06-20
The Levenberg-Marquardt (or simply Marquardt) and differential evolution (DE) optimization methods were recently applied to solve inverse transport problems. The Marquardt method is fast but convergence of the method is dependent on the initial guess. While it has been shown to work extremely well at finding an optimum independent of the initial guess, the DE method does not provide a global optimal solution in some problems. In this paper, we apply the Mesh Adaptive Direct Search (MADS) algorithm to solve the inverse problem of material interface location identification in one-dimensional spherical radiation source/shield systems, and we compare the results obtained by MADS to those obtained by Levenberg-Marquardt and DE.
A p-adaptive stabilized finite element method for fluid dynamics
NASA Astrophysics Data System (ADS)
Karanam, Anil Kumar
2008-10-01
Stabilized finite element methods have been shown to yield robust, accurate numerical solutions to both the compressible and incompressible Navier-Stokes equations for laminar and turbulent flows. This work presents an application of mesh entity based, hierarchical basis functions to a new stabilized finite element formulation, exploiting the capability to grade polynomial order while maintaining C0 continuity while using traditional finite element data structures. The hierarchical basis accomplishes this by starting with vertex interpolants (a linear basis) and then allowing the polynomial order to vary on each entity (edges, faces, and regions) in the mesh which are then multiplied by blends within each element to build a composite function that is locally higher order but still globally continuous. Details of this formulation and its efficient implementation will be presented. Partition weighting schemes were developed to achieve optimal load balance and scalability for parallel simulations. An application is presented, of p-refinement applied to a laminar flow past a surface mounted unit cube placed in a channel. Finally, post-processing techniques are also described for the effective visualization of higher order solutions.
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Dumbser, Michael
2014-10-01
In this paper we present a new family of high order accurate Arbitrary-Lagrangian-Eulerian (ALE) one-step ADER-WENO finite volume schemes for the solution of nonlinear systems of conservative and non-conservative hyperbolic partial differential equations with stiff source terms on moving tetrahedral meshes in three space dimensions. A WENO reconstruction technique is used to achieve high order of accuracy in space, while an element-local space-time Discontinuous Galerkin finite element predictor on moving curved meshes is used to obtain a high order accurate one-step time discretization. Within the space-time predictor the physical element is mapped onto a reference element using a high order isoparametric approach, where the space-time basis and test functions are given by the Lagrange interpolation polynomials passing through a predefined set of space-time nodes. Since our algorithm is cell-centered, the final mesh motion is computed by using a suitable node solver algorithm. A rezoning step as well as a flattener strategy are used in some of the test problems to avoid mesh tangling or excessive element deformations that may occur when the computation involves strong shocks or shear waves. The ALE algorithm presented in this article belongs to the so-called direct ALE methods because the final Lagrangian finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, with the rezoned geometry taken already into account during the computation of the fluxes. We apply our new high order unstructured ALE schemes to the 3D Euler equations of compressible gas dynamics, for which a set of classical numerical test problems has been solved and for which convergence rates up to sixth order of accuracy in space and time have been obtained. We furthermore consider the equations of classical ideal magnetohydrodynamics (MHD) as well as the non-conservative seven-equation Baer-Nunziato model of compressible multi-phase flows with
Optimization of tetrahedral meshes
Briere De L`Isle, E.; George, P.L.
1995-12-31
Finite element computations are all the more exact if we start from {open_quotes}good{close_quotes} elements. We are interested in meshes where the elements are tetrahedra and we shall develop utilities allowing us to improve the quality of these meshes.
Technology Transfer Automated Retrieval System (TEKTRAN)
A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the...
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
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.
Multi-level adaptive finite element methods. 1: Variation problems
NASA Technical Reports Server (NTRS)
Brandt, A.
1979-01-01
A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.
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.
An adaptive finite element method for convective heat transfer with variable fluid properties
NASA Astrophysics Data System (ADS)
Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois
1993-07-01
This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems for which fluid properties present a strong temperature dependence. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Two general purpose error estimators, that take into account fluid properties variations, are presented. The methodology is applied to a problem of practical interest: the thermal convection of corn syrup in an enclosure with localized heating. Predictions are in good agreement with experimental measurements. The method leads to improved accuracy and reliability of finite element predictions.
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.
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.
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 massively parallel adaptive finite element method with dynamic load balancing
Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.
1993-05-01
We construct massively parallel, adaptive finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. We also present results using adaptive p-refinement to reduce the computational cost of the method. We describe tiling, a dynamic, element-based data migration system. Tiling dynamically maintains global load balance in the adaptive method by overlapping neighborhoods of processors, where each neighborhood performs local load balancing. We demonstrate the effectiveness of the dynamic load balancing with adaptive p-refinement examples.
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. PMID:19840985
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.
NASA Astrophysics Data System (ADS)
Padmanabhan, R.; Oliveira, M. C.; Baptista, A. J.; Alves, J. L.; Menezes, L. F.
