Adaptive Mesh Refinement Algorithms for Parallel Unstructured Finite Element Codes
Parsons, I D; Solberg, J M
2006-02-03
This project produced algorithms for and software implementations of adaptive mesh refinement (AMR) methods for solving practical solid and thermal mechanics problems on multiprocessor parallel computers using unstructured finite element meshes. The overall goal is to provide computational solutions that are accurate to some prescribed tolerance, and adaptivity is the correct path toward this goal. These new tools will enable analysts to conduct more reliable simulations at reduced cost, both in terms of analyst and computer time. Previous academic research in the field of adaptive mesh refinement has produced a voluminous literature focused on error estimators and demonstration problems; relatively little progress has been made on producing efficient implementations suitable for large-scale problem solving on state-of-the-art computer systems. Research issues that were considered include: effective error estimators for nonlinear structural mechanics; local meshing at irregular geometric boundaries; and constructing efficient software for parallel computing environments.
Lee, W; Kim, T-S; Cho, M; Lee, S
2005-01-01
In studying bioelectromagnetic problems, finite element method offers several advantages over other conventional methods such as boundary element method. It allows truly volumetric analysis and incorporation of material properties such as anisotropy. Mesh generation is the first requirement in the finite element analysis and there are many different approaches in mesh generation. However conventional approaches offered by commercial packages and various algorithms do not generate content-adaptive meshes, resulting in numerous elements in the smaller volume regions, thereby increasing computational load and demand. In this work, we present an improved content-adaptive mesh generation scheme that is efficient and fast along with options to change the contents of meshes. For demonstration, mesh models of the head from a volume MRI are presented in 2-D and 3-D.
A Mass Conservation Algorithm for Adaptive Unrefinement Meshes Used by Finite Element Methods
2012-01-01
dimensional mesh generation. In: Proc. 4th ACM-SIAM Symp. on Disc. Algorithms. (1993) 83–92 [9] Weatherill, N., Hassan, O., Marcum, D., Marchant, M.: Grid ...Conference on Computational Science, ICCS 2012 A Mass Conservation Algorithm For Adaptive Unrefinement Meshes Used By Finite Element Methods Hung V. Nguyen...velocity fields, and chemical distribution, as well as conserve mass, especially for water quality applications. Solution accuracy depends highly on mesh
Adaptive meshing technique applied to an orthopaedic finite element contact problem.
Roarty, Colleen M; Grosland, Nicole M
2004-01-01
Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants. Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely applied in the analysis and design of hip and knee implants, with additional joints (ankle, shoulder, wrist) attracting increased attention. The objective of this investigation was to develop a simplified adaptive meshing scheme to facilitate the finite element analysis of a dual-curvature total wrist implant. Using currently available software, the analyst has great flexibility in mesh generation, but must prescribe element sizes and refinement schemes throughout the domain of interest. Unfortunately, it is often difficult to predict in advance a mesh spacing that will give acceptable results. Adaptive finite-element mesh capabilities operate to continuously refine the mesh to improve accuracy where it is required, with minimal intervention by the analyst. Such mesh adaptation generally means that in certain areas of the analysis domain, the size of the elements is decreased (or increased) and/or the order of the elements may be increased (or decreased). In concept, mesh adaptation is very appealing. Although there have been several previous applications of adaptive meshing for in-house FE codes, we have coupled an adaptive mesh formulation with the pre-existing commercial programs PATRAN (MacNeal-Schwendler Corp., USA) and ABAQUS (Hibbit Karlson and Sorensen, Pawtucket, RI). In doing so, we have retained several attributes of the commercial software, which are very attractive for orthopaedic implant applications.
Adaptive superposition of finite element meshes in linear and nonlinear dynamic analysis
NASA Astrophysics Data System (ADS)
Yue, Zhihua
2005-11-01
The numerical analysis of transient phenomena in solids, for instance, wave propagation and structural dynamics, is a very important and active area of study in engineering. Despite the current evolutionary state of modern computer hardware, practical analysis of large scale, nonlinear transient problems requires the use of adaptive methods where computational resources are locally allocated according to the interpolation requirements of the solution form. Adaptive analysis of transient problems involves obtaining solutions at many different time steps, each of which requires a sequence of adaptive meshes. Therefore, the execution speed of the adaptive algorithm is of paramount importance. In addition, transient problems require that the solution must be passed from one adaptive mesh to the next adaptive mesh with a bare minimum of solution-transfer error since this form of error compromises the initial conditions used for the next time step. A new adaptive finite element procedure (s-adaptive) is developed in this study for modeling transient phenomena in both linear elastic solids and nonlinear elastic solids caused by progressive damage. The adaptive procedure automatically updates the time step size and the spatial mesh discretization in transient analysis, achieving the accuracy and the efficiency requirements simultaneously. The novel feature of the s-adaptive procedure is the original use of finite element mesh superposition to produce spatial refinement in transient problems. The use of mesh superposition enables the s-adaptive procedure to completely avoid the need for cumbersome multipoint constraint algorithms and mesh generators, which makes the s-adaptive procedure extremely fast. Moreover, the use of mesh superposition enables the s-adaptive procedure to minimize the solution-transfer error. In a series of different solid mechanics problem types including 2-D and 3-D linear elastic quasi-static problems, 2-D material nonlinear quasi-static problems
Lee, W H; Kim, T-S; Cho, M H; Ahn, Y B; Lee, S Y
2006-12-07
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.
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.
NASA Astrophysics Data System (ADS)
Schwing, Alan Michael
For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable
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.
ADER-WENO finite volume schemes with space-time adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.
2013-09-01
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.
Fakhari, Abbas; Lee, Taehun
2014-03-01
An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.
NASA Astrophysics Data System (ADS)
Fakhari, Abbas; Lee, Taehun
2014-03-01
An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.
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.
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.
Lee, Won Hee; Kim, Tae-Seong
2012-01-01
This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions
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.
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.
NASA Astrophysics Data System (ADS)
Viré, Axelle; Xiang, Jiansheng; Milthaler, Frank; Farrell, Patrick Emmet; Piggott, Matthew David; Latham, John-Paul; Pavlidis, Dimitrios; Pain, Christopher Charles
2012-12-01
Fluid-structure interactions are modelled by coupling the finite element fluid/ocean model `Fluidity-ICOM' with a combined finite-discrete element solid model `Y3D'. Because separate meshes are used for the fluids and solids, the present method is flexible in terms of discretisation schemes used for each material. Also, it can tackle multiple solids impacting on one another, without having ill-posed problems in the resolution of the fluid's equations. Importantly, the proposed approach ensures that Newton's third law is satisfied at the discrete level. This is done by first computing the action-reaction force on a supermesh, i.e. a function superspace of the fluid and solid meshes, and then projecting it to both meshes to use it as a source term in the fluid and solid equations. This paper demonstrates the properties of spatial conservation and accuracy of the method for a sphere immersed in a fluid, with prescribed fluid and solid velocities. While spatial conservation is shown to be independent of the mesh resolutions, accuracy requires fine resolutions in both fluid and solid meshes. It is further highlighted that unstructured meshes adapted to the solid concentration field reduce the numerical errors, in comparison with uniformly structured meshes with the same number of elements. The method is verified on flow past a falling sphere. Its potential for ocean applications is further shown through the simulation of vortex-induced vibrations of two cylinders and the flow past two flexible fibres.
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
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
NASA Astrophysics Data System (ADS)
Salinas, Pablo; Pavlidis, Dimitrios; Percival, James; Adam, Alexander; Xie, Zhihua; Pain, Christopher; Jackson, Matthew
2015-11-01
We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at lower cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged.
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.
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.
MeshEZW: an image coder using mesh and finite elements
NASA Astrophysics Data System (ADS)
Landais, Thomas; Bonnaud, Laurent; Chassery, Jean-Marc
2003-08-01
In this paper, we present a new method to compress the information in an image, called MeshEZW. The proposed approach is based on the finite elements method, a mesh construction and a zerotree method. The zerotree method is an adaptive of the EZW algorithm with two new symbols for increasing the performance. These steps allow a progressive representation of the image by the automatic construction of a bitstream. The mesh structure is adapted to the image compression domain and is defined to allow video comrpession. The coder is described and some preliminary results are discussed.
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.
NASA Astrophysics Data System (ADS)
Fakhari, Abbas; Lee, Taehun
2013-11-01
A novel adaptive mesh refinement (AMR) algorithm for the numerical solution of fluid flow problems is presented in this study. The proposed AMR algorithm can be used to solve partial differential equations including, but not limited to, the Navier-Stokes equations using an AMR technique. Here, the lattice Boltzmann method (LBM) is employed as a substitute of the nearly incompressible Navier-Stokes equations. Besides its simplicity, the proposed AMR algorithm is straightforward and yet efficient. The idea is to remove the need for a tree-type data structure by using the pointer attributes in a unique way, along with an appropriate adjustment of the child block's IDs, to determine the neighbors of a certain block. Thanks to the unique way of invoking pointers, there is no need to construct a quad-tree (in 2D) or oct-tree (in 3D) data structure for maintaining the connectivity data between different blocks. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with a clean and efficient algorithm that is easier to implement and use on parallel machines. Several benchmark studies are carried out to assess the accuracy and efficiency of the proposed AMR-LBM, including lid-driven cavity flow, vortex shedding past a square cylinder, and Kelvin-Helmholtz instability for single-phase and multiphase fluids.
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.
Chedid, R.; Najjar, N.
1996-09-01
One of the inconveniences associated with the existing finite-element packages is the need for an educated user to develop a correct mesh at the preprocessing level. Procedures which start with a coarse mesh and attempt serious refinements, as is the case in most adaptive finite-element packages, are time consuming and costly. Hence, it is very important to develop a tool that can provide a mesh that either leads immediately to an acceptable solution, or would require fewer correcting steps to achieve better results. In this paper, the authors present a technique for automatic mesh generation based on artificial neural networks (ANN). The essence of this technique is to predict the mesh density distribution of a given model, and then supply this information to a Kohonen neural network which provides the final mesh. Prediction of mesh density is accomplished by a simple feedforward neural network which has the ability to learn the relationship between mesh density and model geometric features. It will be shown that ANN are able to recognize delicate areas where a sharp variation of the magnetic field is expected. Examples of 2-D models are provided to illustrate the usefulness of the proposed technique.
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
The finite cell method for polygonal meshes: poly-FCM
NASA Astrophysics Data System (ADS)
Duczek, Sascha; Gabbert, Ulrich
2016-10-01
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.
An Adaptive Mesh Algorithm: Mesh Structure and Generation
Scannapieco, Anthony J.
2016-06-21
The purpose of Adaptive Mesh Refinement is to minimize spatial errors over the computational space not to minimize the number of computational elements. The additional result of the technique is that it may reduce the number of computational elements needed to retain a given level of spatial accuracy. Adaptive mesh refinement is a computational technique used to dynamically select, over a region of space, a set of computational elements designed to minimize spatial error in the computational model of a physical process. The fundamental idea is to increase the mesh resolution in regions where the physical variables are represented by a broad spectrum of modes in k-space, hence increasing the effective global spectral coverage of those physical variables. In addition, the selection of the spatially distributed elements is done dynamically by cyclically adjusting the mesh to follow the spectral evolution of the system. Over the years three types of AMR schemes have evolved; block, patch and locally refined AMR. In block and patch AMR logical blocks of various grid sizes are overlaid to span the physical space of interest, whereas in locally refined AMR no logical blocks are employed but locally nested mesh levels are used to span the physical space. The distinction between block and patch AMR is that in block AMR the original blocks refine and coarsen entirely in time, whereas in patch AMR the patches change location and zone size with time. The type of AMR described herein is a locally refi ned AMR. In the algorithm described, at any point in physical space only one zone exists at whatever level of mesh that is appropriate for that physical location. The dynamic creation of a locally refi ned computational mesh is made practical by a judicious selection of mesh rules. With these rules the mesh is evolved via a mesh potential designed to concentrate the nest mesh in regions where the physics is modally dense, and coarsen zones in regions where the physics is modally
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.
Model-Based Nonrigid Motion Analysis Using Natural Feature Adaptive Mesh
Zhang, Y.; Goldgof, D.B.; Sarkar, S.; Tsap, L.V.
2000-04-25
The success of nonrigid motion analysis using physical finite element model is dependent on the mesh that characterizes the object's geometric structure. We suggest a deformable mesh adapted to the natural features of images. The adaptive mesh requires much fewer number of nodes than the fixed mesh which was used in our previous work. We demonstrate the higher efficiency of the adaptive mesh in the context of estimating burn scar elasticity relative to normal skin elasticity using the observed 2D image sequence. Our results show that the scar assessment method based on the physical model using natural feature adaptive mesh can be applied to images which do not have artificial markers.
A study on moving mesh finite element solution of the porous medium equation
NASA Astrophysics Data System (ADS)
Ngo, Cuong; Huang, Weizhang
2017-02-01
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the moving mesh partial differential equation approach and employs its newly developed implementation. The implementation has several improvements over the traditional one, including its explicit, compact form of the mesh velocities, ease to program, and less likelihood of producing singular meshes. Three types of metric tensor that correspond to uniform and arclength-based and Hessian-based adaptive meshes are considered. The method shows first-order convergence for uniform and arclength-based adaptive meshes, and second-order convergence for Hessian-based adaptive meshes. It is also shown that the method can be used for situations with complex free boundaries, emerging and splitting of free boundaries, and the porous medium equation with variable exponents and absorption. Two-dimensional numerical results are presented.
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.
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.
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.
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.
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.
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.
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.
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.
An Adaptive Mesh Algorithm: Mapping the Mesh Variables
Scannapieco, Anthony J.
2016-07-25
Both thermodynamic and kinematic variables must be mapped. The kinematic variables are defined on a separate kinematic mesh; it is the duel mesh to the thermodynamic mesh. The map of the kinematic variables is done by calculating the contributions of kinematic variables on the old thermodynamic mesh, mapping the kinematic variable contributions onto the new thermodynamic mesh and then synthesizing the mapped kinematic variables on the new kinematic mesh. In this document the map of the thermodynamic variables will be described.
Mesh saliency with adaptive local patches
NASA Astrophysics Data System (ADS)
Nouri, Anass; Charrier, Christophe; Lézoray, Olivier
2015-03-01
3D object shapes (represented by meshes) include both areas that attract the visual attention of human observers and others less or not attractive at all. This visual attention depends on the degree of saliency exposed by these areas. In this paper, we propose a technique for detecting salient regions in meshes. To do so, we define a local surface descriptor based on local patches of adaptive size and filled with a local height field. The saliency of mesh vertices is then defined as its degree measure with edges weights computed from adaptive patch similarities. Our approach is compared to the state-of-the-art and presents competitive results. A study evaluating the influence of the parameters establishing this approach is also carried out. The strength and the stability of our approach with respect to noise and simplification are also studied.
NASA Astrophysics Data System (ADS)
Bespalov, Alex; Haberl, Alexander; Praetorius, Dirk
2017-04-01
We prove that for compactly perturbed elliptic problems, where the corresponding bilinear form satisfies a Garding inequality, adaptive mesh-refinement is capable of overcoming the preasymptotic behavior and eventually leads to convergence with optimal algebraic rates. As an important consequence of our analysis, one does not have to deal with the a-priori assumption that the underlying meshes are sufficiently fine. Hence, the overall conclusion of our results is that adaptivity has stabilizing effects and can overcome possibly pessimistic restrictions on the meshes. In particular, our analysis covers adaptive mesh-refinement for the finite element discretization of the Helmholtz equation from where our interest originated.
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.
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.
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.
Adaptive finite element strategies for shell structures
NASA Technical Reports Server (NTRS)
Stanley, G.; Levit, I.; Stehlin, B.; Hurlbut, B.
1992-01-01
The present paper extends existing finite element adaptive refinement (AR) techniques to shell structures, which have heretofore been neglected in the AR literature. Specific challenges in applying AR to shell structures include: (1) physical discontinuities (e.g., stiffener intersections); (2) boundary layers; (3) sensitivity to geometric imperfections; (4) the sensitivity of most shell elements to mesh distortion, constraint definition and/or thinness; and (5) intrinsic geometric nonlinearity. All of these challenges but (5) are addressed here.
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.
Cartesian-cell based grid generation and adaptive mesh refinement
NASA Technical Reports Server (NTRS)
Coirier, William J.; Powell, Kenneth G.
1993-01-01
Viewgraphs on Cartesian-cell based grid generation and adaptive mesh refinement are presented. Topics covered include: grid generation; cell cutting; data structures; flow solver formulation; adaptive mesh refinement; and viscous flow.
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.
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.
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.
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.
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.
Anisotropic norm-oriented mesh adaptation for a Poisson problem
NASA Astrophysics Data System (ADS)
Brèthes, Gautier; Dervieux, Alain
2016-10-01
We present a novel formulation for the mesh adaptation of the approximation of a Partial Differential Equation (PDE). The discussion is restricted to a Poisson problem. The proposed norm-oriented formulation extends the goal-oriented formulation since it is equation-based and uses an adjoint. At the same time, the norm-oriented formulation somewhat supersedes the goal-oriented one since it is basically a solution-convergent method. Indeed, goal-oriented methods rely on the reduction of the error in evaluating a chosen scalar output with the consequence that, as mesh size is increased (more degrees of freedom), only this output is proven to tend to its continuous analog while the solution field itself may not converge. A remarkable quality of goal-oriented metric-based adaptation is the mathematical formulation of the mesh adaptation problem under the form of the optimization, in the well-identified set of metrics, of a well-defined functional. In the new proposed formulation, we amplify this advantage. We search, in the same well-identified set of metrics, the minimum of a norm of the approximation error. The norm is prescribed by the user and the method allows addressing the case of multi-objective adaptation like, for example in aerodynamics, adaptating the mesh for drag, lift and moment in one shot. In this work, we consider the basic linear finite-element approximation and restrict our study to L2 norm in order to enjoy second-order convergence. Numerical examples for the Poisson problem are computed.
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.
On Adaptive Mesh Generation in Two-Dimensions
D'Azevedo, E.
1999-10-11
This work considers the effectiveness of using anisotropic coordinate transformation in adaptive mesh generation. The anisotropic coordinate transformation is derived by interpreting the Hessian matrix of the data function as a metric tensor that measures the local approximation error. The Hessian matrix contains information about the local curvature of the surface and gives guidance in the aspect ratio and orientation for mesh generation. Since theoretically, an asymptotically optimally efficient mesh can be produced by transforming a regular mesh of optimal shape elements, it would be interesting to compare this approach with existing techniques in solution adaptive meshes. PLTMG , a general elliptic solver, is used to generate solution adapted triangular meshes for comparison. The solver has the capability of performing a posteriori error estimates in performing longest edge refinement, vertex unrefinement and mesh smoothing. Numerical experiments on three simple problems suggest the methodology employed in PLTMG is effective in generating near optimally efficient meshes.
Adaptive Mesh Refinement for ICF Calculations
NASA Astrophysics Data System (ADS)
Fyfe, David
2005-10-01
This paper describes our use of the package PARAMESH to create an Adaptive Mesh Refinement (AMR) version of NRL's FASTRAD3D code. PARAMESH was designed to create an MPI-based AMR code from a block structured serial code such as FASTRAD3D. FASTRAD3D is a compressible hydrodynamics code containing the physical effects relevant for the simulation of high-temperature plasmas including inertial confinement fusion (ICF) Rayleigh-Taylor unstable direct drive laser targets. These effects include inverse bremmstrahlung laser energy absorption, classical flux-limited Spitzer thermal conduction, real (table look-up) equation-of-state with either separate or identical electron and ion temperatures, multi-group variable Eddington radiation transport, and multi-group alpha particle transport and thermonuclear burn. Numerically, this physics requires an elliptic solver and a ray tracing approach on the AMR grid, which is the main subject of this paper. A sample ICF calculation will be presented. MacNeice et al., ``PARAMESH: A parallel adaptive mesh refinement community tool,'' Computer Physics Communications, 126 (2000), pp. 330-354.
Current sheets, reconnection and adaptive mesh refinement
NASA Astrophysics Data System (ADS)
Marliani, Christiane
1998-11-01
Adaptive structured mesh refinement methods have proved to be an appropriate tool for the numerical study of a variety of problems where largely separated length scales are involved, e.g. [R. Grauer, C. Marliani, K. Germaschewski, PRL, 80, 4177, (1998)]. A typical example in plasma physics are the current sheets in magnetohydrodynamic flows. Their dynamics is investigated in the framework of incompressible MHD. We present simulations of the ideal and inviscid dynamics in two and three dimensions. In addition, we show numerical simulations for the resistive case in two dimensions. Specifically, we show simulations for the case of the doubly periodic coalescence instability. At the onset of the reconnection process the kinetic energy rises and drops rapidly and afterwards settles into an oscillatory phase. The timescale of the magnetic reconnection process is not affected by these fast events but consistent with the Sweet-Parker model of stationary reconnection. Taking into account the electron inertia terms in the generalized Ohm's law the electron skin depth is introduced as an additional parameter. The modified equations allow for magnetic reconnection in the collisionless regime. Current density and vorticity concentrate in extremely long and thin sheets. Their dynamics becomes numerically accessible by means of adaptive mesh refinement.
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.
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.
A User's Guide to AMR1D: An Instructional Adaptive Mesh Refinement Code for Unstructured Grids
NASA Technical Reports Server (NTRS)
deFainchtein, Rosalinda
1996-01-01
This report documents the code AMR1D, which is currently posted on the World Wide Web (http://sdcd.gsfc.nasa.gov/ESS/exchange/contrib/de-fainchtein/adaptive _mesh_refinement.html). AMR1D is a one-dimensional finite element fluid-dynamics solver, capable of adaptive mesh refinement (AMR). It was written as an instructional tool for AMR on unstructured mesh codes. It is meant to illustrate the minimum requirements for AMR on more than one dimension. For that purpose, it uses the same type of data structure that would be necessary on a two-dimensional AMR code (loosely following the algorithm described by Lohner).
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
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.
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.
Tetrahedral and Hexahedral Mesh Adaptation for CFD Problems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger C.; Chancellor, Marisa K. (Technical Monitor)
1997-01-01
This paper presents two unstructured mesh adaptation schemes for problems in computational fluid dynamics. The procedures allow localized grid refinement and coarsening to efficiently capture aerodynamic flow features of interest. The first procedure is for purely tetrahedral grids; unfortunately, repeated anisotropic adaptation may significantly deteriorate the quality of the mesh. Hexahedral elements, on the other hand, can be subdivided anisotropically without mesh quality problems. Furthermore, hexahedral meshes yield more accurate solutions than their tetrahedral counterparts for the same number of edges. Both the tetrahedral and hexahedral mesh adaptation procedures use edge-based data structures that facilitate efficient subdivision by allowing individual edges to be marked for refinement or coarsening. However, for hexahedral adaptation, pyramids, prisms, and tetrahedra are used as buffer elements between refined and unrefined regions to eliminate hanging vertices. Computational results indicate that the hexahedral adaptation procedure is a viable alternative to adaptive tetrahedral schemes.
Carpet: Adaptive Mesh Refinement for the Cactus Framework
NASA Astrophysics Data System (ADS)
Schnetter, Erik; Hawley, Scott; Hawke, Ian
2016-11-01
Carpet is an adaptive mesh refinement and multi-patch driver for the Cactus Framework (ascl:1102.013). Cactus is a software framework for solving time-dependent partial differential equations on block-structured grids, and Carpet acts as driver layer providing adaptive mesh refinement, multi-patch capability, as well as parallelization and efficient I/O.
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.
Nonhydrostatic adaptive mesh dynamics for multiscale climate models (Invited)
NASA Astrophysics Data System (ADS)
Collins, W.; Johansen, H.; McCorquodale, P.; Colella, P.; Ullrich, P. A.
2013-12-01
Many of the atmospheric phenomena with the greatest potential impact in future warmer climates are inherently multiscale. Such meteorological systems include hurricanes and tropical cyclones, atmospheric rivers, and other types of hydrometeorological extremes. These phenomena are challenging to simulate in conventional climate models due to the relatively coarse uniform model resolutions relative to the native nonhydrostatic scales of the phenomonological dynamics. To enable studies of these systems with sufficient local resolution for the multiscale dynamics yet with sufficient speed for climate-change studies, we have adapted existing adaptive mesh dynamics for the DOE-NSF Community Atmosphere Model (CAM). In this talk, we present an adaptive, conservative finite volume approach for moist non-hydrostatic atmospheric dynamics. The approach is based on the compressible Euler equations on 3D thin spherical shells, where the radial direction is treated implicitly (using a fourth-order Runga-Kutta IMEX scheme) to eliminate time step constraints from vertical acoustic waves. Refinement is performed only in the horizontal directions. The spatial discretization is the equiangular cubed-sphere mapping, with a fourth-order accurate discretization to compute flux averages on faces. By using both space-and time-adaptive mesh refinement, the solver allocates computational effort only where greater accuracy is needed. The resulting method is demonstrated to be fourth-order accurate for model problems, and robust at solution discontinuities and stable for large aspect ratios. We present comparisons using a simplified physics package for dycore comparisons of moist physics. Hadley cell lifting an advected tracer into upper atmosphere, with horizontal adaptivity
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.
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.
Adaptive finite element methods in electrochemistry.
Gavaghan, David J; Gillow, Kathryn; Süli, Endre
2006-12-05
In this article, we review some of our previous work that considers the general problem of numerical simulation of the currents at microelectrodes using an adaptive finite element approach. Microelectrodes typically consist of an electrode embedded (or recessed) in an insulating material. For all such electrodes, numerical simulation is made difficult by the presence of a boundary singularity at the electrode edge (where the electrode meets the insulator), manifested by the large increase in the current density at this point, often referred to as the edge effect. Our approach to overcoming this problem has involved the derivation of an a posteriori bound on the error in the numerical approximation for the current that can be used to drive an adaptive mesh-generation algorithm, allowing calculation of the quantity of interest (the current) to within a prescribed tolerance. We illustrate the generic applicability of the approach by considering a broad range of steady-state applications of the technique.
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.
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.
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.
Procedure for Adapting Direct Simulation Monte Carlo Meshes
NASA Technical Reports Server (NTRS)
Woronowicz, Michael S.; Wilmoth, Richard G.; Carlson, Ann B.; Rault, Didier F. G.
1992-01-01
A technique is presented for adapting computational meshes used in the G2 version of the direct simulation Monte Carlo method. The physical ideas underlying the technique are discussed, and adaptation formulas are developed for use on solutions generated from an initial mesh. The effect of statistical scatter on adaptation is addressed, and results demonstrate the ability of this technique to achieve more accurate results without increasing necessary computational resources.
GPU accelerated spectral finite elements on all-hex meshes
NASA Astrophysics Data System (ADS)
Remacle, J.-F.; Gandham, R.; Warburton, T.
2016-11-01
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An additive Schwartz two-scale preconditioner is employed that allows h-independence convergence. An extensible multi-threading programming API is used as a common kernel language that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.
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.
GAMER: GPU-accelerated Adaptive MEsh Refinement code
NASA Astrophysics Data System (ADS)
Schive, Hsi-Yu; Tsai, Yu-Chih; Chiueh, Tzihong
2016-12-01
GAMER (GPU-accelerated Adaptive MEsh Refinement) serves as a general-purpose adaptive mesh refinement + GPU framework and solves hydrodynamics with self-gravity. The code supports adaptive mesh refinement (AMR), hydrodynamics with self-gravity, and a variety of GPU-accelerated hydrodynamic and Poisson solvers. It also supports hybrid OpenMP/MPI/GPU parallelization, concurrent CPU/GPU execution for performance optimization, and Hilbert space-filling curve for load balance. Although the code is designed for simulating galaxy formation, it can be easily modified to solve a variety of applications with different governing equations. All optimization strategies implemented in the code can be inherited straightforwardly.