2007-05-01
Springback phenomenon associated with the elastic properties of sheet metals makes the design of forming dies a complex task. Thus, to develop consistent algorithms for springback compensation an accurate prediction of the amount of springback is mandatory. The numerical simulation using the finite element method is consensually the only feasible method to predict springback. However, springback prediction is a very complicated task and highly sensitive to various numerical parameters of finite elements (FE), such as: type, order, integration scheme, shape and size, as well the time integration formulae and the unloading strategy. All these numerical parameters make numerical simulation of springback more sensitive to numerical tolerances than the forming operation. In case of an unconstrained cylindrical bending, the in-plane to thickness FE size ratio is more relevant than the number of FE layers through-thickness, for the numerical prediction of final stress and strain states, variables of paramount importance for an accurate springback prediction. The aim of the present work is to evaluate the influence of the refinement of a 3-D FE mesh, namely the in-plane mesh refinement and the number of through-thickness FE layers, in springback prediction. The selected example corresponds to the first stage of the "Numisheet'05 Benchmark♯3", which consists basically in the sheet forming of a channel section in an industrial-scale channel draw die. The physical drawbeads are accurately taken into account in the numerical model in order to accurately reproduce its influence during the forming process simulation. FEM simulations were carried out with the in-house code DD3IMP. Solid finite elements were used. They are recommended for accuracy in FE springback simulation when the ratio between the tool radius and blank thickness is lower than 5-6. In the selected example the drawbead radius is 4.0 mm. The influence of the FE mesh refinement in springback prediction is
NASA Astrophysics Data System (ADS)
von Sydow, Lina
2013-10-01
The discontinuous Galerkin method for time integration of the Black-Scholes partial differential equation for option pricing problems is studied and compared with more standard time-integrators. In space an adaptive finite difference discretization is employed. The results show that the dG method are in most cases at least comparable to standard time-integrators and in some cases superior to them. Together with adaptive spatial grids the suggested pricing method shows great qualities.
Adaptive implicit-explicit finite element algorithms for fluid mechanics problems
NASA Technical Reports Server (NTRS)
Tezduyar, T. E.; Liou, J.
1988-01-01
The adaptive implicit-explicit (AIE) approach is presented for the finite-element solution of various problems in computational fluid mechanics. In the AIE approach, the elements are dynamically (adaptively) arranged into differently treated groups. The differences in treatment could be based on considerations such as the cost efficiency, the type of spatial or temporal discretization employed, the choice of field equations, etc. Several numerical tests are performed to demonstrate that this approach can achieve substantial savings in CPU time and memory.
Wieselquist, William A.; Anistratov, Dmitriy Y.; Morel, Jim E.
2014-09-15
We present a quasidiffusion (QD) method for solving neutral particle transport problems in Cartesian XY geometry on unstructured quadrilateral meshes, including local refinement capability. Neutral particle transport problems are central to many applications including nuclear reactor design, radiation safety, astrophysics, medical imaging, radiotherapy, nuclear fuel transport/storage, shielding design, and oil well-logging. The primary development is a new discretization of the low-order QD (LOQD) equations based on cell-local finite differences. The accuracy of the LOQD equations depends on proper calculation of special non-linear QD (Eddington) factors from a transport solution. In order to completely define the new QD method, a proper discretization of the transport problem is also presented. The transport equation is discretized by a conservative method of short characteristics with a novel linear approximation of the scattering source term and monotonic, parabolic representation of the angular flux on incoming faces. Analytic and numerical tests are used to test the accuracy and spatial convergence of the non-linear method. All tests exhibit O(h{sup 2}) convergence of the scalar flux on orthogonal, random, and multi-level meshes.
Park, S.J.; Song, J.H.
1999-07-01
A two-dimensional elastic-plastic finite element analysis is performed for plane stress conditions with 4-node isoparametric elements to investigate the closure behavior under various variable-amplitude loading, i.e., single overloading, Hi-Lo block loading, and narrow- and wide-band random loading. The closure behavior under single overloading and Hi-Lo block loading can be well simulated by applying the concept of the most appropriate mesh size that will provide numerical results consistent with experimental data under constant-amplitude loading. It is found that the crack opening load under random loading may be predicted approximately by replacing the complicated random load history with the appropriate equivalent, simplified variable load history.
A massively parallel adaptive finite element method with dynamic load balancing
Devine, K.D.; Flaherty, J.E.; Wheat, S.R.; Maccabe, A.B.
1993-12-31
The authors construct massively parallel adaptive finite element methods for the solution of hyperbolic conservation laws. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. The resulting method is of high order and may be parallelized efficiently on MIMD computers. They demonstrate parallel efficiency through computations on a 1024-processor nCUBE/2 hypercube. They present results using adaptive p-refinement to reduce the computational cost of the method, and tiling, a dynamic, element-based data migration system that maintains global load balance of the adaptive method by overlapping neighborhoods of processors that each perform local balancing.
Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites
NASA Technical Reports Server (NTRS)
Gao, Xiujie; Burton, Deborah; Turner, Travis L.; Brinson, Catherine
2005-01-01
Shape memory alloy hybrid composites with adaptive-stiffening or morphing functions are simulated using finite element analysis. The composite structure is a laminated fiber-polymer composite beam with embedded SMA ribbons at various positions with respect to the neutral axis of the beam. Adaptive stiffening or morphing is activated via selective resistance heating of the SMA ribbons or uniform thermal loads on the beam. The thermomechanical behavior of these composites was simulated in ABAQUS using user-defined SMA elements. The examples demonstrate the usefulness of the methods for the design and simulation of SMA hybrid composites. Keywords: shape memory alloys, Nitinol, ABAQUS, finite element analysis, post-buckling control, shape control, deflection control, adaptive stiffening, morphing, constitutive modeling, user element
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.
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.
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.