Output-based mesh adaptation for high order Navier-Stokes simulations on deformable domains
NASA Astrophysics Data System (ADS)
Kast, Steven M.; Fidkowski, Krzysztof J.
2013-11-01
We present an output-based mesh adaptation strategy for Navier-Stokes simulations on deforming domains. The equations are solved with an arbitrary Lagrangian-Eulerian (ALE) approach, using a discontinuous Galerkin finite-element discretization in both space and time. Discrete unsteady adjoint solutions, derived for both the state and the geometric conservation law, provide output error estimates and drive adaptation of the space-time mesh. Spatial adaptation consists of dynamic order increment or decrement on a fixed tessellation of the domain, while a combination of coarsening and refinement is used to provide an efficient time step distribution. Results from compressible Navier-Stokes simulations in both two and three dimensions demonstrate the accuracy and efficiency of the proposed approach. In particular, the method is shown to outperform other common adaptation strategies, which, while sometimes adequate for static problems, struggle in the presence of mesh motion.
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
White Dwarf Mergers on Adaptive Meshes
NASA Astrophysics Data System (ADS)
Katz, Maximilian Peter
The mergers of binary white dwarf systems are potential progenitors of astrophysical explosions such as Type Ia supernovae. These white dwarfs can merge either by orbital decay through the emission of gravitational waves or by direct collisions as a result of orbital perturbations. The coalescence of the stars may ignite nuclear fusion, resulting in the destruction of both stars through a thermonuclear runaway and ensuing detonation. The goal of this dissertation is to simulate binary white dwarf systems using the techniques of computational fluid dynamics and therefore to understand what numerical techniques are necessary to obtain accurate dynamical evolution of the system, as well as to learn what conditions are necessary to enable a realistic detonation. For this purpose I have used software that solves the relevant fluid equations, the Poisson equation for self-gravity, and the systems governing nuclear reactions between atomic species. These equations are modeled on a computational domain that uses the technique of adaptive mesh refinement to have the highest spatial resolution in the areas of the domain that are most sensitive to the need for accurate numerical evolution. I have identified that the most important obstacles to accurate evolution are the numerical violation of conservation of energy and angular momentum in the system, and the development of numerically seeded thermonuclear detonations that do not bear resemblance to physically correct detonations. I then developed methods for ameliorating these problems, and determined what metrics can be used for judging whether a given white dwarf merger simulation is trustworthy. This involved the development of a number of algorithmic improvements to the simulation software, which I describe. Finally, I performed high-resolution simulations of typical cases of white dwarf mergers and head-on collisions to demonstrate the impacts of these choices. The results of these simulations and the corresponding
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.
A two-dimensional adaptive mesh generation method
NASA Astrophysics Data System (ADS)
Altas, Irfan; Stephenson, John W.
1991-05-01
The present, two-dimensional adaptive mesh-generation method allows selective modification of a small portion of the mesh without affecting large areas of adjacent mesh-points, and is applicable with or without boundary-fitted coordinate-generation procedures. The cases of differential equation discretization by, on the one hand, classical difference formulas designed for uniform meshes, and on the other the present difference formulas, are illustrated through the application of the method to the Hiemenz flow for which the Navier-Stokes equation's exact solution is known, as well as to a two-dimensional viscous internal flow problem.
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.
Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo
NASA Astrophysics Data System (ADS)
Garcia, Alejandro L.; Bell, John B.; Crutchfield, William Y.; Alder, Berni 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.
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.
Parallel adaptive mesh refinement techniques for plasticity problems
Barry, W.J.; Jones, M.T. |; Plassmann, P.E.
1997-12-31
The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.
Parallel adaptive mesh refinement techniques for plasticity problems
NASA Technical Reports Server (NTRS)
Barry, W. J.; Jones, M. T.; Plassmann, P. E.
1997-01-01
The accurate modeling of the nonlinear properties of materials can be computationally expensive. Parallel computing offers an attractive way for solving such problems; however, the efficient use of these systems requires the vertical integration of a number of very different software components, we explore the solution of two- and three-dimensional, small-strain plasticity problems. We consider a finite-element formulation of the problem with adaptive refinement of an unstructured mesh to accurately model plastic transition zones. We present a framework for the parallel implementation of such complex algorithms. This framework, using libraries from the SUMAA3d project, allows a user to build a parallel finite-element application without writing any parallel code. To demonstrate the effectiveness of this approach on widely varying parallel architectures, we present experimental results from an IBM SP parallel computer and an ATM-connected network of Sun UltraSparc workstations. The results detail the parallel performance of the computational phases of the application during the process while the material is incrementally loaded.
Adaptive Meshing of Ship Air-Wake Flowfields
2014-03-03
this code are currently generated using Pointwise .[2] This code also uses a second order spatial finite-volume scheme with first order explicit...simulated with the two codes and is shown below. The surface mesh from the 3D mesh generated by Pointwise serves as the geometry for the OctFlow code. A...Geometries", AIAA- 2000-1006,2000. 2. " Pointwise ." Pointwise , Inc., http://www.pointwise.com. 3. O’Connell, M., and Karman, S., "Mesh Rupturing: A
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.
NASA Astrophysics Data System (ADS)
Owens, A. R.; Kópházi, J.; Welch, J. A.; Eaton, M. D.
2017-04-01
In this paper a hanging-node, discontinuous Galerkin, isogeometric discretisation of the multigroup, discrete ordinates (SN) equations is presented in which each energy group has its own mesh. The equations are discretised using Non-Uniform Rational B-Splines (NURBS), which allows the coarsest mesh to exactly represent the geometry for a wide range of engineering problems of interest; this would not be the case using straight-sided finite elements. Information is transferred between meshes via the construction of a supermesh. This is a non-trivial task for two arbitrary meshes, but is significantly simplified here by deriving every mesh from a common coarsest initial mesh. In order to take full advantage of this flexible discretisation, goal-based error estimators are derived for the multigroup, discrete ordinates equations with both fixed (extraneous) and fission sources, and these estimators are used to drive an adaptive mesh refinement (AMR) procedure. The method is applied to a variety of test cases for both fixed and fission source problems. The error estimators are found to be extremely accurate for linear NURBS discretisations, with degraded performance for quadratic discretisations owing to a reduction in relative accuracy of the ;exact; adjoint solution required to calculate the estimators. Nevertheless, the method seems to produce optimal meshes in the AMR process for both linear and quadratic discretisations, and is ≈×100 more accurate than uniform refinement for the same amount of computational effort for a 67 group deep penetration shielding problem.
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.
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.
A 3D moving mesh Finite Element Method for two-phase flows
NASA Astrophysics Data System (ADS)
Anjos, G. R.; Borhani, N.; Mangiavacchi, N.; Thome, J. R.
2014-08-01
A 3D ALE Finite Element Method is developed to study two-phase flow phenomena using a new discretization method to compute the surface tension forces. The computational method is based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a two-phase method with an improved model for the liquid-gas interface. An adaptive mesh update procedure is also proposed for effective management of the mesh to remove, add and repair elements, since the computational mesh nodes move according to the flow. The ALE description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost. Static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics. This paper focuses on the description of the proposed methodology, with particular emphasis on the discretization of the surface tension force, the new remeshing technique, and the validation results. Additionally, a microchannel simulation in complex geometry is presented for two elongated bubbles.
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.
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.
Parallel tetrahedral mesh adaptation with dynamic load balancing
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
2000-06-28
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D-TAG, using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However, performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region, creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D-TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Parallel Tetrahedral Mesh Adaptation with Dynamic Load Balancing
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Gabow, Harold N.
1999-01-01
The ability to dynamically adapt an unstructured grid is a powerful tool for efficiently solving computational problems with evolving physical features. In this paper, we report on our experience parallelizing an edge-based adaptation scheme, called 3D_TAG. using message passing. Results show excellent speedup when a realistic helicopter rotor mesh is randomly refined. However. performance deteriorates when the mesh is refined using a solution-based error indicator since mesh adaptation for practical problems occurs in a localized region., creating a severe load imbalance. To address this problem, we have developed PLUM, a global dynamic load balancing framework for adaptive numerical computations. Even though PLUM primarily balances processor workloads for the solution phase, it reduces the load imbalance problem within mesh adaptation by repartitioning the mesh after targeting edges for refinement but before the actual subdivision. This dramatically improves the performance of parallel 3D_TAG since refinement occurs in a more load balanced fashion. We also present optimal and heuristic algorithms that, when applied to the default mapping of a parallel repartitioner, significantly reduce the data redistribution overhead. Finally, portability is examined by comparing performance on three state-of-the-art parallel machines.
Parallel adaptation of general three-dimensional hybrid meshes
Kavouklis, Christos Kallinderis, Yannis
2010-05-01
A new parallel dynamic mesh adaptation and load balancing algorithm for general hybrid grids has been developed. The meshes considered in this work are composed of four kinds of elements; tetrahedra, prisms, hexahedra and pyramids, which poses a challenge to parallel mesh adaptation. Additional complexity imposed by the presence of multiple types of elements affects especially data migration, updates of local data structures and interpartition data structures. Efficient partition of hybrid meshes has been accomplished by transforming them to suitable graphs and using serial graph partitioning algorithms. Communication among processors is based on the faces of the interpartition boundary and the termination detection algorithm of Dijkstra is employed to ensure proper flagging of edges for refinement. An inexpensive dynamic load balancing strategy is introduced to redistribute work load among processors after adaptation. In particular, only the initial coarse mesh, with proper weighting, is balanced which yields savings in computation time and relatively simple implementation of mesh quality preservation rules, while facilitating coarsening of refined elements. Special algorithms are employed for (i) data migration and dynamic updates of the local data structures, (ii) determination of the resulting interpartition boundary and (iii) identification of the communication pattern of processors. Several representative applications are included to evaluate the method.
Error Estimation and h-Adaptivity for Optimal Finite Element Analysis
NASA Technical Reports Server (NTRS)
Cwik, Tom; Lou, John
1997-01-01
The objective of adaptive meshing and automatic error control in finite element analysis is to eliminate the need for the application engineer from re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software will then autonomously and adaptively refine this mesh where needed, reducing the error in the fields to a user prescribed value. The ideal end result of the simulation is a measurable quantity (e.g. scattered field, input impedance), calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects since an optimal mesh is created.
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.
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.
Multigrid solution of internal flows using unstructured solution adaptive meshes
NASA Technical Reports Server (NTRS)
Smith, Wayne A.; Blake, Kenneth R.
1992-01-01
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.
A finite-volume Euler solver for computing rotary-wing aerodynamics on unstructured meshes
NASA Technical Reports Server (NTRS)
Strawn, Roger C.; Barth, Timothy J.
1992-01-01
An unstructured-grid solver for the unsteady Euler equations has been developed for predicting the aerodynamics of helicopter rotor blades. This flow solver is a finite-volume scheme that computes flow quantities at the vertices of the mesh. Special treatments are used for the flux differencing and boundary conditions in order to compute rotary-wing flowfields, and these are detailed in the paper. The unstructured-grid solver permits adaptive grid refinement in order to improve the resolution of flow features such as shocks, rotor wakes and acoustic waves. These capabilities are demonstrated in the paper. Example calculations are presented for two hovering rotors. In both cases, adaptive-grid refinement is used to resolve high gradients near the rotor surface and also to capture the vortical regions in the rotor wake. The computed results show good agreement with experimental results for surface airloads and wake geometry.
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.
Adaptive mesh refinement for shocks and material interfaces
Dai, William Wenlong
2010-01-01
There are three kinds of adaptive mesh refinement (AMR) in structured meshes. Block-based AMR sometimes over refines meshes. Cell-based AMR treats cells cell by cell and thus loses the advantage of the nature of structured meshes. Patch-based AMR is intended to combine advantages of block- and cell-based AMR, i.e., the nature of structured meshes and sharp regions of refinement. But, patch-based AMR has its own difficulties. For example, patch-based AMR typically cannot preserve symmetries of physics problems. In this paper, we will present an approach for a patch-based AMR for hydrodynamics simulations. The approach consists of clustering, symmetry preserving, mesh continuity, flux correction, communications, management of patches, and load balance. The special features of this patch-based AMR include symmetry preserving, efficiency of refinement across shock fronts and material interfaces, special implementation of flux correction, and patch management in parallel computing environments. To demonstrate the capability of the AMR framework, we will show both two- and three-dimensional hydrodynamics simulations with many levels of refinement.
Hexahedral finite element mesh coarsening using pillowing technique
Staten, Matthew L [Pittsburgh, PA; Woodbury, Adam C [Provo, UT; Benzley, Steven E [Provo, UT; Shepherd, Jason F [Edgewood, NM
2012-06-05
A techniques for coarsening a hexahedral mesh is described. The technique includes identifying a coarsening region within a hexahedral mesh to be coarsened. A boundary sheet of hexahedral elements is inserted into the hexahedral mesh around the coarsening region. A column of hexahedral elements is identified within the boundary sheet. The column of hexahedral elements is collapsed to create an extraction sheet of hexahedral elements contained within the coarsening region. Then, the extraction sheet of hexahedral elements is extracted to coarsen the hexahedral mesh.
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.
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.
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.
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.
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.
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.
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.
Adjoint Methods for Guiding Adaptive Mesh Refinement in Tsunami Modeling
NASA Astrophysics Data System (ADS)
Davis, B. N.; LeVeque, R. J.
2016-12-01
One difficulty in developing numerical methods for tsunami modeling is the fact that solutions contain time-varying regions where much higher resolution is required than elsewhere in the domain, particularly when tracking a tsunami propagating across the ocean. The open source GeoClaw software deals with this issue by using block-structured adaptive mesh refinement to selectively refine around propagating waves. For problems where only a target area of the total solution is of interest (e.g., one coastal community), a method that allows identifying and refining the grid only in regions that influence this target area would significantly reduce the computational cost of finding a solution. In this work, we show that solving the time-dependent adjoint equation and using a suitable inner product with the forward solution allows more precise refinement of the relevant waves. We present the adjoint methodology first in one space dimension for illustration and in a broad context since it could also be used in other adaptive software, and potentially for other tsunami applications beyond adaptive refinement. We then show how this adjoint method has been integrated into the adaptive mesh refinement strategy of the open source GeoClaw software and present tsunami modeling results showing that the accuracy of the solution is maintained and the computational time required is significantly reduced through the integration of the adjoint method into adaptive mesh refinement.
The h-p Version of the Finite Element Method with Quasiuniform Meshes.
1986-05-01
Noetic Technologies, St. Louis).1 The theoretical aspects have been studied only recently. The first theoretical paper appeared in 1981 (see [6...Research Reports :~ :~THE h-p VERSION OF THE FINITE ELEMENT METHOD WITH QUASIUNIFORM MESHES I. Babuska Institute for Physical Science and Technology...p VERSION OF THE FINITE ELEMENT METHOD > ’ WITH QUASIUNIFORM MESHES t. Ba bus aka1 Institute for Physical Science and Technology University of
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.
Parallel Block Structured Adaptive Mesh Refinement on Graphics Processing Units
Beckingsale, D. A.; Gaudin, W. P.; Hornung, R. D.; Gunney, B. T.; Gamblin, T.; Herdman, J. A.; Jarvis, S. A.
2014-11-17
Block-structured adaptive mesh refinement is a technique that can be used when solving partial differential equations to reduce the number of zones necessary to achieve the required accuracy in areas of interest. These areas (shock fronts, material interfaces, etc.) are recursively covered with finer mesh patches that are grouped into a hierarchy of refinement levels. Despite the potential for large savings in computational requirements and memory usage without a corresponding reduction in accuracy, AMR adds overhead in managing the mesh hierarchy, adding complex communication and data movement requirements to a simulation. In this paper, we describe the design and implementation of a native GPU-based AMR library, including: the classes used to manage data on a mesh patch, the routines used for transferring data between GPUs on different nodes, and the data-parallel operators developed to coarsen and refine mesh data. We validate the performance and accuracy of our implementation using three test problems and two architectures: an eight-node cluster, and over four thousand nodes of Oak Ridge National Laboratory’s Titan supercomputer. Our GPU-based AMR hydrodynamics code performs up to 4.87× faster than the CPU-based implementation, and has been scaled to over four thousand GPUs using a combination of MPI and CUDA.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
NASA Technical Reports Server (NTRS)
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
A finite volume method for two-sided fractional diffusion equations on non-uniform meshes
NASA Astrophysics Data System (ADS)
Simmons, Alex; Yang, Qianqian; Moroney, Timothy
2017-04-01
We derive a finite volume method for two-sided fractional diffusion equations with Riemann-Liouville derivatives in one spatial dimension. The method applies to non-uniform meshes, with arbitrary nodal spacing. The discretisation utilises the integral definition of the fractional derivatives, and we show that it leads to a diagonally dominant matrix representation, and a provably stable numerical scheme. Being a finite volume method, the numerical scheme is fully conservative, and the ability to locally refine the mesh can produce solutions with more accuracy for the same number of nodes compared to a uniform mesh, as we demonstrate numerically.
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.
AN ADAPTIVE PARTICLE-MESH GRAVITY SOLVER FOR ENZO
Passy, Jean-Claude; Bryan, Greg L.
2014-11-01
We describe and implement an adaptive particle-mesh algorithm to solve the Poisson equation for grid-based hydrodynamics codes with nested grids. The algorithm is implemented and extensively tested within the astrophysical code Enzo against the multigrid solver available by default. We find that while both algorithms show similar accuracy for smooth mass distributions, the adaptive particle-mesh algorithm is more accurate for the case of point masses, and is generally less noisy. We also demonstrate that the two-body problem can be solved accurately in a configuration with nested grids. In addition, we discuss the effect of subcycling, and demonstrate that evolving all the levels with the same timestep yields even greater precision.
Boltzmann Solver with Adaptive Mesh in Velocity Space
Kolobov, Vladimir I.; Arslanbekov, Robert R.; Frolova, Anna A.
2011-05-20
We describe the implementation of direct Boltzmann solver with Adaptive Mesh in Velocity Space (AMVS) using quad/octree data structure. The benefits of the AMVS technique are demonstrated for the charged particle transport in weakly ionized plasmas where the collision integral is linear. We also describe the implementation of AMVS for the nonlinear Boltzmann collision integral. Test computations demonstrate both advantages and deficiencies of the current method for calculations of narrow-kernel distributions.
Fluidity: a fully-unstructured adaptive mesh computational framework for geodynamics
NASA Astrophysics Data System (ADS)
Kramer, S. C.; Davies, D.; Wilson, C. R.
2010-12-01
Fluidity is a finite element, finite volume fluid dynamics model developed by the Applied Modelling and Computation Group at Imperial College London. Several features of the model make it attractive for use in geodynamics. A core finite element library enables the rapid implementation and investigation of new numerical schemes. For example, the function spaces used for each variable can be changed allowing properties of the discretisation, such as stability, conservation and balance, to be easily varied and investigated. Furthermore, unstructured, simplex meshes allow the underlying resolution to vary rapidly across the computational domain. Combined with dynamic mesh adaptivity, where the mesh is periodically optimised to the current conditions, this allows significant savings in computational cost over traditional chessboard-like structured mesh simulations [1]. In this study we extend Fluidity (using the Portable, Extensible Toolkit for Scientific Computation [PETSc, 2]) to Stokes flow problems relevant to geodynamics. However, due to the assumptions inherent in all models, it is necessary to properly verify and validate the code before applying it to any large-scale problems. In recent years this has been made easier by the publication of a series of ‘community benchmarks’ for geodynamic modelling. We discuss the use of several of these to help validate Fluidity [e.g. 3, 4]. The experimental results of Vatteville et al. [5] are then used to validate Fluidity against laboratory measurements. This test case is also used to highlight the computational advantages of using adaptive, unstructured meshes - significantly reducing the number of nodes and total CPU time required to match a fixed mesh simulation. References: 1. C. C. Pain et al. Comput. Meth. Appl. M, 190:3771-3796, 2001. doi:10.1016/S0045-7825(00)00294-2. 2. B. Satish et al. http://www.mcs.anl.gov/petsc/petsc-2/, 2001. 3. Blankenbach et al. Geophys. J. Int., 98:23-28, 1989. 4. Busse et al. Geophys
AMR++: Object-Oriented Parallel Adaptive Mesh Refinement
Quinlan, D.; Philip, B.
2000-02-02
Adaptive mesh refinement (AMR) computations are complicated by their dynamic nature. The development of solvers for realistic applications is complicated by both the complexity of the AMR and the geometry of realistic problem domains. The additional complexity of distributed memory parallelism within such AMR applications most commonly exceeds the level of complexity that can be reasonable maintained with traditional approaches toward software development. This paper will present the details of our object-oriented work on the simplification of the use of adaptive mesh refinement on applications with complex geometries for both serial and distributed memory parallel computation. We will present an independent set of object-oriented abstractions (C++ libraries) well suited to the development of such seemingly intractable scientific computations. As an example of the use of this object-oriented approach we will present recent results of an application modeling fluid flow in the eye. Within this example, the geometry is too complicated for a single curvilinear coordinate grid and so a set of overlapping curvilinear coordinate grids' are used. Adaptive mesh refinement and the required grid generation work to support the refinement process is coupled together in the solution of essentially elliptic equations within this domain. This paper will focus on the management of complexity within development of the AMR++ library which forms a part of the Overture object-oriented framework for the solution of partial differential equations within scientific computing.
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
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.
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
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).
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.
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.
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.
Design of an Essentially Non-Oscillatory Reconstruction Procedure on Finite-Element Type Meshes
1991-12-01
15] P. G. Ciarlet & P. A. Raviart, General Lagrange and hermite interpolation in 1W with application to Finite Element Methods. Archive for Rational ...meshes. Two related problems are studied : the interpolation of possibly unsmooth multivariate functions on arbitrary meshes and the reconstruction of a...highest coefficients of the Lagrange interpolation function which may admit discontinuities of locally regular curves. This enables us to choose the
CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES
GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT
2016-01-01
We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Thuburn, John; Cotter, Colin J.
2015-06-01
A new numerical method is presented for solving the shallow water equations on a rotating sphere using quasi-uniform polygonal meshes. The method uses special families of finite element function spaces to mimic key mathematical properties of the continuous equations and thereby capture several desirable physical properties related to balance and conservation. The method relies on two novel features. The first is the use of compound finite elements to provide suitable finite element spaces on general polygonal meshes. The second is the use of dual finite element spaces on the dual of the original mesh, along with suitably defined discrete Hodge star operators to map between the primal and dual meshes, enabling the use of a finite volume scheme on the dual mesh to compute potential vorticity fluxes. The resulting method has the same mimetic properties as a finite volume method presented previously, but is more accurate on a number of standard test cases.
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.
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.
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.
Numerical study of three-dimensional liquid jet breakup with adaptive unstructured meshes
NASA Astrophysics Data System (ADS)
Xie, Zhihua; Pavlidis, Dimitrios; Salinas, Pablo; Pain, Christopher; Matar, Omar
2016-11-01
Liquid jet breakup is an important fundamental multiphase flow, often found in many industrial engineering applications. The breakup process is very complex, involving jets, liquid films, ligaments, and small droplets, featuring tremendous complexity in interfacial topology and a large range of spatial scales. The objective of this study is to investigate the fluid dynamics of three-dimensional liquid jet breakup problems, such as liquid jet primary breakup and gas-sheared liquid jet breakup. An adaptive unstructured mesh modelling framework is employed here, which can modify and adapt unstructured meshes to optimally represent the underlying physics of multiphase problems and reduce 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 second-order finite element methods, and a force-balanced algorithm for the surface tension implementation. Numerical examples of some benchmark tests and the dynamics of liquid jet breakup with and without ambient gas are presented to demonstrate the capability of this method.
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.
A mesh re-zoning technique for finite element simulations of metal forming processes
NASA Technical Reports Server (NTRS)
Cheng, J.-C.; Kikuchi, N.
1986-01-01
Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analyzing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.
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.
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.
Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks
NASA Astrophysics Data System (ADS)
Kurguzov, V. D.
2016-12-01
The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.
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.
An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics
NASA Astrophysics Data System (ADS)
Kühnlein, Christian; Smolarkiewicz, Piotr K.
2017-04-01
An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity-the latter being essential for flux-form schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.
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
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.
Efficient Plasma Ion Source Modeling With Adaptive Mesh Refinement (Abstract)
Kim, J.S.; Vay, J.L.; Friedman, A.; Grote, D.P.
2005-03-15
Ion beam drivers for high energy density physics and inertial fusion energy research require high brightness beams, so there is little margin of error allowed for aberration at the emitter. Thus, accurate plasma ion source computer modeling is required to model the plasma sheath region and time-dependent effects correctly.A computer plasma source simulation module that can be used with a powerful heavy ion fusion code, WARP, or as a standalone code, is being developed. In order to treat the plasma sheath region accurately and efficiently, the module will have the capability of handling multiple spatial scale problems by using Adaptive Mesh Refinement (AMR). We will report on our progress on the project.
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.
Mimetic finite difference method for the Stokes problem on polygonal meshes
NASA Astrophysics Data System (ADS)
Beirão da Veiga, L.; Gyrya, V.; Lipnikov, K.; Manzini, G.
2009-10-01
Various approaches to extend finite element methods to non-traditional elements (general polygons, pyramids, polyhedra, etc.) have been developed over the last decade. The construction of basis functions for such elements is a challenging task and may require extensive geometrical analysis. The mimetic finite difference (MFD) method works on general polygonal meshes and has many similarities with low-order finite element methods. Both schemes try to preserve the fundamental properties of the underlying physical and mathematical models. The essential difference between the two schemes is that the MFD method uses only the surface representation of discrete unknowns to build the stiffness and mass matrices. Since no extension of basis functions inside the mesh elements 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 present a new MFD method for the Stokes problem on arbitrary polygonal meshes and analyze its stability. The method is developed for the general case of tensor coefficients, which allows us to apply it to a linear elasticity problem, as well. Numerical experiments show, for the velocity variable, second-order convergence in a discrete L2 norm and first-order convergence in a discrete H1 norm. For the pressure variable, first-order convergence is shown in the L2 norm.
NASA Astrophysics Data System (ADS)
Combet, F.; Gelman, L.
2011-04-01
In this paper, a novel adaptive demodulation technique including a new diagnostic feature is proposed for gear diagnosis in conditions of variable amplitudes of the mesh harmonics. This vibration technique employs the time synchronous average (TSA) of vibration signals. The new adaptive diagnostic feature is defined as the ratio of the sum of the sideband components of the envelope spectrum of a mesh harmonic to the measured power of the mesh harmonic. The proposed adaptation of the technique is justified theoretically and experimentally by the high level of the positive covariance between amplitudes of the mesh harmonics and the sidebands in conditions of variable amplitudes of the mesh harmonics. It is shown that the adaptive demodulation technique preserves effectiveness of local fault detection of gears operating in conditions of variable mesh amplitudes.
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.
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.
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.
Adaptive mesh refinement strategies in isogeometric analysis— A computational comparison
NASA Astrophysics Data System (ADS)
Hennig, Paul; Kästner, Markus; Morgenstern, Philipp; Peterseim, Daniel
2017-04-01
We explain four variants of an adaptive finite element method with cubic splines and compare their performance in simple elliptic model problems. The methods in comparison are Truncated Hierarchical B-splines with two different refinement strategies, T-splines with the refinement strategy introduced by Scott et al. in 2012, and T-splines with an alternative refinement strategy introduced by some of the authors. In four examples, including singular and non-singular problems of linear elasticity and the Poisson problem, the H1-errors of the discrete solutions, the number of degrees of freedom as well as sparsity patterns and condition numbers of the discretized problem are compared.
Adaptive Mesh Refinement in Reactive Transport Modeling of Subsurface Environments
NASA Astrophysics Data System (ADS)
Molins, S.; Day, M.; Trebotich, D.; Graves, D. T.
2015-12-01
Adaptive mesh refinement (AMR) is a numerical technique for locally adjusting the resolution of computational grids. AMR makes it possible to superimpose levels of finer grids on the global computational grid in an adaptive manner allowing for more accurate calculations locally. AMR codes rely on the fundamental concept that the solution can be computed in different regions of the domain with different spatial resolutions. AMR codes have been applied to a wide range of problem including (but not limited to): fully compressible hydrodynamics, astrophysical flows, cosmological applications, combustion, blood flow, heat transfer in nuclear reactors, and land ice and atmospheric models for climate. In subsurface applications, in particular, reactive transport modeling, AMR may be particularly useful in accurately capturing concentration gradients (hence, reaction rates) that develop in localized areas of the simulation domain. Accurate evaluation of reaction rates is critical in many subsurface applications. In this contribution, we will discuss recent applications that bring to bear AMR capabilities on reactive transport problems from the pore scale to the flood plain scale.
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.
Parallel grid library with adaptive mesh refinement for development of highly scalable simulations
NASA Astrophysics Data System (ADS)
Honkonen, I.; von Alfthan, S.; Sandroos, A.; Janhunen, P.; Palmroth, M.
2012-04-01
As the single CPU core performance is saturating while the number of cores in the fastest supercomputers increases exponentially, the parallel performance of simulations on distributed memory machines is crucial. At the same time, utilizing efficiently the large number of available cores presents a challenge, especially in simulations with run-time adaptive mesh refinement. We have developed a generic grid library (dccrg) aimed at finite volume simulations that is easy to use and scales well up to tens of thousands of cores. The grid has several attractive features: It 1) allows an arbitrary C++ class or structure to be used as cell data; 2) provides a simple interface for adaptive mesh refinement during a simulation; 3) encapsulates the details of MPI communication when updating the data of neighboring cells between processes; and 4) provides a simple interface to run-time load balancing, e.g. domain decomposition, through the Zoltan library. Dccrg is freely available for anyone to use, study and modify under the GNU Lesser General Public License v3. We will present the implementation of dccrg, simple and advanced usage examples and scalability results on various supercomputers and problems.
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
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.
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.
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.
Parameter studies of gear cooling using an automatic finites element mesh generator
NASA Technical Reports Server (NTRS)
El-Bayoumy, L. E.; Akin, L. S.; Townsend, D. P.
1984-01-01
The range of accuracies achieved in the gear tooth temperature using an automatic finite element mesh generator were investigated. Gear web contribution to the gear cooling process was studied by introducing a varying size hole at the center of the gear because of the versatility of program TARG in allowing different heat transfer coefficients in different areas of the gear tooth. A study was carried out to evaluate the contribution of the loaded and unloaded faces as well as the top and bottom lands. A general purpose two-dimensional finite element preprocessor ATOGEN has been developed for automatic generation of a finite element mesh over a pie-shaped sector of a gear. The program was used for facilitating the input to an upgraded version of a previously developed program for the thermal analysis of running gears (TARG). The latter program determined the steady state temperature distribution throughout the specified gear. The automatic mesh generator program includes a band width minimization routine for reducing computer cost.
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.
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
An object-oriented approach for parallel self adaptive mesh refinement on block structured grids
NASA Technical Reports Server (NTRS)
Lemke, Max; Witsch, Kristian; Quinlan, Daniel
1993-01-01
Self-adaptive mesh refinement dynamically matches the computational demands of a solver for partial differential equations to the activity in the application's domain. In this paper we present two C++ class libraries, P++ and AMR++, which significantly simplify the development of sophisticated adaptive mesh refinement codes on (massively) parallel distributed memory architectures. The development is based on our previous research in this area. The C++ class libraries provide abstractions to separate the issues of developing parallel adaptive mesh refinement applications into those of parallelism, abstracted by P++, and adaptive mesh refinement, abstracted by AMR++. P++ is a parallel array class library to permit efficient development of architecture independent codes for structured grid applications, and AMR++ provides support for self-adaptive mesh refinement on block-structured grids of rectangular non-overlapping blocks. Using these libraries, the application programmers' work is greatly simplified to primarily specifying the serial single grid application and obtaining the parallel and self-adaptive mesh refinement code with minimal effort. Initial results for simple singular perturbation problems solved by self-adaptive multilevel techniques (FAC, AFAC), being implemented on the basis of prototypes of the P++/AMR++ environment, are presented. Singular perturbation problems frequently arise in large applications, e.g. in the area of computational fluid dynamics. They usually have solutions with layers which require adaptive mesh refinement and fast basic solvers in order to be resolved efficiently.
NASA 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
An adaptive mesh magneto-hydrodynamic analysis of interstellar clouds
NASA Astrophysics Data System (ADS)
Kominsky, Paul J.
Interstellar clouds play a key role in many astrophysical events. The interactions of dense interstellar clouds with shock waves and interstellar wind were investigated using an adaptive three-dimensional Cartesian mesh approach to the magneto-hydrodynamic equations. The mixing of the cloud material with the post-shock material results in complex layers of current density. In both the shock and wind interactions, a tail develops similar to the tail found with comets due to the solar wind. The orientation of this tail structure changes with the direction of the magnetic field, and may be useful to observationally determining the orientation of magnetic fields in the interstellar medium. The octree data structure was analyzed in regard to parallel work units. Larger block sizes have a higher volume to surface ratio and support a higher percentage of computational cells to non-computational cells, but require more cells at the finest grid resolution. Keeping the minimum resolution of the grid fixed, and averaging over all possible grids, the analysis confirms experience that block sizes larger than 8 × 8 × 8 cells do not improve storage efficiency. A novel algorithm was developed to implement rotationally periodic boundary conditions on quadtree and octree data, structures. Astrophysical flows wit h symmetric circulation, such as accretion disks, or periodic instabilities, such supernova remnants, may be able to take advantage of such boundary conditions while maintaining the other benefits of a Cartesian grid.
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.
Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations
1983-03-01
grids. We use either the Coarse Mesh Approximation fethod ( Ciment , [1971]) or interpolation from a coarser grid to get the boundary values. In Berger...Problems, Math. Conp. 31 (1977), 333-390. M. Ciment , Stable Difference Schemes with Uneven Mesh Spacings, Math. Comp. 25 (1971), 219-227. H. Cramr
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.
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.
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.
Development and Verification of Unstructured Adaptive Mesh Technique with Edge Compatibility
NASA Astrophysics Data System (ADS)
Ito, Kei; Kunugi, Tomoaki; Ohshima, Hiroyuki
In the design study of the large-sized sodium-cooled fast reactor (JSFR), one key issue is suppression of gas entrainment (GE) phenomena at a gas-liquid interface. Therefore, the authors have been developed a high-precision CFD algorithm to evaluate the GE phenomena accurately. The CFD algorithm has been developed on unstructured meshes to establish an accurate modeling of JSFR system. For two-phase interfacial flow simulations, a high-precision volume-of-fluid algorithm is employed. It was confirmed that the developed CFD algorithm could reproduce the GE phenomena in a simple GE experiment. Recently, the authors have been developed an important technique for the simulation of the GE phenomena in JSFR. That is an unstructured adaptive mesh technique which can apply fine cells dynamically to the region where the GE occurs in JSFR. In this paper, as a part of the development, a two-dimensional unstructured adaptive mesh technique is discussed. In the two-dimensional adaptive mesh technique, each cell is refined isotropically to reduce distortions of the mesh. In addition, connection cells are formed to eliminate the edge incompatibility between refined and non-refined cells. The two-dimensional unstructured adaptive mesh technique is verified by solving well-known lid-driven cavity flow problem. As a result, the two-dimensional unstructured adaptive mesh technique succeeds in providing a high-precision solution, even though poor-quality distorted initial mesh is employed. In addition, the simulation error on the two-dimensional unstructured adaptive mesh is much less than the error on the structured mesh with a larger number of cells.
Using Adaptive Mesh Refinment to Simulate Storm Surge
NASA Astrophysics Data System (ADS)
Mandli, K. T.; Dawson, C.
2012-12-01
Coastal hazards related to strong storms such as hurricanes and typhoons are one of the most frequently recurring and wide spread hazards to coastal communities. Storm surges are among the most devastating effects of these storms, and their prediction and mitigation through numerical simulations is of great interest to coastal communities that need to plan for the subsequent rise in sea level during these storms. Unfortunately these simulations require a large amount of resolution in regions of interest to capture relevant effects resulting in a computational cost that may be intractable. This problem is exacerbated in situations where a large number of similar runs is needed such as in design of infrastructure or forecasting with ensembles of probable storms. One solution to address the problem of computational cost is to employ adaptive mesh refinement (AMR) algorithms. AMR functions by decomposing the computational domain into regions which may vary in resolution as time proceeds. Decomposing the domain as the flow evolves makes this class of methods effective at ensuring that computational effort is spent only where it is needed. AMR also allows for placement of computational resolution independent of user interaction and expectation of the dynamics of the flow as well as particular regions of interest such as harbors. The simulation of many different applications have only been made possible by using AMR-type algorithms, which have allowed otherwise impractical simulations to be performed for much less computational expense. Our work involves studying how storm surge simulations can be improved with AMR algorithms. We have implemented relevant storm surge physics in the GeoClaw package and tested how Hurricane Ike's surge into Galveston Bay and up the Houston Ship Channel compares to available tide gauge data. We will also discuss issues dealing with refinement criteria, optimal resolution and refinement ratios, and inundation.
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.
Pavarino, E.; Neves, L. A.; Machado, J. M.; de Godoy, M. F.; Shiyou, Y.; Momente, J. C.; Zafalon, G. F. D.; Pinto, A. R.; Valêncio, C. R.
2013-01-01
The Finite Element Method is a well-known technique, being extensively applied in different areas. Studies using the Finite Element Method (FEM) are targeted to improve cardiac ablation procedures. For such simulations, the finite element meshes should consider the size and histological features of the target structures. However, it is possible to verify that some methods or tools used to generate meshes of human body structures are still limited, due to nondetailed models, nontrivial preprocessing, or mainly limitation in the use condition. In this paper, alternatives are demonstrated to solid modeling and automatic generation of highly refined tetrahedral meshes, with quality compatible with other studies focused on mesh generation. The innovations presented here are strategies to integrate Open Source Software (OSS). The chosen techniques and strategies are presented and discussed, considering cardiac structures as a first application context. PMID:23762031
NASA 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.
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
Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert
2016-06-21
A new mesh smoothing method designed to cluster mesh cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered elds, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness to arbitrary Lagrangian Eulerian (ALE) methods.
Composite-Grid Techniques and Adaptive Mesh Refinement in Computational Fluid Dynamics
1990-01-01
the equations govern- ing the flow. The patched adaptive mesh refinement technique, devised at Stanford by Oliger, et al ., copes with these sources of...patched adaptive mesh refinement technique, devised at Stanford by Oliger et al . [OL184], copes with these sources of error efficiently by refining...differential equation, as in the numerical grid generation methods proposed by Thompson et al . [THO85], or simply a list of pairs of points in
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.
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.
NASA Astrophysics Data System (ADS)
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.
Discontinuous deformation analysis with second-order finite element meshed block
NASA Astrophysics Data System (ADS)
Grayeli, Roozbeh; Mortazavi, Ali
2006-12-01
The discontinuous deformation analysis (DDA) with second-order displacement functions was derived based on six-node triangular mesh in order to satisfy the requirement for the accurate calculations in practical applications. The matrices of equilibrium equations for the second-order DDA were given in detail for program coding. By close comparison with widely used finite element method and closed form solutions, the advantages of the modified DDA were illustrated. The program coding was carried out in C++ environment and the new code applied to three examples with known analytical solutions. A very good agreement was achieved between the analytical and numerical results produced by the modified DDA code. Copyright
A Parallel Ocean Model With Adaptive Mesh Refinement Capability For Global Ocean Prediction
Herrnstein, Aaron R.
2005-12-01
An ocean model with adaptive mesh refinement (AMR) capability is presented for simulating ocean circulation on decade time scales. The model closely resembles the LLNL ocean general circulation model with some components incorporated from other well known ocean models when appropriate. Spatial components are discretized using finite differences on a staggered grid where tracer and pressure variables are defined at cell centers and velocities at cell vertices (B-grid). Horizontal motion is modeled explicitly with leapfrog and Euler forward-backward time integration, and vertical motion is modeled semi-implicitly. New AMR strategies are presented for horizontal refinement on a B-grid, leapfrog time integration, and time integration of coupled systems with unequal time steps. These AMR capabilities are added to the LLNL software package SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) and validated with standard benchmark tests. The ocean model is built on top of the amended SAMRAI library. The resulting model has the capability to dynamically increase resolution in localized areas of the domain. Limited basin tests are conducted using various refinement criteria and produce convergence trends in the model solution as refinement is increased. Carbon sequestration simulations are performed on decade time scales in domains the size of the North Atlantic and the global ocean. A suggestion is given for refinement criteria in such simulations. AMR predicts maximum pH changes and increases in CO_{2} concentration near the injection sites that are virtually unattainable with a uniform high resolution due to extremely long run times. Fine scale details near the injection sites are achieved by AMR with shorter run times than the finest uniform resolution tested despite the need for enhanced parallel performance. The North Atlantic simulations show a reduction in passive tracer errors when AMR is applied instead of a uniform coarse resolution. No
2013-01-01
Analysis of Adaptive Mesh Refinement for IMEX Discontinuous Galerkin Solutions of the Compressible Euler Equations with Application to Atmospheric...order discontinuous Galerkin method on quadrilateral grids with non-conforming elements. We perform a detailed analysis of the cost of AMR by comparing...adaptive mesh refinement, discontinuous Galerkin method, non-conforming mesh, IMEX, compressible Euler equations, atmospheric simulations 1. Introduction
NASA Astrophysics Data System (ADS)
Bercea, Gheorghe-Teodor; McRae, Andrew T. T.; Ham, David A.; Mitchell, Lawrence; Rathgeber, Florian; Nardi, Luigi; Luporini, Fabio; Kelly, Paul H. J.
2016-10-01
We present a generic algorithm for numbering and then efficiently iterating over the data values attached to an extruded mesh. An extruded mesh is formed by replicating an existing mesh, assumed to be unstructured, to form layers of prismatic cells. Applications of extruded meshes include, but are not limited to, the representation of three-dimensional high aspect ratio domains employed by geophysical finite element simulations. These meshes are structured in the extruded direction. The algorithm presented here exploits this structure to avoid the performance penalty traditionally associated with unstructured meshes. We evaluate the implementation of this algorithm in the Firedrake finite element system on a range of low compute intensity operations which constitute worst cases for data layout performance exploration. The experiments show that having structure along the extruded direction enables the cost of the indirect data accesses to be amortized after 10-20 layers as long as the underlying mesh is well ordered. We characterize the resulting spatial and temporal reuse in a representative set of both continuous-Galerkin and discontinuous-Galerkin discretizations. On meshes with realistic numbers of layers the performance achieved is between 70 and 90 % of a theoretical hardware-specific limit.
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.
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.
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.
Wang Yaqi; Ragusa, Jean C.
2011-02-01
Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest are functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.
Huang, W.; Zheng, Lingyun; Zhan, X.
2002-01-01
Accurate modelling of groundwater flow and transport with sharp moving fronts often involves high computational cost, when a fixed/uniform mesh is used. In this paper, we investigate the modelling of groundwater problems using a particular adaptive mesh method called the moving mesh partial differential equation approach. With this approach, the mesh is dynamically relocated through a partial differential equation to capture the evolving sharp fronts with a relatively small number of grid points. The mesh movement and physical system modelling are realized by solving the mesh movement and physical partial differential equations alternately. The method is applied to the modelling of a range of groundwater problems, including advection dominated chemical transport and reaction, non-linear infiltration in soil, and the coupling of density dependent flow and transport. Numerical results demonstrate that sharp moving fronts can be accurately and efficiently captured by the moving mesh approach. Also addressed are important implementation strategies, e.g. the construction of the monitor function based on the interpolation error, control of mesh concentration, and two-layer mesh movement. Copyright ?? 2002 John Wiley and Sons, Ltd.
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.
Adaptive moving finite volume scheme for flood inundation modeling under dry and complex topography
NASA Astrophysics Data System (ADS)
Zhou, F.; Chen, G.
2012-04-01
To assess and alleviate the risk of flood inundation on local scale, the use of numerical models with high accuracy, spatial resolution, and efficiency is crucial for the reliability of the solutions to provide the forecasts and early-warnings of flood inundation at large or meso-scales. Different with traditional numerical models on fixed meshes, an adaptive moving finite volume scheme on moving meshes is proposed for flood inundation modeling under dry and complex topography, this scheme aims to improve the predictive accuracy, spatial resolution, and computational efficiency as well as the satisfaction of well-balanced positivity preserving properties. The crucial feature of our scheme is to move fixed number of unstructured triangular meshes adaptively for approximating the time-variant patterns of flow variables and then to update flow variables through PDEs discretization on new meshes. At each time step of simulation, this scheme consists of three parts, giving in time n for instance: (1) adaptive mesh movement equation for adapting vertex from xij(n, v) to xij(n,v+1) where v is the iteration step, this equation can be transferred as Euler-Lagrange ones⛛· (ω⛛x) = 0, in which the monitor functionω is determined by the solution and the gradient of solution; (2) geometrical conservative interpolation for remapping flow variables from Ui(n, v) to Ui(n,v+1), when ||xij(n,v+1)-xij(n, v)||≤10-6 or v=5, then set xij(n, +∞):= xij(n,v+1) and Uj(n, +∞):= Uj(n,v+1), and (3) HLL-based PDEs discretization for updating flow variables from Ui(n,+∞) to Ui(n+1,0), the treatments of bed slope source terms and wet-dry interface are based on second-order reconstruction of Audusse et al., (2004) and Audusse and Bristeau (2005). Two analytical and two experimental test cases were performed to verify the advantages of the proposed scheme over non-adaptive methods. The results revealed two attractive features: (i) this scheme could achieve high-accuracy and high
Adaptive, Tactical Mesh Networking: Control Base MANET Model
2010-09-01
pp. 316–320 Available: IEEE Xplore , http://ieeexplore.ieee.org [Accessed: June 9, 2010]. [5] N. Sidiropoulos, “Multiuser Transmit Beamforming...Mobile Mesh Segments of TNT Testbed .......... 11 Figure 5. Infrastructure and Ad Hoc Mode of IEEE 802.11................................ 13 Figure...6. The Power Spectral Density of OFDM................................................ 14 Figure 7. A Typical IEEE 802.16 Network
Experiences with an adaptive mesh refinement algorithm in numerical relativity.
NASA Astrophysics Data System (ADS)
Choptuik, M. W.
An implementation of the Berger/Oliger mesh refinement algorithm for a model problem in numerical relativity is described. The principles of operation of the method are reviewed and its use in conjunction with leap-frog schemes is considered. The performance of the algorithm is illustrated with results from a study of the Einstein/massless scalar field equations in spherical symmetry.
POD-Galerkin reduced-order modeling with adaptive finite element snapshots
NASA Astrophysics Data System (ADS)
Ullmann, Sebastian; Rotkvic, Marko; Lang, Jens
2016-11-01
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear time-dependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.
Lee, W H; Kim, T S; Kim, Andrew T; Lee, S Y
2008-01-01
Realistic finite element (FE) head models have been successfully applied to bioelectromagnetic problems due to a realistic representation of arbitrary head geometry with inclusion of anisotropic material properties. In this paper, we propose a new automatic FE mesh generation scheme to generate a diffusion tensor MRI (DT-MRI) white matter anisotropy content-adaptive FE head model. We term this kind of mesh as wMesh. With this meshing technique, the anisotropic electrical conductivities derived from DT-MRIs can be best incorporated into the model. The influence of the white matter anisotropy on the EEG forward solutions has been studied via our wMesh head models. The scalp potentials computed from the anisotropic wMesh models against those of the isotropic models have been compared. The results describe that there are substantial changes in the scalp electrical potentials between the isotropic and anisotropic models, indicating that the inclusion of the white matter anisotropy is critical for accurate computation of E/MEG forward and inverse solutions. This fully automatic anisotropy-adaptive wMesh meshing scheme could be useful for modeling of individual-specific FE head models with better incorporation of the white matter anisotropic property towards bioelectromagnetic imaging.
NASA Astrophysics Data System (ADS)
Salinas, P.; Jackson, M.; Pavlidis, D.; Pain, C.; Adam, A.; Xie, Z.; Percival, J. R.
2015-12-01
We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. A given model typically contains numerous such geologic domains. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields, such as pressure, velocity or saturation, whilst preserving the geometry of the geologic domains. Up-, cross- or down-scaling of material properties during mesh optimization is not required, as the properties are uniform within each geologic domain. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media, in which CVs span boundaries between domains of contrasting material properties. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number.
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Xiao, Fei; Nagarajan, Anand
2016-12-01
A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.
NASA Astrophysics Data System (ADS)
Soghrati, Soheil; Xiao, Fei; Nagarajan, Anand
2017-04-01
A Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) technique is introduced for the automated transformation of a structured grid into a conforming mesh with appropriate element aspect ratios. The CISAMR algorithm is composed of three main phases: (i) Structured Adaptive Mesh Refinement (SAMR) of the background grid; (ii) r-adaptivity of the nodes of elements cut by the crack; (iii) sub-triangulation of the elements deformed during the r-adaptivity process and those with hanging nodes generated during the SAMR process. The required considerations for the treatment of crack tips and branching cracks are also discussed in this manuscript. Regardless of the complexity of the problem geometry and without using iterative smoothing or optimization techniques, CISAMR ensures that aspect ratios of conforming elements are lower than three. Multiple numerical examples are presented to demonstrate the application of CISAMR for modeling linear elastic fracture problems with intricate morphologies.
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
NASA Technical Reports Server (NTRS)
Mohan, Ram V.; Tamma, Kumar K.
1993-01-01
An adaptive time stepping strategy for transient thermal analysis of engineering systems is described which computes the time step based on the local truncation error with a good global error control and obtains optimal time steps to be used during the analysis. Combined mesh partitionings involving FEM/FVM meshes based on physical situations to obtain numerically improved physical representations are also proposed. Numerical test cases are described and comparative pros and cons are identified for practical situations.
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.
McCorquodale, Peter; Ullrich, Paul; Johansen, Hans; ...
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.
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.
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
Ying, Wenjun; Henriquez, Craig S
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented.
Ying, Wenjun; Henriquez, Craig S.
2015-01-01
A both space and time adaptive algorithm is presented for simulating electrical wave propagation in the Purkinje system of the heart. The equations governing the distribution of electric potential over the system are solved in time with the method of lines. At each timestep, by an operator splitting technique, the space-dependent but linear diffusion part and the nonlinear but space-independent reactions part in the partial differential equations are integrated separately with implicit schemes, which have better stability and allow larger timesteps than explicit ones. The linear diffusion equation on each edge of the system is spatially discretized with the continuous piecewise linear finite element method. The adaptive algorithm can automatically recognize when and where the electrical wave starts to leave or enter the computational domain due to external current/voltage stimulation, self-excitation, or local change of membrane properties. Numerical examples demonstrating efficiency and accuracy of the adaptive algorithm are presented. PMID:26581455
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.
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
NASA Astrophysics Data System (ADS)
Péron, Stéphanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
Adaptive Mesh Refinement for a High-Symmetry Singular Euler Flow
NASA Astrophysics Data System (ADS)
Germaschewski, K.; Bhattacharjee, A.; Grauer, R.
2002-11-01
Starting from a highly symmetric initial condition motivated by the work of Kida [J. Phys. Soc Jpn. 54, 2132 (1995)] and Boratav and Pelz [Phys. Fluids 6, 2757 (1994)], we use the technique of block-structured adaptive mesh refinement (AMR) to numerically investigate the development of a self-similar singular solution to the incompressible Euler equations. The scheme, previously used by Grauer et al [Phys. Rev. Lett. 84, 4850 (1998)], is particularly well suited to follow the development of singular structures as it allows for effective resolutions far beyond those accessible using fixed grid algorithms. A self-similar collapse is observed in the simulation, where the maximum vorticity blows up as 1/(t_crit-t). Ng and Bhattacharjee [Phys Rev E 54, 1530 (1996)] have presented a sufficient condition for a finite-time singularity in this highly symmetric flow involving the fourth-order spatial derivative of the pressure at and near the origin. We test this sufficient condition and investigate the evolution of the spatial range over which this condition holds in our numerical results. We also demonstrate numerically that this singularity is unstable because in a full simulation that does not build in the symmetries of the initial condition, small perturbations introduced by AMR lead to nonsymmetric evolution of the vortices.
NASA Astrophysics Data System (ADS)
Heumann, Holger; Rapetti, Francesca
2017-04-01
Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in tokamak engineering, is constrained to nodes of the mesh leading to undesired jumps in transient problems. Moreover, recent numerical results for the self-consistent coupling of equilibrium with resistive diffusion and transport suggest the necessity of higher regularity when approximating the flux map. In this work we propose a mortar element method that employs two overlapping meshes. One mesh with Cartesian quadrilaterals covers the vacuum chamber domain accessible by the plasma and one mesh with triangles discretizes the region outside. The two meshes overlap in a narrow region. This approach gives the flexibility to achieve easily and at low cost higher order regularity for the approximation of the flux function in the domain covered by the plasma, while preserving accurate meshing of the geometric details outside this region. The continuity of the numerical solution in the region of overlap is weakly enforced by a mortar-like mapping.
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.
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.
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.
Ibrahim, Ahmad M.; Wilson, Paul P.H.; Sawan, Mohamed 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.
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.
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.
NASA Astrophysics Data System (ADS)
Mostaghimi, P.; Percival, J. R.; Pavlidis, D.; Gorman, G.; Jackson, M.; Neethling, S.; Pain, C. C.
2013-12-01
Numerical simulation of multiphase flow in porous media is of importance in a wide range of applications in science and engineering. We present a novel control volume finite element method (CVFEM) to solve for multi-scale flow in heterogeneous geological formations. It employs a node centred control volume approach to discretize the saturation equation, while a control volume finite element method is applied for the pressure equation. We embed the discrete continuity equation into the pressure equation and assure that the continuity is exactly enforced. Anisotropic mesh adaptivity is used to accurately model the fine grained features of multiphase 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. Moreover, it uses metric advection between adaptive meshes in order to predict the future required density of mesh thereby reducing numerical dispersion at the saturation front. The scheme is capable of capturing multi-scale heterogeneity such as those in fractured porous media through the use of several constraints on the element size in different regions of porous media. We show the application of our method for simulation of flow in some challenging benchmark problems. For flow in fractured reservoirs, the scheme adapts the mesh as the flow penetrates through the fracture and the matrix. The constraints for the element size within the fracture are smaller by several orders of magnitude than the generated mesh within the matrix. We show that the scheme captures the key multi-scale features of flow while preserving the geometry. We demonstrate that mesh adaptation can be used to accurately simulate flow in heterogeneous porous media at low computational cost.
Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F
2010-07-01
Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.
Adaptive finite element methods for the solution of inverse problems in optical tomography
NASA Astrophysics Data System (ADS)
Bangerth, Wolfgang; Joshi, Amit
2008-06-01
Optical tomography attempts to determine a spatially variable coefficient in the interior of a body from measurements of light fluxes at the boundary. Like in many other applications in biomedical imaging, computing solutions in optical tomography is complicated by the fact that one wants to identify an unknown number of relatively small irregularities in this coefficient at unknown locations, for example corresponding to the presence of tumors. To recover them at the resolution needed in clinical practice, one has to use meshes that, if uniformly fine, would lead to intractably large problems with hundreds of millions of unknowns. Adaptive meshes are therefore an indispensable tool. In this paper, we will describe a framework for the adaptive finite element solution of optical tomography problems. It takes into account all steps starting from the formulation of the problem including constraints on the coefficient, outer Newton-type nonlinear and inner linear iterations, regularization, and in particular the interplay of these algorithms with discretizing the problem on a sequence of adaptively refined meshes. We will demonstrate the efficiency and accuracy of these algorithms on a set of numerical examples of clinical relevance related to locating lymph nodes in tumor diagnosis.
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.
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.
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)
Barral, N.; Olivier, G.; Alauzet, F.
2017-02-01
Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space-time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach.
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
NASA Astrophysics Data System (ADS)
Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R. G.
2013-02-01
Small-scale experiments of volcanic ash particle settling in water have demonstrated that ash particles can either settle slowly and individually, or rapidly and collectively as a gravitationally unstable ash-laden plume. This has important implications for the emplacement of tephra deposits on the seabed. Numerical modelling has the potential to extend the results of laboratory experiments to larger scales and explore the conditions under which plumes may form and persist, but many existing models are computationally restricted by the fixed mesh approaches that they employ. In contrast, this paper presents a new multiphase flow model that uses an adaptive unstructured mesh approach. As a simulation progresses, the mesh is optimized to focus numerical resolution in areas important to the dynamics and decrease it where it is not needed, thereby potentially reducing computational requirements. Model verification is performed using the method of manufactured solutions, which shows the correct solution convergence rates. Model validation and application considers 2-D simulations of plume formation in a water tank which replicate published laboratory experiments. The numerically predicted settling velocities for both individual particles and plumes, as well as instability behaviour, agree well with experimental data and observations. Plume settling is clearly hindered by the presence of a salinity gradient, and its influence must therefore be taken into account when considering particles in bodies of saline water. Furthermore, individual particles settle in the laminar flow regime while plume settling is shown (by plume Reynolds numbers greater than unity) to be in the turbulent flow regime, which has a significant impact on entrainment and settling rates. Mesh adaptivity maintains solution accuracy while providing a substantial reduction in computational requirements when compared to the same simulation performed using a fixed mesh, highlighting the benefits of an
Adaptive Meshing of Ship Air-Wake Flowfields
2014-10-21
resolve gradients of the adaptation function. The third method is a meshless method that uses a physics-based force model to move nodes around to...method that uses a physics-based force model to move nodes around to resolve the geometry and flowfield. The initial phase of the research conducted...three codes all solve the unsteady Euler equations, but use different discretization strategies. The target application is an aircraft in a landing
Adaptive finite difference for seismic wavefield modelling in acoustic media.
Yao, Gang; Wu, Di; Debens, Henry Alexander
2016-08-05
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
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.
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.
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.
Reddy, A.V.; Kothe, D.B.; Lam, K.L.
1997-06-01
The Los Alamos National Laboratory (LANL) is currently developing a new casting simulation tool (known as Telluride) that employs robust, high-resolution finite volume algorithms for incompressible fluid flow, volume tracking of interfaces, and solidification physics on three-dimensional (3-D) unstructured meshes. Their finite volume algorithms are based on colocated cell-centered schemes that are formally second order in time and space. The flow algorithm is a 3-D extension of recent work on projection method solutions of the Navier-Stokes (NS) equations. Their volume tracking algorithm can accurately track topologically complex interfaces by approximating the interface geometry as piecewise planar. Coupled to their fluid flow algorithm is a comprehensive binary alloy solidification model that incorporates macroscopic descriptions of heat transfer, solute redistribution, and melt convection as well as a microscopic description of segregation. The finite volume algorithms, which are efficient, parallel, and robust, can yield high-fidelity solutions on a variety of meshes, ranging from those that are structured orthogonal to fully unstructured (finite element). The authors discuss key computer science issues that have enabled them to efficiently parallelize their unstructured mesh algorithms on both distributed and shared memory computing platforms. These include their functionally object-oriented use of Fortran 90 and new parallel libraries for gather/scatter functions (PGSLib) and solutions of linear systems of equations (JTpack90). Examples of their current capabilities are illustrated with simulations of mold filling and solidification of complex 3-D components currently being poured in LANL foundries.
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.
Campbell, J Q; Coombs, D J; Rao, M; Rullkoetter, P J; Petrella, A J
2016-09-06
The purpose of this study was to seek broad verification and validation of human lumbar spine finite element models created using a previously published automated algorithm. The automated algorithm takes segmented CT scans of lumbar vertebrae, automatically identifies important landmarks and contact surfaces, and creates a finite element model. Mesh convergence was evaluated by examining changes in key output variables in response to mesh density. Semi-direct validation was performed by comparing experimental results for a single specimen to the automated finite element model results for that specimen with calibrated material properties from a prior study. Indirect validation was based on a comparison of results from automated finite element models of 18 individual specimens, all using one set of generalized material properties, to a range of data from the literature. A total of 216 simulations were run and compared to 186 experimental data ranges in all six primary bending modes up to 7.8Nm with follower loads up to 1000N. Mesh convergence results showed less than a 5% difference in key variables when the original mesh density was doubled. The semi-direct validation results showed that the automated method produced results comparable to manual finite element modeling methods. The indirect validation results showed a wide range of outcomes due to variations in the geometry alone. The studies showed that the automated models can be used to reliably evaluate lumbar spine biomechanics, specifically within our intended context of use: in pure bending modes, under relatively low non-injurious simulated in vivo loads, to predict torque rotation response, disc pressures, and facet forces.
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.
De Colle, Fabio; Ramirez-Ruiz, Enrico; Granot, Jonathan; Lopez-Camara, Diego
2012-02-20
We report on the development of Mezcal-SRHD, a new adaptive mesh refinement, special relativistic hydrodynamics (SRHD) code, developed with the aim of studying the highly relativistic flows in gamma-ray burst sources. The SRHD equations are solved using finite-volume conservative solvers, with second-order interpolation in space and time. The correct implementation of the algorithms is verified by one-dimensional (1D) and multi-dimensional tests. The code is then applied to study the propagation of 1D spherical impulsive blast waves expanding in a stratified medium with {rho}{proportional_to}r{sup -k}, bridging between the relativistic and Newtonian phases (which are described by the Blandford-McKee and Sedov-Taylor self-similar solutions, respectively), as well as to a two-dimensional (2D) cylindrically symmetric impulsive jet propagating in a constant density medium. It is shown that the deceleration to nonrelativistic speeds in one dimension occurs on scales significantly larger than the Sedov length. This transition is further delayed with respect to the Sedov length as the degree of stratification of the ambient medium is increased. This result, together with the scaling of position, Lorentz factor, and the shock velocity as a function of time and shock radius, is explained here using a simple analytical model based on energy conservation. The method used for calculating the afterglow radiation by post-processing the results of the simulations is described in detail. The light curves computed using the results of 1D numerical simulations during the relativistic stage correctly reproduce those calculated assuming the self-similar Blandford-McKee solution for the evolution of the flow. The jet dynamics from our 2D simulations and the resulting afterglow light curves, including the jet break, are in good agreement with those presented in previous works. Finally, we show how the details of the dynamics critically depend on properly resolving the structure of the
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.
Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania
2016-11-08
Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipatedmore » during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.« less
Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania
2016-11-08
Fracture and fragmentation are extremely nonlinear multiscale processes in which microscale damage mechanisms emerge at the macroscale as new fracture surfaces. Numerous numerical methods have been developed for simulating fracture initiation, propagation, and coalescence. In this paper, we present a computational approach for modeling pervasive fracture in quasi-brittle materials based on random close-packed Voronoi tessellations. Each Voronoi cell is formulated as a polyhedral finite element containing an arbitrary number of vertices and faces. Fracture surfaces are allowed to nucleate only at the intercell faces. Cohesive softening tractions are applied to new fracture surfaces in order to model the energy dissipated during fracture growth. The randomly seeded Voronoi cells provide a regularized discrete random network for representing fracture surfaces. The potential crack paths within the random network are viewed as instances of realizable crack paths within the continuum material. Mesh convergence of fracture simulations is viewed in a weak, or distributional, sense. The explicit facet representation of fractures within this approach is advantageous for modeling contact on new fracture surfaces and fluid flow within the evolving fracture network. Finally, applications of interest include fracture and fragmentation in quasi-brittle materials and geomechanical applications such as hydraulic fracturing, engineered geothermal systems, compressed-air energy storage, and carbon sequestration.
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.
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
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.
Adaptive Finite Element Method for Solving the Exact Kohn-Sham Equation of Density Functional Theory
Bylaska, Eric J.; Holst, Michael; Weare, John H.
2009-04-14
Results of the application of an adaptive finite element (FE) based solution using the FETK library of M. Holst to Density Functional Theory (DFT) approximation to the electronic structure of atoms and molecules are reported. The severe problem associated with the rapid variation of the electronic wave functions in the near singular regions of the atomic centers is treated by implementing completely unstructured simplex meshes that resolve these features around atomic nuclei. This concentrates the computational work in the regions in which the shortest length scales are necessary and provides for low resolution in regions for which there is no electron density. The accuracy of the solutions significantly improved when adaptive mesh refinement was applied, and it was found that the essential difficulties of the Kohn-Sham eigenvalues equation were the result of the singular behavior of the atomic potentials. Even though the matrix representations of the discrete Hamiltonian operator in the adaptive finite element basis are always sparse with a linear complexity in the number of discretization points, the overall memory and computational requirements for the solver implemented were found to be quite high. The number of mesh vertices per atom as a function of the atomic number Z and the required accuracy e (in atomic units) was esitmated to be v (e;Z) = 122:37 * Z2:2346 /1:1173 , and the number of floating point operations per minimization step for a system of NA atoms was found to be 0(N3A*v(e,Z0) (e.g. Z=26, e=0.0015 au, and NA=100, the memory requirement and computational cost would be ~0.2 terabytes and ~25 petaflops). It was found that the high cost of the method could be reduced somewhat by using a geometric based refinement strategy to fix the error near the singularities.
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)
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.
Mesh adaption for efficient multiscale implementation of one-dimensional turbulence
NASA Astrophysics Data System (ADS)
Lignell, D. O.; Kerstein, A. R.; Sun, G.; Monson, E. I.
2013-06-01
One-Dimensional Turbulence (ODT) is a stochastic model for turbulent flow simulation. In an atmospheric context, it is analogous to single-column modeling (SCM) in that it lives on a 1D spatial domain, but different in that it time advances individual flow realizations rather than ensemble-averaged quantities. The lack of averaging enables a physically sound multiscale treatment, which is useful for resolving sporadic localized phenomena, as seen in stably stratified regimes, and sharp interfaces, as observed where a convective layer encounters a stable overlying zone. In such flows, the relevant scale range is so large that it is beneficial to enhance model performance by introducing an adaptive mesh. An adaptive-mesh algorithm that provides the desired performance characteristics is described and demonstrated, and its implications for the ODT advancement scheme are explained.
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.
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.
Numerical Modelling of Volcanic Ash Settling in Water Using Adaptive Unstructured Meshes
NASA Astrophysics Data System (ADS)
Jacobs, C. T.; Collins, G. S.; Piggott, M. D.; Kramer, S. C.; Wilson, C. R.
2011-12-01
At the bottom of the world's oceans lies layer after layer of ash deposited from past volcanic eruptions. Correct interpretation of these layers can provide important constraints on the duration and frequency of volcanism, but requires a full understanding of the complex multi-phase settling and deposition process. Analogue experiments of tephra settling through a tank of water demonstrate that small ash particles can either settle individually, or collectively as a gravitationally unstable ash-laden plume. These plumes are generated when the concentration of particles exceeds a certain threshold such that the density of the tephra-water mixture is sufficiently large relative to the underlying particle-free water for a gravitational Rayleigh-Taylor instability to develop. These ash-laden plumes are observed to descend as a vertical density current at a velocity much greater than that of single particles, which has important implications for the emplacement of tephra deposits on the seabed. To extend the results of laboratory experiments to large scales and explore the conditions under which vertical density currents may form and persist, we have developed a multi-phase extension to Fluidity, a combined finite element / control volume CFD code that uses adaptive unstructured meshes. As a model validation, we present two- and three-dimensional simulations of tephra plume formation in a water tank that replicate laboratory experiments (Carey, 1997, doi:10.1130/0091-7613(1997)025<0839:IOCSOT>2.3.CO;2). An inflow boundary condition at the top of the domain allows particles to flux in at a constant rate of 0.472 gm-2s-1, forming a near-surface layer of tephra particles, which initially settle individually at the predicted Stokes velocity of 1.7 mms-1. As more tephra enters the water and the particle concentration increases, the layer eventually becomes unstable and plumes begin to form, descending with velocities more than ten times greater than those of individual
Knox, J; Kralj, B; Hubsch, P; Middleton, J; Jones, M L
2001-04-01
The objective of this study was to evaluate the influence of bracket base mesh geometry on the stresses generated in the bracket-cement-tooth continuum by a shear/peel load case. A validated three-dimensional finite element model of the bracket-cement-tooth system was constructed consisting of 15,324 nodes and 2971 finite elements. Cement geometric and physical properties were held constant and bracket base geometry was varied, representing a variety of single-mesh configurations and 1 double-mesh design. For the single-mesh designs, increasing wire diameter (100-400 microm) resulted in a decrease in enamel and cement stresses. Increases in wire mesh spacing (200-750 microm) increased the major principal stress recorded in the enamel and adhesive at all wire diameters. Within the bracket, the major principal stress increased significantly at wire spacing above 400-500 microm. However, within the impregnated wire mesh (IWM), the major principal stress decreased as wire space increased. When the double-mesh bracket base was considered, the combined mesh layers resulted in a decrease in the stresses recorded in the most superficial (coarse) mesh layer and an increase in the stresses recorded in the deepest (fine mesh) layer when compared with the single-layer designs in isolation. Modification of single-mesh spacing and wire diameter influences the magnitude and distribution of stresses within the bracket-cement-tooth continuum. The use of a double-mesh design results in a reduction in the stresses recorded in the most superficial mesh. Mesh design influenced stress distribution in this study, primarily by determining the flexibility of the bracket base.
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.
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.
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.
Adaptive Mesh Euler Equation Computation of Vortex Breakdown in Delta Wing Flow.
NASA Astrophysics Data System (ADS)
Modiano, David Laurence
A solution method for the three-dimensional Euler equations is formulated and implemented. The solver uses an unstructured mesh of tetrahedral cells and performs adaptive refinement by mesh-point embedding to increase mesh resolution in regions of interesting flow features. The fourth-difference artificial dissipation is increased to a higher order of accuracy using the method of Holmes and Connell. A new method of temporal integration is developed to accelerate the explicit computation of unsteady flows. The solver is applied to the solution of the flow around a sharp edged delta wing, with emphasis on the behavior of the leading edge vortex above the leeside of the wing at high angle of attack, under which conditions the vortex suffers from vortex breakdown. Large deviations in entropy, which indicate vortical regions of the flow, specify the region in which adaptation is performed. Adaptive flow calculations are performed at ten different angles of attack, at seven of which vortex breakdown occurs. The aerodynamic normal force coefficients show excellent agreement with wind tunnel data measured by Jarrah, which demonstrates the importance of adaptation in obtaining an accurate solution. The pitching moment coefficient and the location of vortex breakdown are compared with experimental data measured by Hummel and Srinivasan, with which fairly good agreement is seen in cases in which the location of breakdown is over the wing. A series of unsteady calculations involving a pitching delta wing were performed. The use of the acceleration technique is validated. A hysteresis in the normal force is observed, as in experiments, and a lag in the breakdown position is demonstrated. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).
Gonzales, Matthew J.; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M.; Zhang, Yongjie; Segars, W. Paul; McCulloch, Andrew D.
2013-01-01
High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the “local-to-global” derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 millimeters, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. PMID:23602918
Gonzales, Matthew J; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M; Zhang, Yongjie; Segars, W Paul; McCulloch, Andrew D
2013-07-01
High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology.
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)
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.
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-mesh-based algorithm for fluorescence molecular tomography using an analytical solution
NASA Astrophysics Data System (ADS)
Wang, Daifa; Song, Xiaolei; Bai, Jing
2007-07-01
Fluorescence molecular tomography (FMT) has become an important method for in-vivo imaging of small animals. It has been widely used for tumor genesis, cancer detection, metastasis, drug discovery, and gene therapy. In this study, an algorithm for FMT is proposed to obtain accurate and fast reconstruction by combining an adaptive mesh refinement technique and an analytical solution of diffusion equation. Numerical studies have been performed on a parallel plate FMT system with matching fluid. The reconstructions obtained show that the algorithm is efficient in computation time, and they also maintain image quality.
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
2010-08-10
Implicit integration factor (IIF) method, a class of efficient semi-implicit temporal scheme, was introduced recently for stiff reaction-diffusion equations. To reduce cost of IIF, compact implicit integration factor (cIIF) method was later developed for efficient storage and calculation of exponential matrices associated with the diffusion operators in two and three spatial dimensions for Cartesian coordinates with regular meshes. Unlike IIF, cIIF cannot be directly extended to other curvilinear coordinates, such as polar and spherical coordinate, due to the compact representation for the diffusion terms in cIIF. In this paper, we present a method to generalize cIIF for other curvilinear coordinates through examples of polar and spherical coordinates. The new cIIF method in polar and spherical coordinates has similar computational efficiency and stability properties as the cIIF in Cartesian coordinate. In addition, we present a method for integrating cIIF with adaptive mesh refinement (AMR) to take advantage of the excellent stability condition for cIIF. Because the second order cIIF is unconditionally stable, it allows large time steps for AMR, unlike a typical explicit temporal scheme whose time step is severely restricted by the smallest mesh size in the entire spatial domain. Finally, we apply those methods to simulating a cell signaling system described by a system of stiff reaction-diffusion equations in both two and three spatial dimensions using AMR, curvilinear and Cartesian coordinates. Excellent performance of the new methods is observed.
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.
NASA Astrophysics Data System (ADS)
Cai, Hongzhu; Hu, Xiangyun; Li, Jianhui; Endo, Masashi; Xiong, Bin
2017-02-01
We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling.
NASA Astrophysics Data System (ADS)
Li, Weidong; Luo, Li-Shi
2016-12-01
This work proposes a fully implicit lattice Boltzmann (LB) scheme based on finite-volume (FV) discretization on arbitrary unstructured meshes. The linear system derived from the finite-volume lattice Boltzmann equation (LBE) is solved by the block lower-upper (BLU) symmetric-Gauss-Seidel (SGS) algorithm. The proposed implicit FV-LB scheme is efficient and robust, and has a low-storage requirement. The effectiveness and efficiency of the proposed implicit FV-LB scheme are validated and verified by the simulations of three test cases in two dimensions: (a) the laminar Blasius flow over a flat plate with Re =105; (b) the steady viscous flow past a circular cylinder with Re = 10, 20, and 40; and (c) the inviscid flow past a circular cylinder. The proposed implicit FV-LB scheme is shown to be not only effective and efficient for simulations of steady viscous flows, but also robust and efficient for simulations of inviscid flows in particular.
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)
Parkinson, S. D.; Hill, J.; Piggott, M. D.; Allison, P. A.
2014-09-01
High-resolution direct numerical simulations (DNSs) 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 model performance in capturing the range of dynamics on a range of meshes. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. The use of adaptive mesh optimisation is shown to reduce the required element count by approximately two orders of magnitude in comparison with fixed, uniform mesh simulations. This leads to a substantial reduction in computational cost. The computational savings and flexibility afforded by adaptivity along with the flexibility of FE methods make this model well suited to simulating turbidity currents in complex domains.
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.
Lapelosa, Mauro; Abrams, Cameron F
2013-10-01
Rare events between states in complex systems are fundamental in many scientific fields and can be studied by building reaction pathways. A theoretical framework to analyze reaction pathways is provided by transition-path theory (TPT). The central object in TPT is the committor function, which is found by solution of the backward-Kolmogorov equation on a given potential. Once determined, the committor can be used to calculate reactive fluxes and rates, among other important quantities. We demonstrate here that the committor can be calculated using the method of finite elements on non-uniform meshes. We show that this approach makes it feasible to perform TPT calculations on 3D potentials because it requires many fewer degrees of freedom than a regular-mesh finite-difference approach. In various illustrative 2D and 3D problems, we calculate the committor function and reaction rates at different temperatures, and we discuss effects of temperatures and simple entropic barriers on the structure of the committor and the reaction rate constants.
A DAFT DL_POLY distributed memory adaptation of the Smoothed Particle Mesh Ewald method
NASA Astrophysics Data System (ADS)
Bush, I. J.; Todorov, I. T.; Smith, W.
2006-09-01
The Smoothed Particle Mesh Ewald method [U. Essmann, L. Perera, M.L. Berkowtz, T. Darden, H. Lee, L.G. Pedersen, J. Chem. Phys. 103 (1995) 8577] for calculating long ranged forces in molecular simulation has been adapted for the parallel molecular dynamics code DL_POLY_3 [I.T. Todorov, W. Smith, Philos. Trans. Roy. Soc. London 362 (2004) 1835], making use of a novel 3D Fast Fourier Transform (DAFT) [I.J. Bush, The Daresbury Advanced Fourier transform, Daresbury Laboratory, 1999] that perfectly matches the Domain Decomposition (DD) parallelisation strategy [W. Smith, Comput. Phys. Comm. 62 (1991) 229; M.R.S. Pinches, D. Tildesley, W. Smith, Mol. Sim. 6 (1991) 51; D. Rapaport, Comput. Phys. Comm. 62 (1991) 217] of the DL_POLY_3 code. In this article we describe software adaptations undertaken to import this functionality and provide a review of its performance.
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
Anderson, R W; Pember, R B; Elliot, N S
2000-09-26
A new method for the solution of the unsteady Euler equations has been developed. The method combines staggered grid Lagrangian techniques with structured local adaptive mesh refinement (AMR). This method is a precursor to a more general adaptive arbitrary Lagrangian Eulerian (ALE-AMR) algorithm under development, which will facilitate the solution of problems currently at and beyond the boundary of soluble problems by traditional ALE methods by focusing computational resources where they are required. Many of the core issues involved in the development of the ALE-AMR method hinge upon the integration of AMR with a Lagrange step, which is the focus of the work described here. The novel components of the method are mainly driven by the need to reconcile traditional AMR techniques, which are typically employed on stationary meshes with cell-centered quantities, with the staggered grids and grid motion employed by Lagrangian methods. These new algorithmic components are first developed in one dimension and are then generalized to two dimensions. Solutions of several model problems involving shock hydrodynamics are presented and discussed.
AMRSim: an object-oriented performance simulator for parallel adaptive mesh refinement
Miller, B; Philip, B; Quinlan, D; Wissink, A
2001-01-08
Adaptive mesh refinement is complicated by both the algorithms and the dynamic nature of the computations. In parallel the complexity of getting good performance is dependent upon the architecture and the application. Most attempts to address the complexity of AMR have lead to the development of library solutions, most have developed object-oriented libraries or frameworks. All attempts to date have made numerous and sometimes conflicting assumptions which make the evaluation of performance of AMR across different applications and architectures difficult or impracticable. The evaluation of different approaches can alternatively be accomplished through simulation of the different AMR processes. In this paper we outline our research work to simulate the processing of adaptive mesh refinement grids using a distributed array class library (P++). This paper presents a combined analytic and empirical approach, since details of the algorithms can be readily predicted (separated into specific phases), while the performance associated with the dynamic behavior must be studied empirically. The result, AMRSim, provides a simple way to develop bounds on the expected performance of AMR calculations subject to constraints given by the algorithms, frameworks, and architecture.
GAMER: A GRAPHIC PROCESSING UNIT ACCELERATED ADAPTIVE-MESH-REFINEMENT CODE FOR ASTROPHYSICS
Schive, H.-Y.; Tsai, Y.-C.; Chiueh Tzihong
2010-02-01
We present the newly developed code, GPU-accelerated Adaptive-MEsh-Refinement code (GAMER), which adopts a novel approach in improving the performance of adaptive-mesh-refinement (AMR) astrophysical simulations by a large factor with the use of the graphic processing unit (GPU). The AMR implementation is based on a hierarchy of grid patches with an oct-tree data structure. We adopt a three-dimensional relaxing total variation diminishing scheme for the hydrodynamic solver and a multi-level relaxation scheme for the Poisson solver. Both solvers have been implemented in GPU, by which hundreds of patches can be advanced in parallel. The computational overhead associated with the data transfer between the CPU and GPU is carefully reduced by utilizing the capability of asynchronous memory copies in GPU, and the computing time of the ghost-zone values for each patch is diminished by overlapping it with the GPU computations. We demonstrate the accuracy of the code by performing several standard test problems in astrophysics. GAMER is a parallel code that can be run in a multi-GPU cluster system. We measure the performance of the code by performing purely baryonic cosmological simulations in different hardware implementations, in which detailed timing analyses provide comparison between the computations with and without GPU(s) acceleration. Maximum speed-up factors of 12.19 and 10.47 are demonstrated using one GPU with 4096{sup 3} effective resolution and 16 GPUs with 8192{sup 3} effective resolution, respectively.
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.
NASA Astrophysics Data System (ADS)
Boscheri, Walter; Balsara, Dinshaw S.; Dumbser, Michael
2014-06-01
In this paper we use the genuinely multidimensional HLL Riemann solvers recently developed by Balsara et al. in [13] to construct a new class of computationally efficient high order Lagrangian ADER-WENO one-step ALE finite volume schemes on unstructured triangular meshes. A nonlinear WENO reconstruction operator allows the algorithm to achieve high order of accuracy in space, while high order of accuracy in time is obtained by the use of an ADER time-stepping technique based on a local space-time Galerkin predictor. The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the grid, considering the entire Voronoi neighborhood of each node and allow for larger time steps than conventional one-dimensional Riemann solvers. The results produced by the multidimensional Riemann solver are then used twice in our one-step ALE algorithm: first, as a node solver that assigns a unique velocity vector to each vertex, in order to preserve the continuity of the computational mesh; second, as a building block for genuinely multidimensional numerical flux evaluation that allows the scheme to run with larger time steps compared to conventional finite volume schemes that use classical one-dimensional Riemann solvers in normal direction. The space-time flux integral computation is carried out at the boundaries of each triangular space-time control volume using the Simpson quadrature rule in space and Gauss-Legendre quadrature in time. A rezoning step may be necessary in order to overcome element overlapping or crossing-over. Since our one-step ALE finite volume scheme is based directly on a space-time conservation formulation of the governing PDE system, the remapping stage is not needed, making our algorithm a so-called direct ALE method.
Selvan, S Easter; Borckmans, Pierre B; Chattopadhyay, A; Absil, P-A
2013-09-01
It is seemingly paradoxical to the classical definition of the independent component analysis (ICA), that in reality, the true sources are often not strictly uncorrelated. With this in mind, this letter concerns a framework to extract quasi-uncorrelated sources with finite supports by optimizing a range-based contrast function under unit-norm constraints (to handle the inherent scaling indeterminacy of ICA) but without orthogonality constraints. Albeit the appealing contrast properties of the range-based function (e.g., the absence of mixing local optima), the function is not differentiable everywhere. Unfortunately, there is a dearth of literature on derivative-free optimizers that effectively handle such a nonsmooth yet promising contrast function. This is the compelling reason for the design of a nonsmooth optimization algorithm on a manifold of matrices having unit-norm columns with the following objectives: to ascertain convergence to a Clarke stationary point of the contrast function and adhere to the necessary unit-norm constraints more naturally. The proposed nonsmooth optimization algorithm crucially relies on the design and analysis of an extension of the mesh adaptive direct search (MADS) method to handle locally Lipschitz objective functions defined on the sphere. The applicability of the algorithm in the ICA domain is demonstrated with simulations involving natural, face, aerial, and texture images.
Scalable and Adaptive Streaming of 3D Mesh to Heterogeneous Devices
NASA Astrophysics Data System (ADS)
Abderrahim, Zeineb; Bouhlel, Mohamed Salim
2016-12-01
This article comprises a presentation of a web platform for the diffusion and visualization of 3D compressed data on the web. Indeed, the major goal of this work resides in the proposal of the transfer adaptation of the three-dimensional data to resources (network bandwidth, the type of visualization terminals, display resolution, user's preferences...). Also, it is an attempt to provide an effective consultation adapted to the user's request (preferences, levels of the requested detail, etc.). Such a platform can adapt the levels of detail to the change in the bandwidth and the rendering time when loading the mesh at the client level. In addition, the levels of detail are adapted to the distance between the object and the camera. These features are able to minimize the latency time and to make the real time interaction possible. The experiences as well as the comparison with the existing solutions show auspicious results in terms of latency, scalability and the quality of the experience offered to the users.
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.
WHITE DWARF MERGERS ON ADAPTIVE MESHES. I. METHODOLOGY AND CODE VERIFICATION
Katz, Max P.; Zingale, Michael; Calder, Alan C.; Swesty, F. Douglas; Almgren, Ann S.; Zhang, Weiqun
2016-03-10
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.
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.
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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Chilton, Sven; Colella, Phillip
2010-11-01
Adaptive mesh refinement (AMR) is an efficient technique for solving systems of partial differential equations numerically. The underlying algorithm determines where and when a base spatial and temporal grid must be resolved further in order to achieve the desired precision and accuracy in the numerical solution. However, propagating wave solutions prove problematic for AMR. In systems with low degrees of dissipation (e.g. the Maxwell-Vlasov system) a wave traveling from a finely resolved region into a coarsely resolved region encounters a numerical impedance mismatch, resulting in spurious reflections off of the coarse-fine grid boundary. These reflected waves then become trapped inside the fine region. Here, we present a scheme for damping these spurious reflections. We demonstrate its application to the scalar wave equation and an implementation for Maxwell's Equations. We also discuss a possible extension to the Maxwell-Vlasov system.
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.
A GPU implementation of adaptive mesh refinement to simulate tsunamis generated by landslides
NASA Astrophysics Data System (ADS)
de la Asunción, Marc; Castro, Manuel J.
2016-04-01
In this work we propose a CUDA implementation for the simulation of landslide-generated tsunamis using a two-layer Savage-Hutter type model and adaptive mesh refinement (AMR). The AMR method consists of dynamically increasing the spatial resolution of the regions of interest of the domain while keeping the rest of the domain at low resolution, thus obtaining better runtimes and similar results compared to increasing the spatial resolution of the entire domain. Our AMR implementation uses a patch-based approach, it supports up to three levels, power-of-two ratios of refinement, different refinement criteria and also several user parameters to control the refinement and clustering behaviour. A strategy based on the variation of the cell values during the simulation is used to interpolate and propagate the values of the fine cells. Several numerical experiments using artificial and realistic scenarios are presented.
MPI parallelization of full PIC simulation code with Adaptive Mesh Refinement
NASA Astrophysics Data System (ADS)
Matsui, Tatsuki; Nunami, Masanori; Usui, Hideyuki; Moritaka, Toseo
2010-11-01
A new parallelization technique developed for PIC method with adaptive mesh refinement (AMR) is introduced. In AMR technique, the complicated cell arrangements are organized and managed as interconnected pointers with multiple resolution levels, forming a fully threaded tree structure as a whole. In order to retain this tree structure distributed over multiple processes, remote memory access, an extended feature of MPI2 standards, is employed. Another important feature of the present simulation technique is the domain decomposition according to the modified Morton ordering. This algorithm can group up the equal number of particle calculation loops, which allows for the better load balance. Using this advanced simulation code, preliminary results for basic physical problems are exhibited for the validity check, together with the benchmarks to test the performance and the scalability.
Performance Improvements for Coarse Mesh Finite Difference Acceleration L3:RTM.PRT.P13.02
Collins, Benjamin S.; Hamilton, Steven P.; Stimpson, Shane; Yee, Ben; Larsen, Edward W.; Kochunas, Brendan
2016-05-31
The development of VERA-CS in recent years has focused on developing the capability to simulate multiple cycles of operating commercial nuclear power plants. Now that these capabilities have advanced to the point where it is being deployed to users, the focus is on improving the computational performance of various components in VERA-CS. In this work, the focus is on the Coarse Mesh Finite Difference (CMFD) [1] solution in MPACT. CMFD serves multiple purposes in the 2D/1D solution methodology. First, it is a natural mechanism to tie together the radial MOC transport and the axial SP3 solution. Because the CMFD system solves the multigroup three-dimensional core in one system, it pulls together the global response of the system. In addition, the CMFD solution provides a framework to accelerate the convergence of the eigenvalue problem.
Stabilized Conservative Level Set Method with Adaptive Wavelet-based Mesh Refinement
NASA Astrophysics Data System (ADS)
Shervani-Tabar, Navid; Vasilyev, Oleg V.
2016-11-01
This paper addresses one of the main challenges of the conservative level set method, namely the ill-conditioned behavior of the normal vector away from the interface. An alternative formulation for reconstruction of the interface is proposed. Unlike the commonly used methods which rely on the unit normal vector, Stabilized Conservative Level Set (SCLS) uses a modified renormalization vector with diminishing magnitude away from the interface. With the new formulation, in the vicinity of the interface the reinitialization procedure utilizes compressive flux and diffusive terms only in the normal direction to the interface, thus, preserving the conservative level set properties, while away from the interfaces the directional diffusion mechanism automatically switches to homogeneous diffusion. The proposed formulation is robust and general. It is especially well suited for use with adaptive mesh refinement (AMR) approaches due to need for a finer resolution in the vicinity of the interface in comparison with the rest of the domain. All of the results were obtained using the Adaptive Wavelet Collocation Method, a general AMR-type method, which utilizes wavelet decomposition to adapt on steep gradients in the solution while retaining a predetermined order of accuracy.
Adaptive Mesh Refinement With Spectral Accuracy for Magnetohydrodynamics in Two Space Dimensions
NASA Astrophysics Data System (ADS)
Rosenberg, D.; Pouquet, A.; Mininni, P.
2006-12-01
We examine the effect of accuracy of high-order adaptive mesh refinement (AMR) in the context of a classical configuration of magnetic reconnection in two space dimensions, the so-called Orszag-Tang vortex made up of a magnetic X-point centered 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 Elsasser formulation on high-order elements. It automatically takes advantage of the adaptive grid mechanics that have been described elsewhere [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] in the fluid context, allowing both statically refined and dynamically refined grids. Comparisons with pseudo-spectral computations are performed. Refinement and coarsening criteria are examined, and several tests are described. We show that low-order truncation--even with a comparable number of global degrees of freedom--fails to correctly model some strong (inf-norm) quantities in this problem, even though it satisfies adequately the weak (integrated) balance diagnostics.
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
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.
ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION.
Holst, Michael; McCammon, James Andrew; Yu, Zeyun; Zhou, Youngcheng; Zhu, Yunrong
2012-01-01
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
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)
Conley, Rebecca; Delaney, Tristan J.; Jiao, Xiangmin
2016-11-01
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial (GLP) basis functions, which we construct using local weighted least-squares approximations. The method preserves the theoretical framework of FEM, and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES-FEM can use higher-degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES-FEM, and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poison equation and a time-independent convection-diffusion equation. The numerical results demonstrate that AES-FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor-quality meshes
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.
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.
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.
Consistent properties reconstruction on adaptive Cartesian meshes for complex fluids computations
Xia, Guoping . E-mail: xiag@purdue.edu; Li, Ding; Merkle, Charles L.
2007-07-01
An efficient reconstruction procedure for evaluating the constitutive properties of a complex fluid from general or specialized thermodynamic databases is presented. Properties and their pertinent derivatives are evaluated by means of an adaptive Cartesian mesh in the thermodynamic plane that provides user-specified accuracy over any selected domain. The Cartesian grid produces a binary tree data structure whose search efficiency is competitive with that for an equally spaced table or with simple equations of state such as a perfect gas. Reconstruction is accomplished on a triangular subdivision of the 2D Cartesian mesh that ensures function continuity across cell boundaries in equally and unequally spaced portions of the table to C {sup 0}, C {sup 1} or C {sup 2} levels. The C {sup 0} and C {sup 1} reconstructions fit the equation of state and enthalpy relations separately, while the C {sup 2} reconstruction fits the Helmholtz or Gibbs function enabling EOS/enthalpy consistency also. All three reconstruction levels appear effective for CFD solutions obtained to date. The efficiency of the method is demonstrated through storage and data retrieval examples for air, water and carbon dioxide. The time required for property evaluations is approximately two orders of magnitude faster with the reconstruction procedure than with the complete thermodynamic equations resulting in estimated 3D CFD savings of from 30 to 60. Storage requirements are modest for today's computers, with the C {sup 1} method requiring slightly less storage than those for the C {sup 0} and C {sup 2} reconstructions when the same accuracy is specified. Sample fluid dynamic calculations based upon the procedure show that the C {sup 1} and C {sup 2} methods are approximately a factor of two slower than the C {sup 0} method but that the reconstruction procedure enables arbitrary fluid CFD calculations that are as efficient as those for a perfect gas or an incompressible fluid for all three accuracy
Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers
NASA Astrophysics Data System (ADS)
Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.
2009-11-01
The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.
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.
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
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
Finite element simulation of adaptive aerospace structures with SMA actuators
NASA Astrophysics Data System (ADS)
Frautschi, Jason; Seelecke, Stefan
2003-07-01
The particular demands of aerospace engineering have spawned many of the developments in the field of adaptive structures. Shape memory alloys are particularly attractive as actuators in these types of structures due to their large strains, high specific work output and potential for structural integration. However, the requisite extensive physical testing has slowed development of potential applications and highlighted the need for a simulation tool for feasibility studies. In this paper we present an implementation of an extended version of the M'ller-Achenbach SMA model into a commercial finite element code suitable for such studies. Interaction between the SMA model and the solution algorithm for the global FE equations is thoroughly investigated with respect to the effect of tolerances and time step size on convergence, computational cost and accuracy. Finally, a simulation of a SMA-actuated flexible trailing edge of an aircraft wing modeled with beam elements is presented.
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.
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.
Multigroup radiation hydrodynamics with flux-limited diffusion and adaptive mesh refinement
NASA Astrophysics Data System (ADS)
González, M.; Vaytet, N.; Commerçon, B.; Masson, J.
2015-06-01
Context. Radiative transfer plays a crucial role in the star formation process. Because of the high computational cost, radiation-hydrodynamics simulations performed up to now have mainly been carried out in the grey approximation. In recent years, multifrequency radiation-hydrodynamics models have started to be developed in an attempt to better account for the large variations in opacities as a function of frequency. Aims: We wish to develop an efficient multigroup algorithm for the adaptive mesh refinement code RAMSES which is suited to heavy proto-stellar collapse calculations. Methods: Because of the prohibitive timestep constraints of an explicit radiative transfer method, we constructed a time-implicit solver based on a stabilized bi-conjugate gradient algorithm, and implemented it in RAMSES under the flux-limited diffusion approximation. Results: We present a series of tests that demonstrate the high performance of our scheme in dealing with frequency-dependent radiation-hydrodynamic flows. We also present a preliminary simulation of a 3D proto-stellar collapse using 20 frequency groups. Differences between grey and multigroup results are briefly discussed, and the large amount of information this new method brings us is also illustrated. Conclusions: We have implemented a multigroup flux-limited diffusion algorithm in the RAMSES code. The method performed well against standard radiation-hydrodynamics tests, and was also shown to be ripe for exploitation in the computational star formation context.
Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion
NASA Astrophysics Data System (ADS)
Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.
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.
Output-Based Adaptive Meshing Applied to Space Launch System Booster Separation Analysis
NASA Technical Reports Server (NTRS)
Dalle, Derek J.; Rogers, Stuart E.
2015-01-01
This paper presents details of Computational Fluid Dynamic (CFD) simulations of the Space Launch System during solid-rocket booster separation using the Cart3D inviscid code with comparisons to Overflow viscous CFD results and a wind tunnel test performed at NASA Langley Research Center's Unitary PlanWind Tunnel. The Space Launch System (SLS) launch vehicle includes two solid-rocket boosters that burn out before the primary core stage and thus must be discarded during the ascent trajectory. The main challenges for creating an aerodynamic database for this separation event are the large number of basis variables (including orientation of the core, relative position and orientation of the boosters, and rocket thrust levels) and the complex flow caused by the booster separation motors. The solid-rocket boosters are modified from their form when used with the Space Shuttle Launch Vehicle, which has a rich flight history. However, the differences between the SLS core and the Space Shuttle External Tank result in the boosters separating with much narrower clearances, and so reducing aerodynamic uncertainty is necessary to clear the integrated system for flight. This paper discusses an approach that has been developed to analyze about 6000 wind tunnel simulations and 5000 flight vehicle simulations using Cart3D in adaptive-meshing mode. In addition, a discussion is presented of Overflow viscous CFD runs used for uncertainty quantification. Finally, the article presents lessons learned and improvements that will be implemented in future separation databases.
Collins, David C.; Norman, Michael L.; Padoan, Paolo; Xu Hao
2011-04-10
In this work, we present the mass and magnetic distributions found in a recent adaptive mesh refinement magnetohydrodynamic simulation of supersonic, super-Alfvenic, self-gravitating turbulence. Power-law tails are found in both mass density and magnetic field probability density functions, with P({rho}) {proportional_to} {rho}{sup -1.6} and P(B) {proportional_to} B{sup -2.7}. A power-law relationship is also found between magnetic field strength and density, with B {proportional_to} {rho}{sup 0.5}, throughout the collapsing gas. The mass distribution of gravitationally bound cores is shown to be in excellent agreement with recent observation of prestellar cores. The mass-to-flux distribution of cores is also found to be in excellent agreement with recent Zeeman splitting measurements. We also compare the relationship between velocity dispersion and density to the same cores, and find an increasing relationship between the two, with {sigma} {proportional_to} n{sup 0.25}, also in agreement with the observations. We then estimate the potential effects of ambipolar diffusion in our cores and find that due to the weakness of the magnetic field in our simulation, the inclusion of ambipolar diffusion in our simulation will not cause significant alterations of the flow dynamics.
Effenberger, Frederic; Thust, Kay; Grauer, Rainer; Dreher, Juergen; Arnold, Lukas
2011-03-15
The formation of a thin current sheet in a magnetic quasiseparatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-{beta}, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al. [Astron. Astrophys. 444, 961 (2005)]. In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is finally limited by lack of resolution even in the AMR studies, the current sheet moves upward, following a global expansion of the magnetic structure during the quasistatic evolution. The sheet is locally one-dimensional and the plasma flow in its vicinity, when transformed into a comoving frame, qualitatively resembles a stagnation point flow. In conclusion, our simulations support the idea that extremely high current densities are generated in the vicinities of QSLs as a response to external perturbations, with no sign of saturation.
GPU accelerated cell-based adaptive mesh refinement on unstructured quadrilateral grid
NASA Astrophysics Data System (ADS)
Luo, Xisheng; Wang, Luying; Ran, Wei; Qin, Fenghua
2016-10-01
A GPU accelerated inviscid flow solver is developed on an unstructured quadrilateral grid in the present work. For the first time, the cell-based adaptive mesh refinement (AMR) is fully implemented on GPU for the unstructured quadrilateral grid, which greatly reduces the frequency of data exchange between GPU and CPU. Specifically, the AMR is processed with atomic operations to parallelize list operations, and null memory recycling is realized to improve the efficiency of memory utilization. It is found that results obtained by GPUs agree very well with the exact or experimental results in literature. An acceleration ratio of 4 is obtained between the parallel code running on the old GPU GT9800 and the serial code running on E3-1230 V2. With the optimization of configuring a larger L1 cache and adopting Shared Memory based atomic operations on the newer GPU C2050, an acceleration ratio of 20 is achieved. The parallelized cell-based AMR processes have achieved 2x speedup on GT9800 and 18x on Tesla C2050, which demonstrates that parallel running of the cell-based AMR method on GPU is feasible and efficient. Our results also indicate that the new development of GPU architecture benefits the fluid dynamics computing significantly.
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.
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.
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.
Kleinstreuer, C.; Patterson, M.R.
1980-05-01
A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables.
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.
A goal-oriented adaptive finite-element approach for plane wave 3-D electromagnetic modelling
NASA Astrophysics Data System (ADS)
Ren, Zhengyong; Kalscheuer, Thomas; Greenhalgh, Stewart; Maurer, Hansruedi
2013-08-01
We have developed a novel goal-oriented adaptive mesh refinement approach for finite-element methods to model plane wave electromagnetic (EM) fields in 3-D earth models based on the electric field differential equation. To handle complicated models of arbitrary conductivity, magnetic permeability and dielectric permittivity involving curved boundaries and surface topography, we employ an unstructured grid approach. The electric field is approximated by linear curl-conforming shape functions which guarantee the divergence-free condition of the electric field within each tetrahedron and continuity of the tangential component of the electric field across the interior boundaries. Based on the non-zero residuals of the approximated electric field and the yet to be satisfied boundary conditions of continuity of both the normal component of the total current density and the tangential component of the magnetic field strength across the interior interfaces, three a-posterior error estimators are proposed as a means to drive the goal-oriented adaptive refinement procedure. The first a-posterior error estimator relies on a combination of the residual of the electric field, the discontinuity of the normal component of the total current density and the discontinuity of the tangential component of the magnetic field strength across the interior faces shared by tetrahedra. The second a-posterior error estimator is expressed in terms of the discontinuity of the normal component of the total current density (conduction plus displacement current). The discontinuity of the tangential component of the magnetic field forms the third a-posterior error estimator. Analytical solutions for magnetotelluric (MT) and radiomagnetotelluric (RMT) fields impinging on a homogeneous half-space model are used to test the performances of the newly developed goal-oriented algorithms using the above three a-posterior error estimators. A trapezoidal topographical model, using normally incident EM waves
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.
NASA Astrophysics Data System (ADS)
Kopera, Michal A.; Giraldo, Francis X.
2014-10-01
The resolutions of interests in atmospheric simulations require prohibitively large computational resources. Adaptive mesh refinement (AMR) tries to mitigate this problem by putting high resolution in crucial areas of the domain. We investigate the performance of a tree-based AMR algorithm for the high order discontinuous Galerkin method on quadrilateral grids with non-conforming elements. We perform a detailed analysis of the cost of AMR by comparing this to uniform reference simulations of two standard atmospheric test cases: density current and rising thermal bubble. The analysis shows up to 15 times speed-up of the AMR simulations with the cost of mesh adaptation below 1% of the total runtime. We pay particular attention to the implicit-explicit (IMEX) time integration methods and show that the ARK2 method is more robust with respect to dynamically adapting meshes than BDF2. Preliminary analysis of preconditioning reveals that it can be an important factor in the AMR overhead. The compiler optimizations provide significant runtime reduction and positively affect the effectiveness of AMR allowing for speed-ups greater than it would follow from the simple performance model.
Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control
NASA Astrophysics Data System (ADS)
Basin, Michael; Bharath Panathula, Chandrasekhara; Shtessel, Yuri
2016-09-01
This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.
NASA Astrophysics Data System (ADS)
Hintermüller, M.; Hinze, M.; Kahle, C.
2013-02-01
An adaptive a posteriori error estimator based finite element method for the numerical solution of a coupled Cahn-Hilliard/Navier-Stokes system with a double-obstacle homogenous free (interfacial) energy density is proposed. A semi-implicit Euler scheme for the time-integration is applied which results in a system coupling a quasi-Stokes or Oseen-type problem for the fluid flow to a variational inequality for the concentration and the chemical potential according to the Cahn-Hilliard model [16]. A Moreau-Yosida regularization is employed which relaxes the constraints contained in the variational inequality and, thus, enables semi-smooth Newton solvers with locally superlinear convergence in function space. Moreover, upon discretization this yields a mesh independent method for a fixed relaxation parameter. For the finite dimensional approximation of the concentration and the chemical potential piecewise linear and globally continuous finite elements are used, and for the numerical approximation of the fluid velocity Taylor-Hood finite elements are employed. The paper ends by a report on numerical examples showing the efficiency of the new method.
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 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 Astrophysics Data System (ADS)
Phillips, Carolyn L.
2014-09-01
In a complex self-organizing system, small changes in the interactions between the system's components can result in different emergent macrostructures or macrobehavior. In chemical engineering and material science, such spontaneously self-assembling systems, using polymers, nanoscale or colloidal-scale particles, DNA, or other precursors, are an attractive way to create materials that are precisely engineered at a fine scale. Changes to the interactions can often be described by a set of parameters. Different contiguous regions in this parameter space correspond to different ordered states. Since these ordered states are emergent, often experiment, not analysis, is necessary to create a diagram of ordered states over the parameter space. By issuing queries to points in the parameter space (e.g., performing a computational or physical experiment), ordered states can be discovered and mapped. Queries can be costly in terms of resources or time, however. In general, one would like to learn the most information using the fewest queries. Here we introduce a learning heuristic for issuing queries to map and search a two-dimensional parameter space. Using a method inspired by adaptive mesh refinement, the heuristic iteratively issues batches of queries to be executed in parallel based on past information. By adjusting the search criteria, different types of searches (for example, a uniform search, exploring boundaries, sampling all regions equally) can be flexibly implemented. We show that this method will densely search the space, while preferentially targeting certain features. Using numerical examples, including a study simulating the self-assembly of complex crystals, we show how this heuristic can discover new regions and map boundaries more accurately than a uniformly distributed set of queries.
NASA Astrophysics Data System (ADS)
Henshaw, William D.; Schwendeman, Donald W.
2008-08-01
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 accuracy of the numerical solutions is assessed quantitatively through an estimation of the errors from a grid convergence study. The parallel performance of the
Henshaw, W; Schwendeman, D
2007-11-15
This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid within the overlapping grid structure and its associated refinement grids can be independently partitioned over a chosen set of processors. A modified bin-packing algorithm is used to specify the partition for each grid so that the computational work is evenly distributed amongst the processors. All components of the AMR algorithm such as error estimation, regridding, and interpolation are performed in parallel. The parallel time-stepping algorithm is illustrated for initial-boundary-value problems involving a linear advection-diffusion equation and the (nonlinear) reactive Euler equations. Numerical results are presented for both equations to demonstrate the accuracy and correctness of the parallel approach. Exact solutions of the advection-diffusion equation are constructed, and these are used to check the corresponding numerical solutions for a variety of tests involving different overlapping grids, different numbers of refinement levels and refinement ratios, and different numbers of processors. The problem of planar shock diffraction by a sphere is considered as an illustration of the numerical approach for the Euler equations, and a problem involving the initiation of a detonation from a hot spot in a T-shaped pipe is considered to demonstrate the numerical approach for the reactive case. For both problems, the solutions are shown to be well resolved on the finest grid. The parallel performance of the approach is examined in detail for the shock diffraction problem.
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.
NASA Astrophysics Data System (ADS)
Donmez, Orhan
We present a general procedure to solve the General Relativistic Hydrodynamical (GRH) equations with Adaptive-Mesh Refinement (AMR) and model of an accretion disk around a black hole. To do this, the GRH equations are written in a conservative form to exploit their hyperbolic character. The numerical solutions of the general relativistic hydrodynamic equations is done by High Resolution Shock Capturing schemes (HRSC), specifically designed to solve non-linear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. We use Marquina fluxes with MUSCL left and right states to solve GRH equations. First, we carry out different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations to verify the second order convergence of the code in 1D, 2 D and 3D. Second, we solve the GRH equations and use the general relativistic test problems to compare the numerical solutions with analytic ones. In order to this, we couple the flux part of general relativistic hydrodynamic equation with a source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time. The test problems examined include shock tubes, geodesic flows, and circular motion of particle around the black hole. Finally, we apply this code to the accretion disk problems around the black hole using the Schwarzschild metric at the background of the computational domain. We find spiral shocks on the accretion disk. They are observationally expected results. We also examine the star-disk interaction near a massive black hole. We find that when stars are grounded down or a hole is punched on the accretion disk, they create shock waves which destroy the accretion disk.
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).
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.
Fission-Fusion Adaptivity in Finite Elements for Nonlinear Dynamics of Shells
1988-11-30
where mesh refinement will prove useful. In fact, the deviation of a bilinear element from a smooth shell midsurface can be related to the angle between...comparisons with nonadaptive meshes. Conclusions and further discussions are given in Section 6. -5- 2. FINITE ELEMENT FORMULATION The shape of the midsurface ...8217 22 , and e3 is defined so that e, and e2 are tangent to the midsurface and rotate with the element; 2. for each node, a triad b i is defined so that
M-Adapting Low Order Mimetic Finite Differences for Dielectric Interface Problems
McGregor, Duncan A.; Gyrya, Vitaliy; Manzini, Gianmarco
2016-03-07
We consider a problem of reducing numerical dispersion for electromagnetic wave in the domain with two materials separated by a at interface in 2D with a factor of two di erence in wave speed. The computational mesh in the homogeneous parts of the domain away from the interface consists of square elements. Here the method construction is based on m-adaptation construction in homogeneous domain that leads to fourth-order numerical dispersion (vs. second order in non-optimized method). The size of the elements in two domains also di ers by a factor of two, so as to preserve the same value of Courant number in each. Near the interface where two meshes merge the mesh with larger elements consists of degenerate pentagons. We demonstrate that prior to m-adaptation the accuracy of the method falls from second to rst due to breaking of symmetry in the mesh. Next we develop m-adaptation framework for the interface region and devise an optimization criteria. We prove that for the interface problem m-adaptation cannot produce increase in method accuracy. This is in contrast to homogeneous medium where m-adaptation can increase accuracy by two orders.
Masterlark, Timothy; Lu, Zhong; Rykhus, Russell P.
2006-01-01
nterferometric 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 (2.1×107m3) 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.
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.
Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert
2017-01-27
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fractionmore » or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Lastly, dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.« less
NASA Astrophysics Data System (ADS)
Greene, Patrick T.; Schofield, Samuel P.; Nourgaliev, Robert
2017-04-01
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well as the actual level set for mesh smoothing. Meshes generated for a number of interface geometries are presented, including cases with multiple level sets. Dynamic cases with moving interfaces show the new method is capable of maintaining a desired resolution near the interface with an acceptable number of relaxation iterations per time step, which demonstrates the method's potential to be used as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods.
NASA Astrophysics Data System (ADS)
Lichtenberg, Tim; Schleicher, Dominik R. G.
2015-07-01
The astonishing diversity in the observed planetary population requires theoretical efforts and advances in planet formation theories. The use of numerical approaches provides a method to tackle the weaknesses of current models and is an important tool to close gaps in poorly constrained areas such as the rapid formation of giant planets in highly evolved systems. So far, most numerical approaches make use of Lagrangian-based smoothed-particle hydrodynamics techniques or grid-based 2D axisymmetric simulations. We present a new global disk setup to model the first stages of giant planet formation via gravitational instabilities (GI) in 3D with the block-structured adaptive mesh refinement (AMR) hydrodynamics code enzo. With this setup, we explore the potential impact of AMR techniques on the fragmentation and clumping due to large-scale instabilities using different AMR configurations. Additionally, we seek to derive general resolution criteria for global simulations of self-gravitating disks of variable extent. We run a grid of simulations with varying AMR settings, including runs with a static grid for comparison. Additionally, we study the effects of varying the disk radius. The physical settings involve disks with Rdisk = 10,100 and 300 AU, with a mass of Mdisk ≈ 0.05 M⊙ and a central object of subsolar mass (M⋆ = 0.646 M⊙). To validate our thermodynamical approach we include a set of simulations with a dynamically stable profile (Qinit = 3) and similar grid parameters. The development of fragmentation and the buildup of distinct clumps in the disk is strongly dependent on the chosen AMR grid settings. By combining our findings from the resolution and parameter studies we find a general lower limit criterion to be able to resolve GI induced fragmentation features and distinct clumps, which induce turbulence in the disk and seed giant planet formation. Irrespective of the physical extension of the disk, topologically disconnected clump features are only
Simulations of recoiling black holes: adaptive mesh refinement and radiative transfer
NASA Astrophysics Data System (ADS)
Meliani, Zakaria; Mizuno, Yosuke; Olivares, Hector; Porth, Oliver; Rezzolla, Luciano; Younsi, Ziri
2017-01-01
Context. In many astrophysical phenomena, and especially in those that involve the high-energy regimes that always accompany the astronomical phenomenology of black holes and neutron stars, physical conditions that are achieved are extreme in terms of speeds, temperatures, and gravitational fields. In such relativistic regimes, numerical calculations are the only tool to accurately model the dynamics of the flows and the transport of radiation in the accreting matter. Aims: We here continue our effort of modelling the behaviour of matter when it orbits or is accreted onto a generic black hole by developing a new numerical code that employs advanced techniques geared towards solving the equations of general-relativistic hydrodynamics. Methods: More specifically, the new code employs a number of high-resolution shock-capturing Riemann solvers and reconstruction algorithms, exploiting the enhanced accuracy and the reduced computational cost of adaptive mesh-refinement (AMR) techniques. In addition, the code makes use of sophisticated ray-tracing libraries that, coupled with general-relativistic radiation-transfer calculations, allow us to accurately compute the electromagnetic emissions from such accretion flows. Results: We validate the new code by presenting an extensive series of stationary accretion flows either in spherical or axial symmetry that are performed either in two or three spatial dimensions. In addition, we consider the highly nonlinear scenario of a recoiling black hole produced in the merger of a supermassive black-hole binary interacting with the surrounding circumbinary disc. In this way, we can present for the first time ray-traced images of the shocked fluid and the light curve resulting from consistent general-relativistic radiation-transport calculations from this process. Conclusions: The work presented here lays the ground for the development of a generic computational infrastructure employing AMR techniques to accurately and self
A solution-adaptive mesh algorithm for dynamic/static refinement of two and three dimensional grids
NASA Technical Reports Server (NTRS)
Benson, Rusty A.; Mcrae, D. S.
1991-01-01
An adaptive grid algorithm has been developed in two and three dimensions that can be used dynamically with a solver or as part of a grid refinement process. The algorithm employs a transformation from the Cartesian coordinate system to a general coordinate space, which is defined as a parallelepiped in three dimensions. A weighting function, independent for each coordinate direction, is developed that will provide the desired refinement criteria in regions of high solution gradient. The adaptation is performed in the general coordinate space and the new grid locations are returned to the Cartesian space via a simple, one-step inverse mapping. The algorithm for relocation of the mesh points in the parametric space is based on the center of mass for distributed weights. Dynamic solution-adaptive results are presented for laminar flows in two and three dimensions.
On a Moving Mesh Method Applied to the Shallow Water Equations
NASA Astrophysics Data System (ADS)
Felcman, J.; Kadrnka, L.
2010-09-01
The moving mesh method is applied to the numerical solution of the shallow water equations. The original numerical flux of the Vijayasundaram type is used in the finite volume method. The mesh adaptation procedure is described. The relevant numerical examples are presented.
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.
NASA Astrophysics Data System (ADS)
Greene, Patrick; Schofield, Sam; Nourgaliev, Robert
2016-11-01
A new mesh smoothing method designed to cluster cells near a dynamically evolving interface is presented. The method is based on weighted condition number mesh relaxation with the weight function being computed from a level set representation of the interface. The weight function is expressed as a Taylor series based discontinuous Galerkin (DG) projection, which makes the computation of the derivatives of the weight function needed during the condition number optimization process a trivial matter. For cases when a level set is not available, a fast method for generating a low-order level set from discrete cell-centered fields, such as a volume fraction or index function, is provided. Results show that the low-order level set works equally well for the weight function as the actual level set. The method retains the excellent smoothing capabilities of condition number relaxation, while providing a method for clustering mesh cells near regions of interest. Dynamic cases for moving interfaces are presented to demonstrate the method's potential usefulness as a mesh relaxer for arbitrary Lagrangian Eulerian (ALE) methods. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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.
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)
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.
NASA Astrophysics Data System (ADS)
Yang, Sheng; Kuo, C.-C. Jay
2002-07-01
An Internet-based interactive walkthrough virtual environment is presented in this work to facilitate interactive streaming and browsing of 3D graphic models across the Internet. The models are compressed by the view-dependent progressive mesh compression algorithm to enable the decorrelation of partitions and finer granularity. Following the fundamental framework of mesh representation, an interactive protocol based on the real time streaming protocol (RTSP) is developed to enhance the interaction between the server and the client. Finally, the data of the virtual world is re-organized and transmitted according to the viewer's requests. Experimental results demonstrate that the proposed algorithm reduces the required transmission bandwidth, and provides an acceptable visual quality even at low bit rates.
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.
Divett, T; Vennell, R; Stevens, C
2013-02-28
At tidal energy sites, large arrays of hundreds of turbines will be required to generate economically significant amounts of energy. Owing to wake effects within the array, the placement of turbines within will be vital to capturing the maximum energy from the resource. This study presents preliminary results using Gerris, an adaptive mesh flow solver, to investigate the flow through four different arrays of 15 turbines each. The goal is to optimize the position of turbines within an array in an idealized channel. The turbines are represented as areas of increased bottom friction in an adaptive mesh model so that the flow and power capture in tidally reversing flow through large arrays can be studied. The effect of oscillating tides is studied, with interesting dynamics generated as the tidal current reverses direction, forcing turbulent flow through the array. The energy removed from the flow by each of the four arrays is compared over a tidal cycle. A staggered array is found to extract 54 per cent more energy than a non-staggered array. Furthermore, an array positioned to one side of the channel is found to remove a similar amount of energy compared with an array in the centre of the channel.
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)
Schroeder, Philipp W.; Lube, Gert
2017-04-01
This paper presents heavily grad-div and pressure jump stabilised, equal- and mixed-order discontinuous Galerkin finite element methods for non-isothermal incompressible flows based on the Oberbeck-Boussinesq approximation. In this framework, the enthalpy-porosity model for multiphase flow in melting and solidification problems can be employed. By considering the differentially heated cavity and the melting of pure gallium in a rectangular enclosure, it is shown that both boundary layers and sharp moving interior layers can be handled naturally by the proposed class of non-conforming methods. Due to the stabilising effect of the grad-div term and the robustness of discontinuous Galerkin methods, it is possible to solve the underlying problems accurately on coarse, non-adapted meshes. The interaction of heavy grad-div stabilisation and discontinuous Galerkin methods significantly improves the mass conservation properties and the overall accuracy of the numerical scheme which is observed for the first time. Hence, it is inferred that stabilised discontinuous Galerkin methods are highly robust as well as computationally efficient numerical methods to deal with natural convection problems arising in incompressible computational thermo-fluid dynamics.
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)
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.
NASA Astrophysics Data System (ADS)
Fakhari, Abbas; Bolster, Diogo
2016-11-01
A three-dimensional (3D) adaptive mesh refinement (AMR) algorithm on structured Cartesian grids is developed, and supplemented by a mesoscopic multiphase-flow solver based on state-of-the-art lattice Boltzmann methods (LBM). Using this in-house AMR-LBM routine, we present fully 3D simulations of partial coalescence of a liquid drop with an initially flat interface at small Ohnesorge and Bond numbers. Qualitatively, our numerical simulations are in excellent agreement with experimental observations. Partial coalescence cascades are successfully observed at very small Ohnesorge numbers (Oh 10-4). The fact that the partial coalescence is absent in similar 2D simulations suggests that the Rayleigh-Plateau instability may be the principle driving mechanism responsible for this phenomenon.
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.
NASA Astrophysics Data System (ADS)
Zhang, A.; Guo, Z.; Xiong, S.-M.
2017-03-01
Eutectic pattern transition under an externally imposed temperature gradient was studied using the phase field method coupled with a novel parallel adaptive-mesh-refinement (Para-AMR) algorithm. Numerical tests revealed that the Para-AMR algorithm could improve the computational efficiency by two orders of magnitude and thus made it possible to perform large-scale simulations without any compromising accuracy. Results showed that the direction of the temperature gradient played a crucial role in determining the eutectic patterns during solidification, which agreed well with experimental observations. In particular, the presence of the transverse temperature gradient could tilt the eutectic patterns, and in 3D simulations, the eutectic microstructure would alter from lamellar to rod-like and/or from rod-like to dumbbell-shaped. Furthermore, under a radial temperature gradient, the eutectic would evolve from a dumbbell-shaped or clover-shaped pattern to an isolated rod-like pattern.
N-body simulations for f(R) gravity using a self-adaptive particle-mesh code
Zhao Gongbo; Koyama, Kazuya; Li Baojiu
2011-02-15
We perform high-resolution N-body simulations for f(R) gravity based on a self-adaptive particle-mesh code MLAPM. The chameleon mechanism that recovers general relativity on small scales is fully taken into account by self-consistently solving the nonlinear equation for the scalar field. We independently confirm the previous simulation results, including the matter power spectrum, halo mass function, and density profiles, obtained by Oyaizu et al.[Phys. Rev. D 78, 123524 (2008)] and Schmidt et al.[Phys. Rev. D 79, 083518 (2009)], and extend the resolution up to k{approx}20 h/Mpc for the measurement of the matter power spectrum. Based on our simulation results, we discuss how the chameleon mechanism affects the clustering of dark matter and halos on full nonlinear scales.
NASA Astrophysics Data System (ADS)
Cui, Xiongwei; Yao, Xiongliang; Wang, Zhikai; Liu, Minghao
2017-03-01
A second generation wavelet-based adaptive finite-difference Lattice Boltzmann method (FD-LBM) is developed in this paper. In this approach, the adaptive wavelet collocation method (AWCM) is firstly, to the best of our knowledge, incorporated into the FD-LBM. According to the grid refinement criterion based on the wavelet amplitudes of density distribution functions, an adaptive sparse grid is generated by the omission and addition of collocation points. On the sparse grid, the finite differences are used to approximate the derivatives. To eliminate the special treatments in using the FD-based derivative approximation near boundaries, the immersed boundary method (IBM) is also introduced into FD-LBM. By using the adaptive technique, the adaptive code requires much less grid points as compared to the uniform-mesh code. As a consequence, the computational efficiency can be improved. To justify the proposed method, a series of test cases, including fixed boundary cases and moving boundary cases, are invested. A good agreement between the present results and the data in previous literatures is obtained, which demonstrates the accuracy and effectiveness of the present AWCM-IB-LBM.
An adaptive finite element approach to modelling sediment laden density currents
NASA Astrophysics Data System (ADS)
Parkinson, S.; Hill, J.; Allison, P. A.; Piggott, M. D.
2012-04-01
Modelling sediment-laden density currents at real-world scales is a challenging task. Here we present Fluidity, which uses dynamic adaptive re-meshing to reduce computational costs whilst maintaining sufficient resolution where and when it is required. This allows small-scale processes to be captured in large scale simulations. Density currents, also known as gravity or buoyancy currents, occur wherever two fluids with different densities meet. They can occur at scales of up to hundred kilometres in the ocean when continental shelves collapse. This process releases large quantities of sediment into the ocean which increase the bulk density of the fluid to form a density current. These currents can carry sediment hundreds of kilometres, at speeds of up to a hundred kilometres per hour, over the sea bed. They can be tsunamigenic and they have the potential to cause significant damage to submarine infrastructure, such as submarine telecommunications cables or oil and gas infrastructure. They are also a key process for movement of organic material into the depths of the ocean. Due to this, they play an important role in the global carbon cycle on the Earth, forming a significant component of the stratigraphic record, and their deposits can form useful sources of important hydrocarbons. Modelling large scale sediment laden density currents is a very challenging problem. Particles within the current are suspended by turbulence that occurs at length scales that are several orders of magnitude smaller than the size of the current. Models that resolve the vertical structure of the flow require a very large, highly resolved mesh, and substantial computing power to solve. Here, we verify our adaptive model by comparison with a set of laboratory experiments by Gladstone et al. [1998] on the propagation and sediment deposition of bidisperse gravity currents. Comparisons are also made with fixed mesh solutions, and it is shown that accuracy can be maintained with fewer elements
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
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.
3-D grid refinement using the University of Michigan adaptive mesh library for a pure advective test
NASA Astrophysics Data System (ADS)
Oehmke, R.; Vandenberg, D.; Andronova, N.; Penner, J.; Stout, Q.; Zubov, V.; Jablonowski, C.
2008-05-01
The numerical representation of the partial differential equations (PDE) for high resolution atmospheric dynamical and physical features requires division of the atmospheric volume into a set of 3D grids, each of which has a not quite rectangular form. Each location on the grid contains multiple data that together represent the state of Earth's atmosphere. For successful numerical integration of the PDEs the size of each grid box is used to define the Courant-Friedrichs-Levi criterion in setting the time step. 3D adaptive representations of a sphere are needed to represent the evolution of clouds. In this paper we present the University of Michigan adaptive mesh library - a library that supports the production of parallel codes with use of adaptation on a sphere. The library manages the block-structured data layout, handles ghost cell updates among neighboring blocks and splits blocks 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. Users provide data manipulation functions for performing interpolation of user data when refining blocks. We rigorously test the library using refinement of the modeled vertical transport of a tracer with prescribed atmospheric sources and sinks. It is both a 2 and a 3D test, and bridges the performance of the model's dynamics and physics needed for inclusion of cloud formation.
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.
Multislope MUSCL method for general unstructured meshes
NASA Astrophysics Data System (ADS)
Le Touze, C.; Murrone, A.; Guillard, H.
2015-03-01
The multislope concept has been recently introduced in the literature to deal with MUSCL reconstructions on triangular and tetrahedral unstructured meshes in the finite volume cell-centered context. Dedicated scalar slopes are used to compute the interpolations on each face of a given element, in opposition to the monoslope methods in which a unique limited gradient is used. The multislope approach reveals less expensive and potentially more accurate than the classical gradient techniques. Besides, it may also help the robustness when dealing with hyperbolic systems involving complex solutions, with large discontinuities and high density ratios. However some important limitations on the mesh topology still have to be overcome with the initial multislope formalism. In this paper, a generalized multislope MUSCL method is introduced for cell-centered finite volume discretizations. The method is freed from constraints on the mesh topology, thereby operating on completely general unstructured meshes. Moreover optimal second-order accuracy is reached at the faces centroids. The scheme can be written with nonnegative coefficients, which makes it L∞-stable. Special attention has also been paid to equip the reconstruction procedure with well-adapted dedicated limiters, potentially CFL-dependent. Numerical tests are provided to prove the ability of the method to deal with completely general meshes, while exhibiting second-order accuracy.
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.
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.
A parallel second-order adaptive mesh algorithm for incompressible flow in porous media.
Pau, George S H; Almgren, Ann S; Bell, John B; Lijewski, Michael J
2009-11-28
In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behaviour of the method.
A Parallel Second-Order Adaptive Mesh Algorithm for Incompressible Flow in Porous Media
Pau, George Shu Heng; Almgren, Ann S.; Bell, John B.; Lijewski, Michael J.
2008-04-01
In this paper we present a second-order accurate adaptive algorithm for solving multiphase, incompressible flows in porous media. We assume a multiphase form of Darcy's law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting the total velocity, defined to be the sum of the phase velocities, is divergence-free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids areadvanced multiple steps to reach the same time as the coarse grids and the data atdifferent levels are then synchronized. The single grid algorithm is described briefly,but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm's accuracy and convergence properties and to illustrate the behavior of the method.
JCMmode: an adaptive finite element solver for the computation of leaky modes
NASA Astrophysics Data System (ADS)
Zschiedrich, Lin W.; Burger, Sven; Klose, Roland; Schaedle, Achim; Schmidt, Frank
2005-03-01
We present our simulation tool JCMmode for calculating propagating modes of an optical waveguide. As ansatz functions we use higher order, vectorial elements (Nedelec elements, edge elements). Further we construct transparent boundary conditions to deal with leaky modes even for problems with inhomogeneous exterior domains as for integrated hollow core Arrow waveguides. We have implemented an error estimator which steers the adaptive mesh refinement. This allows the precise computation of singularities near the metal's corner of a Plasmon-Polariton waveguide even for irregular shaped metal films on a standard personal computer.
NASA Astrophysics Data System (ADS)
Noel, Jean
The feasibility of a two dimensional computation code for electric arc plasma is addressed. The nonstationary physics of a plasma arc can intervene at high gradients on all the variables, a high convection, as well as the considerable pressure variations (in space and time). Here the spatial finesse needed for the treatment of high gradient zones, is obtained by the use of a finite element method, improved by a mesh auto-adaptivity. The chosen time integration method is of the Runge-Kutta type with time step adjustment. This is presented, with the numerical methodology principles (multimesh, regularization, time step control). Results obtained in the study of classical partial differential equation systems, simplified versions of the Navier-Stokes equations (Burger equation, Dwyer-Sanders flame model), are presented. The numerical treatment of a confined arc plasma required the preliminary definition of a representative system of equations. This system is presented, with the thermal and dynamic modelings carried out. Different aspects of the models introduced are illustrated, and results obtained for an unstationary one dimensional arc plasma in industrial conditions are presented. Comparisons between these results and available experimental data are encouraging, but suggest that a better dynamic modeling is indispensable.
Mesh adaptivity driven by goal-oriented locally equilibrated superconvergent patch recovery
NASA Astrophysics Data System (ADS)
González-Estrada, O. A.; Nadal, E.; Ródenas, J. J.; Kerfriden, P.; Bordas, S. P. A.; Fuenmayor, F. J.
2014-05-01
Goal-oriented error estimates (GOEE) have become popular tools to quantify and control the local error in quantities of interest (QoI), which are often more pertinent than local errors in energy for design purposes (e.g. the mean stress or mean displacement in a particular area, the stress intensity factor for fracture problems). These GOEE are one of the key unsolved problems of advanced engineering applications in, for example, the aerospace industry. This work presents a simple recovery-based error estimation technique for QoIs whose main characteristic is the use of an enhanced version of the Superconvergent Patch Recovery (SPR) technique previously used for error estimation in the energy norm. This enhanced SPR technique is used to recover both the primal and dual solutions. It provides a nearly statically admissible stress field that results in accurate estimations of the local contributions to the discretisation error in the QoI and, therefore, in an accurate estimation of this magnitude. This approach leads to a technique with a reasonable computational cost that could easily be implemented into already available finite element codes, or as an independent postprocessing tool.
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
Adaptivity via mesh movement with three-dimensional block-structured grids
Catherall, D.
1996-12-31
The method described here is one in which grid nodes are redistributed so that they are attracted towards regions of high solution activity. The major difficulty in attempting this arises from the degree of grid smoothness and orthogonality required by the flow solver. These requirements are met by suitable choice of grid equations, to be satisfied by the adapted grid, and by the inclusion of certain source terms, for added control in regions where grid movement is limited by the local geometry. The method has been coded for multiblock grids, so that complex configurations may be treated. It is demonstrated here for inviscid supercritical flow with two test cases: an ONERA M6 wing with a rounded tip, and a forward-swept wing/fuselage configuration (M151).
Adaptive optimal quantization for 3D mesh representation in the spherical coordinate system
NASA Astrophysics Data System (ADS)
Ahn, Jeong-Hwan; Ho, Yo-Sung
1998-12-01
In recent days, applications using 3D models are increasing. Since the 3D model contains a huge amount of information, compression of the 3D model data is necessary for efficient storage or transmission. In this paper, we propose an adaptive encoding scheme to compress the geometry information of the 3D model. Using the Levinson-Durbin algorithm, the encoder first predicts vertex positions along a vertex spanning tree. After each prediction error is normalized, the prediction error vector of each vertex point is represented in the spherical coordinate system (r,(theta) ,(phi) ). Each r is then quantizes by an optimal uniform quantizer. A pair of each ((theta) ,(phi) ) is also successively encoded by partitioning the surface of the sphere according to the quantized value of r. The proposed scheme demonstrates improved coding efficiency by exploiting the statistical properties of r and ((theta) ,(phi) ).
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.
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.
The 2D and 3D hypersonic flows with unstructured meshes
NASA Technical Reports Server (NTRS)
Thareja, Rajiv
1993-01-01
Viewgraphs on 2D and 3D hypersonic flows with unstructured meshes are presented. Topics covered include: mesh generation, mesh refinement, shock-shock interaction, velocity contours, mesh movement, vehicle bottom surface, and adapted meshes.
Computation of variably saturated subsurface flow by adaptive mixed hybrid finite element methods
NASA Astrophysics Data System (ADS)
Bause, M.; Knabner, P.
2004-06-01
We present adaptive mixed hybrid finite element discretizations of the Richards equation, a nonlinear parabolic partial differential equation modeling the flow of water into a variably saturated porous medium. The approach simultaneously constructs approximations of the flux and the pressure head in Raviart-Thomas spaces. The resulting nonlinear systems of equations are solved by a Newton method. For the linear problems of the Newton iteration a multigrid algorithm is used. We consider two different kinds of error indicators for space adaptive grid refinement: superconvergence and residual based indicators. They can be calculated easily by means of the available finite element approximations. This seems attractive for computations since no additional (sub-)problems have to be solved. Computational experiments conducted for realistic water table recharge problems illustrate the effectiveness and robustness of the approach.
A numerical study of 2D detonation waves with adaptive finite volume methods on unstructured grids
NASA Astrophysics Data System (ADS)
Hu, Guanghui
2017-02-01
In this paper, a framework of adaptive finite volume solutions for the reactive Euler equations on unstructured grids is proposed. The main ingredients of the algorithm include a second order total variation diminishing Runge-Kutta method for temporal discretization, and the finite volume method with piecewise linear solution reconstruction of the conservative variables for the spatial discretization in which the least square method is employed for the reconstruction, and weighted essentially nonoscillatory strategy is used to restrain the potential numerical oscillation. To resolve the high demanding on the computational resources due to the stiffness of the system caused by the reaction term and the shock structure in the solutions, the h-adaptive method is introduced. OpenMP parallelization of the algorithm is also adopted to further improve the efficiency of the implementation. Several one and two dimensional benchmark tests on the ZND model are studied in detail, and numerical results successfully show the effectiveness of the proposed method.
Performance Analysis of Adaptive Volterra Filters in the Finite-Alphabet Input Case
NASA Astrophysics Data System (ADS)
Besbes, Hichem; Jaïdane, Mériem; Ezzine, Jelel
2004-12-01
This paper deals with the analysis of adaptive Volterra filters, driven by the LMS algorithm, in the finite-alphabet inputs case. A tailored approach for the input context is presented and used to analyze the behavior of this nonlinear adaptive filter. Complete and rigorous mean square analysis is provided without any constraining independence assumption. Exact transient and steady-state performances expressed in terms of critical step size, rate of transient decrease, optimal step size, excess mean square error in stationary mode, and tracking nonstationarities are deduced.
Controlling Reflections from Mesh Refinement Interfaces in Numerical Relativity
NASA Technical Reports Server (NTRS)
Baker, John G.; Van Meter, James R.
2005-01-01
A leading approach to improving the accuracy on numerical relativity simulations of black hole systems is through fixed or adaptive mesh refinement techniques. We describe a generic numerical error which manifests as slowly converging, artificial reflections from refinement boundaries in a broad class of mesh-refinement implementations, potentially limiting the effectiveness of mesh- refinement techniques for some numerical relativity applications. We elucidate this numerical effect by presenting a model problem which exhibits the phenomenon, but which is simple enough that its numerical error can be understood analytically. Our analysis shows that the effect is caused by variations in finite differencing error generated across low and high resolution regions, and that its slow convergence is caused by the presence of dramatic speed differences among propagation modes typical of 3+1 relativity. Lastly, we resolve the problem, presenting a class of finite-differencing stencil modifications which eliminate this pathology in both our model problem and in numerical relativity examples.
NASA Astrophysics Data System (ADS)
Skutnik, Steven E.; Davis, David R.
2016-05-01
The use of passive gamma and neutron signatures from fission indicators is a common means of estimating used fuel burnup, enrichment, and cooling time. However, while characteristic fission product signatures such as 134Cs, 137Cs, 154Eu, and others are generally reliable estimators for used fuel burnup within the context where the assembly initial enrichment and the discharge time are known, in the absence of initial enrichment and/or cooling time information (such as when applying NDA measurements in a safeguards/verification context), these fission product indicators no longer yield a unique solution for assembly enrichment, burnup, and cooling time after discharge. Through the use of a new Mesh-Adaptive Direct Search (MADS) algorithm, it is possible to directly probe the shape of this "degeneracy space" characteristic of individual nuclides (and combinations thereof), both as a function of constrained parameters (such as the assembly irradiation history) and unconstrained parameters (e.g., the cooling time before measurement and the measurement precision for particular indicator nuclides). In doing so, this affords the identification of potential means of narrowing the uncertainty space of potential assembly enrichment, burnup, and cooling time combinations, thereby bounding estimates of assembly plutonium content. In particular, combinations of gamma-emitting nuclides with distinct half-lives (e.g., 134Cs with 137Cs and 154Eu) in conjunction with gross neutron counting (via 244Cm) are able to reasonably constrain the degeneracy space of possible solutions to a space small enough to perform useful discrimination and verification of fuel assemblies based on their irradiation history.
Moving Overlapping Grids with Adaptive Mesh Refinement for High-Speed Reactive and Non-reactive Flow
Henshaw, W D; Schwendeman, D W
2005-08-30
We consider the solution of the reactive and non-reactive Euler equations on two-dimensional domains that evolve in time. The domains are discretized using moving overlapping grids. In a typical grid construction, boundary-fitted grids are used to represent moving boundaries, and these grids overlap with stationary background Cartesian grids. Block-structured adaptive mesh refinement (AMR) is used to resolve fine-scale features in the flow such as shocks and detonations. Refinement grids are added to base-level grids according to an estimate of the error, and these refinement grids move with their corresponding base-level grids. The numerical approximation of the governing equations takes place in the parameter space of each component grid which is defined by a mapping from (fixed) parameter space to (moving) physical space. The mapped equations are solved numerically using a second-order extension of Godunov's method. The stiff source term in the reactive case is handled using a Runge-Kutta error-control scheme. We consider cases when the boundaries move according to a prescribed function of time and when the boundaries of embedded bodies move according to the surface stress exerted by the fluid. In the latter case, the Newton-Euler equations describe the motion of the center of mass of the each body and the rotation about it, and these equations are integrated numerically using a second-order predictor-corrector scheme. Numerical boundary conditions at slip walls are described, and numerical results are presented for both reactive and non-reactive flows in order to demonstrate the use and accuracy of the numerical approach.
NASA Astrophysics Data System (ADS)
Grauer, R.; Germaschewski, K.
The goal of this presentation is threefold. First, the role of singular structures like shocks, vortex tubes and current sheets for understanding intermittency in small scale turbulence is demonstrated. Secondly, in order to investigate the time evolution of singular structures, effective numerical techniques have to be applied, like block structured adaptive mesh refinement combined with recent advances in treating hyperbolic equations. And thirdly, the developed numerical techniques can perfectly be applied to the question of fast reconnection demonstrated by the example of compressible Hall-MHD including electron and ion inertia. 1 Why is it worth studying singular structures? The motivation for studying singular structures has several sources. In turbulent fluid and plasma flows the formation of nearly singular structures like shocks, vortex tubes or current sheets provide an effective mechanism to transport energy from large to small scales. In the last years it has become clear that the nature of the singular structures is a key feature of small scale intermittency. In a phenomenological way this is established in She-Leveque like models (She and Leveque, 1994; Grauer, Krug and Marliani, 1994; Politano and Pouquet, 1995; M¨uller and Biskamp, 2000), which are able to describe some of the scaling properties of high order structure functions. An additional source which highlights the importance of singular structures originates from studies of a toy model of turbulence, the so-called Burgers turbulence. The very left tail of the probability distribution of velocity increments can be calculated using the instanton approach (Balkovsky, Falkovich, Kolokolov and Lebedev, 1997). Here it is interesting to note that the main contribution in the relevant path integral stems from the the singular structures which are shocks in the burgers turbulence. From a mathematical point of view the question whether
A 3D finite-volume scheme for the Euler equations on adaptive tetrahedral grids
Vijayan, P.; Kallinderis, Y. )
1994-08-01
The paper describes the development and application of a new Euler solver for adaptive tetrahedral grids. Spatial discretization uses a finite-volume, node-based scheme that is of central-differencing type. A second-order Taylor series expansion is employed to march the solution in time according to the Lax-Wendroff approach. Special upwind-like smoothing operators for unstructured grids are developed for shock-capturing, as well as for suppression of solution oscillations. The scheme is formulated so that all operations are edge-based, which reduces the computational effort significantly. An adaptive grid algorithm is employed in order to resolve local flow features. This is achieved by dividing the tetrahedral cells locally, guided by a flow feature detection algorithm. Application cases include transonic flow around the ONERA M6 wing and transonic flow past a transport aircraft configuration. Comparisons with experimental data evaluate accuracy of the developed adaptive solver. 31 refs., 33 figs.
George, D.L.
2011-01-01
The simulation of advancing flood waves over rugged topography, by solving the shallow-water equations with well-balanced high-resolution finite volume methods and block-structured dynamic adaptive mesh refinement (AMR), is described and validated in this paper. The efficiency of block-structured AMR makes large-scale problems tractable, and allows the use of accurate and stable methods developed for solving general hyperbolic problems on quadrilateral grids. Features indicative of flooding in rugged terrain, such as advancing wet-dry fronts and non-stationary steady states due to balanced source terms from variable topography, present unique challenges and require modifications such as special Riemann solvers. A well-balanced Riemann solver for inundation and general (non-stationary) flow over topography is tested in this context. The difficulties of modeling floods in rugged terrain, and the rationale for and efficacy of using AMR and well-balanced methods, are presented. The algorithms are validated by simulating the Malpasset dam-break flood (France, 1959), which has served as a benchmark problem previously. Historical field data, laboratory model data and other numerical simulation results (computed on static fitted meshes) are shown for comparison. The methods are implemented in GEOCLAW, a subset of the open-source CLAWPACK software. All the software is freely available at. Published in 2010 by John Wiley & Sons, Ltd.
NASA Astrophysics Data System (ADS)
Gill, Stuart P. D.; Knebe, Alexander; Gibson, Brad K.; Flynn, Chris; Ibata, Rodrigo A.; Lewis, Geraint F.
2003-04-01
An adaptive multi grid approach to simulating the formation of structure from collisionless dark matter is described. MLAPM (Multi-Level Adaptive Particle Mesh) is one of the most efficient serial codes available on the cosmological "market" today. As part of Swinburne University's role in the development of the Square Kilometer Array, we are implementing hydrodynamics, feedback, and radiative transfer within the MLAPM adaptive mesh, in order to simulate baryonic processes relevant to the interstellar and intergalactic media at high redshift. We will outline our progress to date in applying the existing MLAPM to a study of the decay of satellite galaxies within massive host potentials.
1983-03-01
AN ANALYSIS OF A FINITE ELEMENT METHOD FOR CONVECTION- DIFFUSION PROBLEMS PART II: A POSTERIORI ERROR ESTIMATES AND ADAPTIVITY by W. G. Szymczak Y 6a...PERIOD COVERED AN ANALYSIS OF A FINITE ELEMENT METHOD FOR final life of the contract CONVECTION- DIFFUSION PROBLEM S. Part II: A POSTERIORI ERROR ...Element Method for Convection- Diffusion Problems. Part II: A Posteriori Error Estimates and Adaptivity W. G. Szvmczak and I. Babu~ka# Laboratory for
NASA Astrophysics Data System (ADS)
Dumbser, Michael; Loubère, Raphaël
2016-08-01
In this paper we propose a simple, robust and accurate nonlinear a posteriori stabilization of the Discontinuous Galerkin (DG) finite element method for the solution of nonlinear hyperbolic PDE systems on unstructured triangular and tetrahedral meshes in two and three space dimensions. This novel a posteriori limiter, which has been recently proposed for the simple Cartesian grid case in [62], is able to resolve discontinuities at a sub-grid scale and is substantially extended here to general unstructured simplex meshes in 2D and 3D. It can be summarized as follows: At the beginning of each time step, an approximation of the local minimum and maximum of the discrete solution is computed for each cell, taking into account also the vertex neighbors of an element. Then, an unlimited discontinuous Galerkin scheme of approximation degree N is run for one time step to produce a so-called candidate solution. Subsequently, an a posteriori detection step checks the unlimited candidate solution at time t n + 1 for positivity, absence of floating point errors and whether the discrete solution has remained within or at least very close to the bounds given by the local minimum and maximum computed in the first step. Elements that do not satisfy all the previously mentioned detection criteria are flagged as troubled cells. For these troubled cells, the candidate solution is discarded as inappropriate and consequently needs to be recomputed. Within these troubled cells the old discrete solution at the previous time tn is scattered onto small sub-cells (Ns = 2 N + 1 sub-cells per element edge), in order to obtain a set of sub-cell averages at time tn. Then, a more robust second order TVD finite volume scheme is applied to update the sub-cell averages within the troubled DG cells from time tn to time t n + 1. The new sub-grid data at time t n + 1 are finally gathered back into a valid cell-centered DG polynomial of degree N by using a classical conservative and higher order
MGGHAT: Elliptic PDE software with adaptive refinement, multigrid and high order finite elements
NASA Technical Reports Server (NTRS)
Mitchell, William F.
1993-01-01
MGGHAT (MultiGrid Galerkin Hierarchical Adaptive Triangles) is a program for the solution of linear second order elliptic partial differential equations in two dimensional polygonal domains. This program is now available for public use. It is a finite element method with linear, quadratic or cubic elements over triangles. The adaptive refinement via newest vertex bisection and the multigrid iteration are both based on a hierarchical basis formulation. Visualization is available at run time through an X Window display, and a posteriori through output files that can be used as GNUPLOT input. In this paper, we describe the methods used by MGGHAT, define the problem domain for which it is appropriate, illustrate use of the program, show numerical and graphical examples, and explain how to obtain the software.
Finite Element Analysis of Adaptive-Stiffening and Shape-Control SMA Hybrid Composites
NASA Technical Reports Server (NTRS)
Gao, Xiu-Jie; Turner, Travis L.; Burton, Deborah; Brinson, L. Catherine
2005-01-01
The usage of shape memory materials has extended rapidly to many fields, including medical devices, actuators, composites, structures and MEMS devices. For these various applications, shape memory alloys (SMAs) are available in various forms: bulk, wire, ribbon, thin film, and porous. In this work, the focus is on SMA hybrid composites with adaptive-stiffening or morphing functions. These composites are created by using SMA ribbons or wires embedded in a polymeric based composite panel/beam. Adaptive stiffening or morphing is activated via selective resistance heating or uniform thermal loads. To simulate the thermomechanical behavior of these composites, a SMA model was implemented using ABAQUS user element interface and finite element simulations of the systems were studied. Several examples are presented which show that the implemented model can be a very useful design and simulation tool for SMA hybrid composites.
Arbitrary-level hanging nodes for adaptive hphp-FEM approximations in 3D
Pavel Kus; Pavel Solin; David Andrs
2014-11-01
In this paper we discuss constrained approximation with arbitrary-level hanging nodes in adaptive higher-order finite element methods (hphp-FEM) for three-dimensional problems. This technique enables using highly irregular meshes, and it greatly simplifies the design of adaptive algorithms as it prevents refinements from propagating recursively through the finite element mesh. The technique makes it possible to design efficient adaptive algorithms for purely hexahedral meshes. We present a detailed mathematical description of the method and illustrate it with numerical examples.
A mesh density study for application to large deformation rolling process evaluations
Martin, J.A.
1997-12-01
When addressing large deformation through an elastic-plastic analysis the mesh density is paramount in determining the accuracy of the solution. However, given the nonlinear nature of the problem, a highly-refined mesh will generally require a prohibitive amount of computer resources. This paper addresses finite element mesh optimization studies considering accuracy of results and computer resource needs as applied to large deformation rolling processes. In particular, the simulation of the thread rolling manufacturing process is considered using the MARC software package and a Cray C90 supercomputer. Both mesh density and adaptive meshing on final results for both indentation of a rigid body to a specified depth and contact rolling along a predetermined length are evaluated.
Tangle-Free Mesh Motion for Ablation Simulations
NASA Technical Reports Server (NTRS)
Droba, Justin
2016-01-01
Problems involving mesh motion-which should not be mistakenly associated with moving mesh methods, a class of adaptive mesh redistribution techniques-are of critical importance in numerical simulations of the thermal response of melting and ablative materials. Ablation is the process by which material vaporizes or otherwise erodes due to strong heating. Accurate modeling of such materials is of the utmost importance in design of passive thermal protection systems ("heatshields") for spacecraft, the layer of the vehicle that ensures survival of crew and craft during re-entry. In an explicit mesh motion approach, a complete thermal solve is first performed. Afterwards, the thermal response is used to determine surface recession rates. These values are then used to generate boundary conditions for an a posteriori correction designed to update the location of the mesh nodes. Most often, linear elastic or biharmonic equations are used to model this material response, traditionally in a finite element framework so that complex geometries can be simulated. A simple scheme for moving the boundary nodes involves receding along the surface normals. However, for all but the simplest problem geometries, evolution in time following such a scheme will eventually bring the mesh to intersect and "tangle" with itself, inducing failure. This presentation demonstrates a comprehensive and sophisticated scheme that analyzes the local geometry of each node with help from user-provided clues to eliminate the tangle and enable simulations on a wide-class of difficult problem geometries. The method developed is demonstrated for linear elastic equations but is general enough that it may be adapted to other modeling equations. The presentation will explicate the inner workings of the tangle-free mesh motion algorithm for both two and three-dimensional meshes. It will show abstract examples of the method's success, including a verification problem that demonstrates its accuracy and
Method of modifying a volume mesh using sheet extraction
Borden, Michael J.; Shepherd, Jason F.
2007-02-20
A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet extraction. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of determining a sheet of hexahedral mesh elements, generating nodes for merging, and merging the nodes to delete the sheet of hexahedral mesh elements and modify the volume mesh.
Klein, R.I. |; Bell, J.; Pember, R.; Kelleher, T.
1993-04-01
The authors present results for high resolution hydrodynamic calculations of the growth and development of instabilities in shock driven imploding spherical geometries in both 2D and 3D. They solve the Eulerian equations of hydrodynamics with a high order Godunov approach using local adaptive mesh refinement to study the temporal and spatial development of the turbulent mixing layer resulting from both Richtmyer Meshkov and Rayleigh Taylor instabilities. The use of a high resolution Eulerian discretization with adaptive mesh refinement permits them to study the detailed three-dimensional growth of multi-mode perturbations far into the non-linear regime for converging geometries. They discuss convergence properties of the simulations by calculating global properties of the flow. They discuss the time evolution of the turbulent mixing layer and compare its development to a simple theory for a turbulent mix model in spherical geometry based on Plesset`s equation. Their 3D calculations show that the constant found in the planar incompressible experiments of Read and Young`s may not be universal for converging compressible flow. They show the 3D time trace of transitional onset to a mixing state using the temporal evolution of volume rendered imaging. Their preliminary results suggest that the turbulent mixing layer loses memory of its initial perturbations for classical Richtmyer Meshkov and Rayleigh Taylor instabilities in spherically imploding shells. They discuss the time evolution of mixed volume fraction and the role of vorticity in converging 3D flows in enhancing the growth of a turbulent mixing layer.
NASA Astrophysics Data System (ADS)
Lu, Yujie; Zhu, Banghe; Shen, Haiou; Rasmussen, John C.; Wang, Ge; Sevick-Muraca, Eva M.
2011-03-01
Fluorescence-enhanced optical imaging/tomography may play an important role in preclinical research and clinical diagnostics as a type of optical molecular. Time- and frequency-domain measurement can acquire more measurement information, reducing the ill-posedness and improving the reconstruction quality of fluorescence-enhanced optical tomography. Although the diffusion approximation (DA) theory has been extensively in optical imaging, high-order photon migration models must be further investigated for application to complex and small tissue volumes. In this paper, a frequency-domain fully parallel adaptive finite element solver is developed with the simplified spherical harmonics (SPN) approximations. To fully evaluate the performance of the SPN approximations, a fast tetrahedron-based Monte Carlo simulator suitable for complex heterogeneous geometries is developed using the convolution strategy to realize the simulation of the fluorescence excitation and emission. With simple and real digital mouse phantoms, the results show that the significant precision and speed improvements are obtained from the parallel adaptive mesh evolution strategy.
A tetrahedral mesh generation approach for 3D marine controlled-source electromagnetic modeling
NASA Astrophysics Data System (ADS)
Um, Evan Schankee; Kim, Seung-Sep; Fu, Haohuan
2017-03-01
3D finite-element (FE) mesh generation is a major hurdle for marine controlled-source electromagnetic (CSEM) modeling. In this paper, we present a FE discretization operator (FEDO) that automatically converts a 3D finite-difference (FD) model into reliable and efficient tetrahedral FE meshes for CSEM modeling. FEDO sets up wireframes of a background seabed model that precisely honors the seafloor topography. The wireframes are then partitioned into multiple regions. Outer regions of the wireframes are discretized with coarse tetrahedral elements whose maximum size is as large as a skin depth of the regions. We demonstrate that such coarse meshes can produce accurate FE solutions because numerical dispersion errors of tetrahedral meshes do not accumulate but oscillates. In contrast, central regions of the wireframes are discretized with fine tetrahedral elements to describe complex geology in detail. The conductivity distribution is mapped from FD to FE meshes in a volume-averaged sense. To avoid excessive mesh refinement around receivers, we introduce an effective receiver size. Major advantages of FEDO are summarized as follow. First, FEDO automatically generates reliable and economic tetrahedral FE meshes without adaptive meshing or interactive CAD workflows. Second, FEDO produces FE meshes that precisely honor the boundaries of the seafloor topography. Third, FEDO derives multiple sets of FE meshes from a given FD model. Each FE mesh is optimized for a different set of sources and receivers and is fed to a subgroup of processors on a parallel computer. This divide and conquer approach improves the parallel scalability of the FE solution. Both accuracy and effectiveness of FEDO are demonstrated with various CSEM examples.
Multigrid techniques for unstructured meshes
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1995-01-01
An overview of current multigrid techniques for unstructured meshes is given. The basic principles of the multigrid approach are first outlined. Application of these principles to unstructured mesh problems is then described, illustrating various different approaches, and giving examples of practical applications. Advanced multigrid topics, such as the use of algebraic multigrid methods, and the combination of multigrid techniques with adaptive meshing strategies are dealt with in subsequent sections. These represent current areas of research, and the unresolved issues are discussed. The presentation is organized in an educational manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.
An unstructured-mesh atmospheric model for nonhydrostatic dynamics: Towards optimal mesh resolution
NASA Astrophysics Data System (ADS)
Szmelter, Joanna; Zhang, Zhao; Smolarkiewicz, Piotr K.
2015-08-01
The paper advances the limited-area anelastic model (Smolarkiewicz et al. (2013) [45]) for investigation of nonhydrostatic dynamics in mesoscale atmospheric flows. New developments include the extension to a tetrahedral-based median-dual option for unstructured meshes and a static mesh adaptivity technique using an error indicator based on inherent properties of the Multidimensional Positive Definite Advection Transport Algorithm (MPDATA). The model employs semi-implicit nonoscillatory forward-in-time integrators for soundproof PDEs, built on MPDATA and a robust non-symmetric Krylov-subspace elliptic solver. Finite-volume spatial discretisation adopts an edge-based data structure. Simulations of stratified orographic flows and the associated gravity-wave phenomena in media with uniform and variable dispersive properties verify the advancement and demonstrate the potential of heterogeneous anisotropic discretisation with large variation in spatial resolution for study of complex stratified flows that can be computationally unattainable with regular grids.
toolkit computational mesh conceptual model.
Baur, David G.; Edwards, Harold Carter; Cochran, William K.; Williams, Alan B.; Sjaardema, Gregory D.
2010-03-01
The Sierra Toolkit computational mesh is a software library intended to support massively parallel multi-physics computations on dynamically changing unstructured meshes. This domain of intended use is inherently complex due to distributed memory parallelism, parallel scalability, heterogeneity of physics, heterogeneous discretization of an unstructured mesh, and runtime adaptation of the mesh. Management of this inherent complexity begins with a conceptual analysis and modeling of this domain of intended use; i.e., development of a domain model. The Sierra Toolkit computational mesh software library is designed and implemented based upon this domain model. Software developers using, maintaining, or extending the Sierra Toolkit computational mesh library must be familiar with the concepts/domain model presented in this report.
Friedman, A.; Miller, W. Jr.
1993-12-31
The program was divided into segments: (Week 1) geometric modeling and mesh generation (Weeks 2 and 3) error estimation and adaptive strategies. Participants in the program came from a wide variety of disciplines dealing with remarkably analogous problems in this area. Ideas were exchanged and interdisciplinary collaboration was initiated in informal contexts as well as in the talks and question periods. In the talks, a number of algorithms were described along with specific applications to problems of great current interest in various scientific and engineering disciplines. In this emerging field, participants developed criteria for evaluation of algorithms and established guidelines for selection of algorithms appropriate to any specific problem. Special features of a problem may include curved surfaces, complicated boundaries, evolving interfaces (such as occur in coating flows), and/or criticality of error estimation.
CUBIT mesh generation environment. Volume 1: Users manual
Blacker, T.D.; Bohnhoff, W.J.; Edwards, T.L.
1994-05-01
The CUBIT mesh generation environment is a two- and three-dimensional finite element mesh generation tool which is being developed to pursue the goal of robust and unattended mesh generation--effectively automating the generation of quadrilateral and hexahedral elements. It is a solid-modeler based preprocessor that meshes volume and surface solid models for finite element analysis. A combination of techniques including paving, mapping, sweeping, and various other algorithms being developed are available for discretizing the geometry into a finite element mesh. CUBIT also features boundary layer meshing specifically designed for fluid flow problems. Boundary conditions can be applied to the mesh through the geometry and appropriate files for analysis generated. CUBIT is specifically designed to reduce the time required to create all-quadrilateral and all-hexahedral meshes. This manual is designed to serve as a reference and guide to creating finite element models in the CUBIT environment.
Unstructured mesh algorithms for aerodynamic calculations
NASA Technical Reports Server (NTRS)
Mavriplis, D. J.
1992-01-01
The use of unstructured mesh techniques for solving complex aerodynamic flows is discussed. The principle advantages of unstructured mesh strategies, as they relate to complex geometries, adaptive meshing capabilities, and parallel processing are emphasized. The various aspects required for the efficient and accurate solution of aerodynamic flows are addressed. These include mesh generation, mesh adaptivity, solution algorithms, convergence acceleration, and turbulence modeling. Computations of viscous turbulent two-dimensional flows and inviscid three-dimensional flows about complex configurations are demonstrated. Remaining obstacles and directions for future research are also outlined.
Moving and adaptive grid methods for compressible flows
NASA Technical Reports Server (NTRS)
Trepanier, Jean-Yves; Camarero, Ricardo
1995-01-01
This paper describes adaptive grid methods developed specifically for compressible flow computations. The basic flow solver is a finite-volume implementation of Roe's flux difference splitting scheme or arbitrarily moving unstructured triangular meshes. The grid adaptation is performed according to geometric and flow requirements. Some results are included to illustrate the potential of the methodology.
NASA Astrophysics Data System (ADS)
Ghabraei, Soheil; Moradi, Hamed; Vossoughi, Gholamreza
2016-06-01
Large amplitude oscillation of the power transmission lines, which is also known as galloping phenomenon, has hazardous consequences such as short circuiting and failure of transmission line. In this article, to suppress the undesirable vibrations of the transmission lines, first the governing equations of transmission line are derived via mode summation technique. Then, due to the occurrence of large amplitude vibrations, nonlinear quadratic and cubic terms are included in the derived linear equations. To suppress the vibrations, arbitrary number of the piezoelectric actuators is assumed to exert the actuation forces. Afterwards, a Lyapunov based approach is proposed for the robust adaptive suppression of the undesirable vibrations in the finite time. To compensate the supposed parametric uncertainties with unknown bands, proper adaption laws are introduced. To avoid the vibration devastating consequences as quickly as possible, appropriate control laws are designed. The vibration suppression in the finite time with supposed adaption and control laws is mathematically proved via Lyapunov finite time stability theory. Finally, to illustrate and validate the efficiency and robustness of the proposed finite time control scheme, a parametric case study with three piezoelectric actuators is performed. It is observed that the proposed active control strategy is more efficient and robust than the passive control methods.
Finite element analysis of low-cost membrane deformable mirrors for high-order adaptive optics
NASA Astrophysics Data System (ADS)
Winsor, Robert S.; Sivaramakrishnan, Anand; Makidon, Russell B.
1999-10-01
We demonstrate the feasibility of glass membrane deformable mirror (DM) support structures intended for very high order low-stroke adaptive optics systems. We investigated commercially available piezoelectric ceramics. Piezoelectric tubes were determined to offer the largest amount of stroke for a given amount of space on the mirror surface that each actuator controls. We estimated the minimum spacing and the maximum expected stroke of such actuators. We developed a quantitative understanding of the response of a membrane mirror surface by performing a Finite Element Analysis (FEA) study. The results of the FEA analysis were used to develop a design and fabrication process for membrane deformable mirrors of 200 - 500 micron thicknesses. Several different values for glass thickness and actuator spacing were analyzed to determine the best combination of actuator stoke and surface deformation quality. We considered two deformable mirror configurations. The first configuration uses a vacuum membrane attachment system where the actuator tubes' central holes connect to an evacuated plenum, and atmospheric pressure holds the membrane against the actuators. This configuration allows the membrane to be removed from the actuators, facilitating easy replacement of the glass. The other configuration uses precision bearing balls epoxied to the ends of the actuator tubes, with the glass membrane epoxied to the ends of the ball bearings. While this kind of DM is not serviceable, it allows actuator spacings of 4 mm, in addition to large stroke. Fabrication of a prototype of the latter kind of DM was started.
NASA Astrophysics Data System (ADS)
Zhang, Xiu; Wang, Xingyu; Wang, Bei; Sugi, Takenao; Nakamura, Masatoshi
Surface electromyogram (EMG) from elbow, wrist and hand has been widely used as an input of multifunction prostheses for many years. However, for patients with high-level limb deficiencies, muscle activities in upper-limbs are not strong enough to be used as control signals. In this paper, EMG from lower-limbs is acquired and applied to drive a meal assistance robot. An onset detection method with adaptive threshold based on EMG power is proposed to recognize different muscle contractions. Predefined control commands are output by finite state machine (FSM), and applied to operate the robot. The performance of EMG control is compared with joystick control by both objective and subjective indices. The results show that FSM provides the user with an easy-performing control strategy, which successfully operates robots with complicated control commands by limited muscle motions. The high accuracy and comfortableness of the EMG-control meal assistance robot make it feasible for users with upper limbs motor disabilities.
NASA Astrophysics Data System (ADS)
Dönmez, Orhan
2004-09-01
In this paper, the general procedure to solve the general relativistic hydrodynamical (GRH) equations with adaptive-mesh refinement (AMR) is presented. In order to achieve, the GRH equations are written in the conservation form to exploit their hyperbolic character. The numerical solutions of GRH equations are obtained by high resolution shock Capturing schemes (HRSC), specifically designed to solve nonlinear hyperbolic systems of conservation laws. These schemes depend on the characteristic information of the system. The Marquina fluxes with MUSCL left and right states are used to solve GRH equations. First, different test problems with uniform and AMR grids on the special relativistic hydrodynamics equations are carried out to verify the second-order convergence of the code in one, two and three dimensions. Results from uniform and AMR grid are compared. It is found that adaptive grid does a better job when the number of resolution is increased. Second, the GRH equations are tested using two different test problems which are Geodesic flow and Circular motion of particle In order to do this, the flux part of GRH equations is coupled with source part using Strang splitting. The coupling of the GRH equations is carried out in a treatment which gives second order accurate solutions in space and time.
NASA Astrophysics Data System (ADS)
Szilagyi, Bela
2011-04-01
Spectral numerical methods are known for giving faster convergence than finite difference methods, when evolving smooth quantities. In binary black hole simulations of the SpEC code this exponential convergence is clearly visible. However, the same exponential dependence of the numerical error on the grid-resolution will also mean that a linear order mismatch between the grid-structure and the actual data will lead to exponential loss of accuracy. In my talk I will show the way the Caltech-Cornell-CITA code deals with this, by use of what we call Spectral AMR. In our algorithm we monitor truncation error estimates in various regions of the grid as the simulation proceeds, and adjust the grid as necessary. Supported by Sherman Fairchild Foundation and NSF grants PHY-061459 and PHY-0652995 to Caltech.
Method of modifying a volume mesh using sheet insertion
Borden, Michael J.; Shepherd, Jason F.
2006-08-29
A method and machine-readable medium provide a technique to modify a hexahedral finite element volume mesh using dual generation and sheet insertion. After generating a dual of a volume stack (mesh), a predetermined algorithm may be followed to modify (refine) the volume mesh of hexahedral elements. The predetermined algorithm may include the steps of locating a sheet of hexahedral mesh elements, determining a plurality of hexahedral elements within the sheet to refine, shrinking the plurality of elements, and inserting a new sheet of hexahedral elements adjacently to modify the volume mesh. Additionally, another predetermined algorithm using mesh cutting may be followed to modify a volume mesh.
Workshop on adaptive grid methods for fusion plasmas
Wiley, J.C.
1995-07-01
The author describes a general `hp` finite element method with adaptive grids. The code was based on the work of Oden, et al. The term `hp` refers to the method of spatial refinement (h), in conjunction with the order of polynomials used as a part of the finite element discretization (p). This finite element code seems to handle well the different mesh grid sizes occuring between abuted grids with different resolutions.
Valentín, A; Humphrey, J D; Holzapfel, G A
2013-08-01
We implemented a constrained mixture model of arterial growth and remodeling in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and nonhomogenous degradation of elastin or loss of smooth muscle function. The nonlinear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons with prior results for two special cases: uniform transmural changes in mass and differential growth and remodeling within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement.
Valentín, A.; Humphrey, J. D.; Holzapfel, G. A.
2013-01-01
We implemented a constrained mixture model of arterial growth and remodeling (G&R) in a nonlinear finite element framework to facilitate numerical analyses of diverse cases of arterial adaptation and maladaptation, including disease progression, resulting in complex evolving geometries and compositions. This model enables hypothesis testing by predicting consequences of postulated characteristics of cell and matrix turnover, including evolving quantities and orientations of fibrillar constituents and non-homogenous degradation of elastin or loss of smooth muscle function. The non-linear finite element formulation is general within the context of arterial mechanics, but we restricted our present numerical verification to cylindrical geometries to allow comparisons to prior results for two special cases: uniform transmural changes in mass and differential G&R within a two-layered cylindrical model of the human aorta. The present finite element model recovers the results of these simplified semi-inverse analyses with good agreement. PMID:23713058
A Posteriori Error Estimation of Adaptive Finite Difference Schemes for Hyperbolic Systems
1988-06-01
scheme have been studied by Ciment (ref 24), Fritts (ref 25), Hoffman (ref 26), Osher.- and Sanders (ref 27), Sanders (ref 28), and Mastin (ref 29...Methods for Partial Differential Equations, SIAM, Philadelphia, 1983. 24. Ciment , M., "Stable Difference Schemes With Uneven Mesh Spacings," Math. Comp
Gradient scaling for nonuniform meshes
Margolin, L.G.; Ruppel, H.M.; Demuth, R.B.
1985-01-01
This paper is concerned with the effect of nonuniform meshes on the accuracy of finite-difference calculations of fluid flow. In particular, when a simple shock propagates through a nonuniform mesh, one may fail to model the jump conditions across the shock even when the equations are differenced in manifestly conservative fashion. We develop an approximate dispersion analysis of the numerical equations and identify the source of the mesh dependency with the form of the artificial viscosity. We then derive an algebraic correction to the numerical equations - a scaling factor for the pressure gradient - to essentially eliminate the mesh dependency. We present several calculations to illustrate our theory. We conclude with an alternate interpretation of our results. 14 refs., 5 figs.
Neuert, Mark A C; Dunning, Cynthia E
2013-09-01
Strain energy-based adaptive material models are used to predict bone resorption resulting from stress shielding induced by prosthetic joint implants. Generally, such models are governed by two key parameters: a homeostatic strain-energy state (K) and a threshold deviation from this state required to initiate bone reformation (s). A refinement procedure has been performed to estimate these parameters in the femur and glenoid; this study investigates the specific influences of these parameters on resulting density distributions in the distal ulna. A finite element model of a human ulna was created using micro-computed tomography (µCT) data, initialized to a homogeneous density distribution, and subjected to approximate in vivo loading. Values for K and s were tested, and the resulting steady-state density distribution compared with values derived from µCT images. The sensitivity of these parameters to initial conditions was examined by altering the initial homogeneous density value. The refined model parameters selected were then applied to six additional human ulnae to determine their performance across individuals. Model accuracy using the refined parameters was found to be comparable with that found in previous studies of the glenoid and femur, and gross bone structures, such as the cortical shell and medullary canal, were reproduced. The model was found to be insensitive to initial conditions; however, a fair degree of variation was observed between the six specimens. This work represents an important contribution to the study of changes in load transfer in the distal ulna following the implementation of commercial orthopedic implants.
NASA Astrophysics Data System (ADS)
Ma, Xibo; Tian, Jie; Zhang, Bo; Zhang, Xing; Xue, Zhenwen; Dong, Di; Han, Dong
2011-03-01
Among many optical molecular imaging modalities, bioluminescence imaging (BLI) has more and more wide application in tumor detection and evaluation of pharmacodynamics, toxicity, pharmacokinetics because of its noninvasive molecular and cellular level detection ability, high sensitivity and low cost in comparison with other imaging technologies. However, BLI can not present the accurate location and intensity of the inner bioluminescence sources such as in the bone, liver or lung etc. Bioluminescent tomography (BLT) shows its advantage in determining the bioluminescence source distribution inside a small animal or phantom. Considering the deficiency of two-dimensional imaging modality, we developed three-dimensional tomography to reconstruct the information of the bioluminescence source distribution in transgenic mOC-Luc mice bone with the boundary measured data. In this paper, to study the osteocalcin (OC) accumulation in transgenic mOC-Luc mice bone, a BLT reconstruction method based on multilevel adaptive finite element (FEM) algorithm was used for localizing and quantifying multi bioluminescence sources. Optical and anatomical information of the tissues are incorporated as a priori knowledge in this method, which can reduce the ill-posedness of BLT. The data was acquired by the dual modality BLT and Micro CT prototype system that was developed by us. Through temperature control and absolute intensity calibration, a relative accurate intensity can be calculated. The location of the OC accumulation was reconstructed, which was coherent with the principle of bone differentiation. This result also was testified by ex vivo experiment in the black 96-plate well using the BLI system and the chemiluminescence apparatus.
Multigrid for refined triangle meshes
Shapira, Yair
1997-02-01
A two-level preconditioning method for the solution of (locally) refined finite element schemes using triangle meshes is introduced. In the isotropic SPD case, it is shown that the condition number of the preconditioned stiffness matrix is bounded uniformly for all sufficiently regular triangulations. This is also verified numerically for an isotropic diffusion problem with highly discontinuous coefficients.
Finite elements: Theory and application
NASA Technical Reports Server (NTRS)
Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)
1988-01-01
Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.
NASA Astrophysics Data System (ADS)
Li, Pak Shing; Martin, Daniel F.; Klein, Richard I.; McKee, Christopher F.
2012-02-01
Performing a stable, long-duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and constrained transport electromotive force averaging schemes that can meet this challenge, and using this strategy, we have developed a new adaptive mesh refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma β0 of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers ({{\\cal M}_rms}= 17.3) and smaller plasma beta (β0 = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
Li, Pak Shing; Klein, Richard I.; Martin, Daniel F.; McKee, Christopher F. E-mail: klein@astron.berkeley.edu E-mail: cmckee@astro.berkeley.edu
2012-02-01
Performing a stable, long-duration simulation of driven MHD turbulence with a high thermal Mach number and a strong initial magnetic field is a challenge to high-order Godunov ideal MHD schemes because of the difficulty in guaranteeing positivity of the density and pressure. We have implemented a robust combination of reconstruction schemes, Riemann solvers, limiters, and constrained transport electromotive force averaging schemes that can meet this challenge, and using this strategy, we have developed a new adaptive mesh refinement (AMR) MHD module of the ORION2 code. We investigate the effects of AMR on several statistical properties of a turbulent ideal MHD system with a thermal Mach number of 10 and a plasma {beta}{sub 0} of 0.1 as initial conditions; our code is shown to be stable for simulations with higher Mach numbers (M{sub rms}= 17.3) and smaller plasma beta ({beta}{sub 0} = 0.0067) as well. Our results show that the quality of the turbulence simulation is generally related to the volume-averaged refinement. Our AMR simulations show that the turbulent dissipation coefficient for supersonic MHD turbulence is about 0.5, in agreement with unigrid simulations.
A density driven mesh generator guided by a neural network
Lowther, D.A.; Dyck, D.N. )
1993-03-01
A neural network guided mesh generator is described. The mesh generator used density information provided by the neural network to determine the size and placement of elements. This system is coupled with an adaptive meshing and solving process and is shown to have major computational benefits compared with adaptation alone.
Method of generating a surface mesh
Shepherd, Jason F.; Benzley, Steven; Grover, Benjamin T.
2008-03-04
A method and machine-readable medium provide a technique to generate and modify a quadrilateral finite element surface mesh using dual creation and modification. After generating a dual of a surface (mesh), a predetermined algorithm may be followed to generate and modify a surface mesh of quadrilateral elements. The predetermined algorithm may include the steps of generating two-dimensional cell regions in dual space, determining existing nodes in primal space, generating new nodes in the dual space, and connecting nodes to form the quadrilateral elements (faces) for the generated and modifiable surface mesh.
Finite element methods of analysis for 3D inviscid compressible flows
NASA Technical Reports Server (NTRS)
Peraire, Jaime
1990-01-01
The applicants have developed a finite element based approach for the solution of three-dimensional compressible flows. The procedure enables flow solutions to be obtained on tetrahedral discretizations of computational domains of complex form. A further development was the incorporation of a solution adaptive mesh strategy in which the adaptivity is achieved by complete remeshing of the solution domain. During the previous year, the applicants were working with the Advanced Aerodynamics Concepts Branch at NASA Ames Research Center with an implementation of the basic meshing and solution procedure. The objective of the work to be performed over this twelve month period was the transfer of the adaptive mesh technology and also the undertaking of basic research into alternative flow algorithms for the Euler equations on unstructured meshes.
Cubit Mesh Generation Toolkit V11.1
HANKS, BYRON; KERR, ROBERT; KNUPP, PATRICK; MAEZ, JONATHAN; WHITE, DAVID; MITCHELL, SCOTT; OWEN, STEVEN; SHEPHERD, JASON; TAUTGES, TIMOTHY; MELANDER, DARRYL; BLACKER, TEDDY; BORDEN, MICHAEL; BREWER, MICHAEL; CLARK, BRETT; FORTIER, LESLIE; KALLAHER, JENNA; PEBAY, PHILIPPE; STATEN, MATTHEW; VINEYARD, CRAIG; GROVER, BENJAMIN; BENZLEY, STEVEN; SIMPSON, CLINTON; NIELSON, ERIC; KOPP, JOEL; STORM, STEVE; NUGENT, MARK; WALTON, KIRK; BORDEN, MIKE; ERNST, CORY; FOWLER, JOHN; KRAFTCHECL, JASON; STEPHNSON, MIKE; YEOU, RAMMAGAY; MERKLEY, KARL; METERS, RAY; DEWET, MARK; RICHARDS, SARA; PENDLEY, KEVIN; MORRIS, RANDY; RICHARDSON, MARK; VYAS, VED; SHOWMAN, SAM; HAYS, ALEX; TIDWELL, BOYD; MILLAR, ALEX
2009-03-25
CUBIT prepares models to be used in computer-based simulation of real-world events. CUBIT is a full-featured software toolkit for robust generation of two- and three-dimensional finite element meshes (grids) and geometry preparation. Its main goal is to reduce the time to generate meshes, particularly large hex meshes of complicated, interlocking assemblies.
NASA Technical Reports Server (NTRS)
Demkowicz, L.; Oden, J. T.; Rachowicz, W.
1990-01-01
A new finite element method solving compressible Navier-Stokes equations is proposed. The method is based on a version of Strang's operator splitting and an h-p adaptive finite element approximation in space. This paper contains the formulation of the method with a detailed discussion of boundary conditions, a sample adaptive strategy and numerical examples involving compressible viscous flow over a flat plate with Reynolds number Re = 1000 and Re = 10,000.
6th International Meshing Roundtable '97
White, D.
1997-09-01
The goal of the 6th International Meshing Roundtable is to bring together researchers and developers from industry, academia, and government labs in a stimulating, open environment for the exchange of technical information related to the meshing process. In the pas~ the Roundtable has enjoyed significant participation born each of these groups from a wide variety of countries. The Roundtable will consist of technical presentations from contributed papers and abstracts, two invited speakers, and two invited panels of experts discussing topics related to the development and use of automatic mesh generation tools. In addition, this year we will feature a "Bring Your Best Mesh" competition and poster session to encourage discussion and participation from a wide variety of mesh generation tool users. The schedule and evening social events are designed to provide numerous opportunities for informal dialog. A proceedings will be published by Sandia National Laboratories and distributed at the Roundtable. In addition, papers of exceptionally high quaIity will be submitted to a special issue of the International Journal of Computational Geometry and Applications. Papers and one page abstracts were sought that present original results on the meshing process. Potential topics include but are got limited to: Unstructured triangular and tetrahedral mesh generation Unstructured quadrilateral and hexahedral mesh generation Automated blocking and structured mesh generation Mixed element meshing Surface mesh generation Geometry decomposition and clean-up techniques Geometry modification techniques related to meshing Adaptive mesh refinement and mesh quality control Mesh visualization Special purpose meshing algorithms for particular applications Theoretical or novel ideas with practical potential Technical presentations from industrial researchers.
TESS: A RELATIVISTIC HYDRODYNAMICS CODE ON A MOVING VORONOI MESH
Duffell, Paul C.; MacFadyen, Andrew I. E-mail: macfadyen@nyu.edu
2011-12-01
We have generalized a method for the numerical solution of hyperbolic systems of equations using a dynamic Voronoi tessellation of the computational domain. The Voronoi tessellation is used to generate moving computational meshes for the solution of multidimensional systems of conservation laws in finite-volume form. The mesh-generating points are free to move with arbitrary velocity, with the choice of zero velocity resulting in an Eulerian formulation. Moving the points at the local fluid velocity makes the formulation effectively Lagrangian. We have written the TESS code to solve the equations of compressible hydrodynamics and magnetohydrodynamics for both relativistic and non-relativistic fluids on a dynamic Voronoi mesh. When run in Lagrangian mode, TESS is significantly less diffusive than fixed mesh codes and thus preserves contact discontinuities to high precision while also accurately capturing strong shock waves. TESS is written for Cartesian, spherical, and cylindrical coordinates and is modular so that auxiliary physics solvers are readily integrated into the TESS framework and so that this can be readily adapted to solve general systems of equations. We present results from a series of test problems to demonstrate the performance of TESS and to highlight some of the advantages of the dynamic tessellation method for solving challenging problems in astrophysical fluid dynamics.
An adaptive streamline diffusion finite element method for hyperbolic systems in gas dynamics
NASA Astrophysics Data System (ADS)
Zhou, Guohui
1992-09-01
The paintwise error analysis of the streamline diffusion method for two dimensional stationary problem with constant coefficients is extended to the time dependent problem. The purpose of the study is to justify a local mesh refinement strategy. The one dimensional Euler equations coming from the shock tube and Riemann's problem in gas dynamics are used. The gas is assumed to be at rest on both sides of the membrane, with pressure and density different on each side. The case where the problem is scalar and linear is discussed. Linear systems of hyperbolic type in one space variable and nonlinear scalar problems are studied.
NASA Astrophysics Data System (ADS)
Schartmann, M.; Ballone, A.; Burkert, A.; Gillessen, S.; Genzel, R.; Pfuhl, O.; Eisenhauer, F.; Plewa, P. M.; Ott, T.; George, E. M.; Habibi, M.
2015-10-01
The dusty, ionized gas cloud G2 is currently passing the massive black hole in the Galactic Center at a distance of roughly 2400 Schwarzschild radii. We explore the possibility of a starting point of the cloud within the disks of young stars. We make use of the large amount of new observations in order to put constraints on G2's origin. Interpreting the observations as a diffuse cloud of gas, we employ three-dimensional hydrodynamical adaptive mesh refinement (AMR) simulations with the PLUTO code and do a detailed comparison with observational data. The simulations presented in this work update our previously obtained results in multiple ways: (1) high resolution three-dimensional hydrodynamical AMR simulations are used, (2) the cloud follows the updated orbit based on the Brackett-γ data, (3) a detailed comparison to the observed high-quality position-velocity (PV) diagrams and the evolution of the total Brackett-γ luminosity is done. We concentrate on two unsolved problems of the diffuse cloud scenario: the unphysical formation epoch only shortly before the first detection and the too steep Brackett-γ light curve obtained in simulations, whereas the observations indicate a constant Brackett-γ luminosity between 2004 and 2013. For a given atmosphere and cloud mass, we find a consistent model that can explain both, the observed Brackett-γ light curve and the PV diagrams of all epochs. Assuming initial pressure equilibrium with the atmosphere, this can be reached for a starting date earlier than roughly 1900, which is close to apo-center and well within the disks of young stars.
Schartmann, M.; Ballone, A.; Burkert, A.; Gillessen, S.; Genzel, R.; Pfuhl, O.; Eisenhauer, F.; Plewa, P. M.; Ott, T.; George, E. M.; Habibi, M.
2015-10-01
The dusty, ionized gas cloud G2 is currently passing the massive black hole in the Galactic Center at a distance of roughly 2400 Schwarzschild radii. We explore the possibility of a starting point of the cloud within the disks of young stars. We make use of the large amount of new observations in order to put constraints on G2's origin. Interpreting the observations as a diffuse cloud of gas, we employ three-dimensional hydrodynamical adaptive mesh refinement (AMR) simulations with the PLUTO code and do a detailed comparison with observational data. The simulations presented in this work update our previously obtained results in multiple ways: (1) high resolution three-dimensional hydrodynamical AMR simulations are used, (2) the cloud follows the updated orbit based on the Brackett-γ data, (3) a detailed comparison to the observed high-quality position–velocity (PV) diagrams and the evolution of the total Brackett-γ luminosity is done. We concentrate on two unsolved problems of the diffuse cloud scenario: the unphysical formation epoch only shortly before the first detection and the too steep Brackett-γ light curve obtained in simulations, whereas the observations indicate a constant Brackett-γ luminosity between 2004 and 2013. For a given atmosphere and cloud mass, we find a consistent model that can explain both, the observed Brackett-γ light curve and the PV diagrams of all epochs. Assuming initial pressure equilibrium with the atmosphere, this can be reached for a starting date earlier than roughly 1900, which is close to apo-center and well within the disks of young stars.
Spherical geodesic mesh generation
Fung, Jimmy; Kenamond, Mark Andrew; Burton, Donald E.; Shashkov, Mikhail Jurievich
2015-02-27
In ALE simulations with moving meshes, mesh topology has a direct influence on feature representation and code robustness. In three-dimensional simulations, modeling spherical volumes and features is particularly challenging for a hydrodynamics code. Calculations on traditional spherical meshes (such as spin meshes) often lead to errors and symmetry breaking. Although the underlying differencing scheme may be modified to rectify this, the differencing scheme may not be accessible. This work documents the use of spherical geodesic meshes to mitigate solution-mesh coupling. These meshes are generated notionally by connecting geodesic surface meshes to produce triangular-prismatic volume meshes. This mesh topology is fundamentally different from traditional mesh topologies and displays superior qualities such as topological symmetry. This work describes the geodesic mesh topology as well as motivating demonstrations with the FLAG hydrocode.
NASA Astrophysics Data System (ADS)
Peeters, J.; Arroud, G.; Ribbens, B.; Dirckx, J. J. J.; Steenackers, G.
2015-12-01
In non-destructive evaluation the use of finite element models to evaluate structural behavior and experimental setup optimization can complement with the inspector's experience. A new adaptive response surface methodology, especially adapted for thermal problems, is used to update the experimental setup parameters in a finite element model to the state of the test sample measured by pulsed thermography. Poly Vinyl Chloride (PVC) test samples are used to examine the results for thermal insulator models. A comparison of the achieved results is made by changing the target values from experimental pulsed thermography data to a fixed validation model. Several optimizers are compared and discussed with the focus on speed and accuracy. A time efficiency increase of over 20 and an accuracy of over 99.5% are achieved by the choice of the correct parameter sets and optimizer. Proper parameter set selection criteria are defined and the influence of the choice of the optimization algorithm and parameter set on the accuracy and convergence time are investigated.
Conformal refinement of unstructured quadrilateral meshes
Garmella, Rao
2009-01-01
We present a multilevel adaptive refinement technique for unstructured quadrilateral meshes in which the mesh is kept conformal at all times. This means that the refined mesh, like the original, is formed of only quadrilateral elements that intersect strictly along edges or at vertices, i.e., vertices of one quadrilateral element do not lie in an edge of another quadrilateral. Elements are refined using templates based on 1:3 refinement of edges. We demonstrate that by careful design of the refinement and coarsening strategy, we can maintain high quality elements in the refined mesh. We demonstrate the method on a number of examples with dynamically changing refinement regions.
MOAB : a mesh-oriented database.
Tautges, Timothy James; Ernst, Corey; Stimpson, Clint; Meyers, Ray J.; Merkley, Karl
2004-04-01
A finite element mesh is used to decompose a continuous domain into a discretized representation. The finite element method solves PDEs on this mesh by modeling complex functions as a set of simple basis functions with coefficients at mesh vertices and prescribed continuity between elements. The mesh is one of the fundamental types of data linking the various tools in the FEA process (mesh generation, analysis, visualization, etc.). Thus, the representation of mesh data and operations on those data play a very important role in FEA-based simulations. MOAB is a component for representing and evaluating mesh data. MOAB can store structured and unstructured mesh, consisting of elements in the finite element 'zoo'. The functional interface to MOAB is simple yet powerful, allowing the representation of many types of metadata commonly found on the mesh. MOAB is optimized for efficiency in space and time, based on access to mesh in chunks rather than through individual entities, while also versatile enough to support individual entity access. The MOAB data model consists of a mesh interface instance, mesh entities (vertices and elements), sets, and tags. Entities are addressed through handles rather than pointers, to allow the underlying representation of an entity to change without changing the handle to that entity. Sets are arbitrary groupings of mesh entities and other sets. Sets also support parent/child relationships as a relation distinct from sets containing other sets. The directed-graph provided by set parent/child relationships is useful for modeling topological relations from a geometric model or other metadata. Tags are named data which can be assigned to the mesh as a whole, individual entities, or sets. Tags are a mechanism for attaching data to individual entities and sets are a mechanism for describing relations between entities; the combination of these two mechanisms is a powerful yet simple interface for representing metadata or application
Higher-Order Adaptive Finite-Element Methods for Kohn-Sham Density Functional Theory
2012-07-03
employ the finite-temperature Fermi- Dirac smearing [3] to suppress the charge sloshing associated with degenerate or close to degenerate eigenstates...elements up to degree eight (HEX27, HEX125SPECT, HEX343SPECT, HEX729SPECT). The numbers following the words ‘TET’ and ‘HEX’ denote the number of nodes in...work are constructed as Lagrange polynomials interpolated through an optimal distribution of nodes corre- sponding to the roots of derivatives of
Higher-Order, Space-Time Adaptive Finite Volume Methods: Algorithms, Analysis and Applications
Minion, Michael
2014-04-29
The four main goals outlined in the proposal for this project were: 1. Investigate the use of higher-order (in space and time) finite-volume methods for fluid flow problems. 2. Explore the embedding of iterative temporal methods within traditional block-structured AMR algorithms. 3. Develop parallel in time methods for ODEs and PDEs. 4. Work collaboratively with the Center for Computational Sciences and Engineering (CCSE) at Lawrence Berkeley National Lab towards incorporating new algorithms within existing DOE application codes.
Adaptation of a program for nonlinear finite element analysis to the CDC STAR 100 computer
NASA Technical Reports Server (NTRS)
Pifko, A. B.; Ogilvie, P. L.
1978-01-01
The conversion of a nonlinear finite element program to the CDC STAR 100 pipeline computer is discussed. The program called DYCAST was developed for the crash simulation of structures. Initial results with the STAR 100 computer indicated that significant gains in computation time are possible for operations on gloval arrays. However, for element level computations that do not lend themselves easily to long vector processing, the STAR 100 was slower than comparable scalar computers. On this basis it is concluded that in order for pipeline computers to impact the economic feasibility of large nonlinear analyses it is absolutely essential that algorithms be devised to improve the efficiency of element level computations.
An approximate waves-bordering algorithm for adaptive finite elements analysis
NASA Astrophysics Data System (ADS)
Morandi Cecchi, M.; Marcuzzi, F.
1999-09-01
In this paper an Approximate Waves-Bordering algorithm (AWB) is presented. It computes the finite elements linear system solution-update after a refinement/unrefinement step. This is done taking into consideration only the equations that correspond to the nodes whose solution is modified above a certain tolerance and it appears to be very efficient. The algorithm considers an increasing set of equations that updates recursively and stops when the norm of the residual has gone under a user-defined threshold.
NASA Technical Reports Server (NTRS)
Chung, T. J. (Editor); Karr, Gerald R. (Editor)
1989-01-01
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
NASA Astrophysics Data System (ADS)
Xue, Cheng; Tang, Fuk-Hay
2014-03-01
A patient specific registration model based on finite element method was investigated in this study. Image registration of Positron Emission Tomography (PET) and Magnetic Resonance imaging (MRI) has been studied a lot. Surface-based registration is extensively applied in medical imaging. We develop and evaluate a registration method combine surface-based registration with biomechanical modeling. .Four sample cases of patients with PET and MRI breast scans performed within 30 days were collected from hospital. K-means clustering algorithm was used to segment images into two parts, which is fat tissue and neoplasm [2]. Instead of placing extrinsic landmarks on patients' body which may be invasive, we proposed a new boundary condition to simulate breast deformation during two screening. Then a three dimensional model with meshes was built. Material properties were assigned to this model according to previous studies. The whole registration was based on a biomechanical finite element model, which could simulate deformation of breast under pressure.
NASA Technical Reports Server (NTRS)
Lombard, C. K.; Lombard, M. P.; Menees, G. P.; Yang, J. Y.
1980-01-01
Several aspects connected with the notion of computation with flow oriented mesh systems are presented. Simple, effective approaches to the ideas discussed are demonstrated in current applications to blown forebody shock layer flow and full bluff body shock layer flow including the massively separated wake region.
Mesh quality control for multiply-refined tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1994-01-01
A new algorithm for controlling the quality of multiply-refined tetrahedral meshes is presented in this paper. The basic dynamic mesh adaption procedure allows localized grid refinement and coarsening to efficiently capture aerodynamic flow features in computational fluid dynamics problems; however, repeated application of the procedure may significantly deteriorate the quality of the mesh. Results presented show the effectiveness of this mesh quality algorithm and its potential in the area of helicopter aerodynamics and acoustics.
Blacker, Teddy Dean; Staten, Matthew L.; Kerr, Robert A.; Owen, Steven James
2010-03-01
The generation of all-hexahedral finite element meshes has been an area of ongoing research for the past two decades and remains an open problem. Unconstrained plastering is a new method for generating all-hexahedral finite element meshes on arbitrary volumetric geometries. Starting from an unmeshed volume boundary, unconstrained plastering generates the interior mesh topology without the constraints of a pre-defined boundary mesh. Using advancing fronts, unconstrained plastering forms partially defined hexahedral dual sheets by decomposing the geometry into simple shapes, each of which can be meshed with simple meshing primitives. By breaking from the tradition of previous advancing-front algorithms, which start from pre-meshed boundary surfaces, unconstrained plastering demonstrates that for the tested geometries, high quality, boundary aligned, orientation insensitive, all-hexahedral meshes can be generated automatically without pre-meshing the boundary. Examples are given for meshes from both solid mechanics and geotechnical applications.
Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients
Kalchev, D
2012-04-02
This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the
Adaptive Local Grid Refinement in Computational Fluid Mechanics.
1987-11-01
Adaptive mesh refinements in reservoir simulation applications (R.E. Ew- ing), Proceedings Intl. Conference on Accuracy Est. and Adaptive Refine... reservoir simulation (R.E. Ewing and .J.V. 1{oebbe), Innovati’ve Numerical Mlethods in Engineering, (R.P. Shaw, J. Pc- riaux, A. Chaudouet, J. Wu...Universities, Cheyenne, Wyoming, February 21, 1986, O 9. Finite element techniques for reservoir simulation , Fourth International Sym- posium on Numerical
Robust moving mesh algorithms for hybrid stretched meshes: Application to moving boundaries problems
NASA Astrophysics Data System (ADS)
Landry, Jonathan; Soulaïmani, Azzeddine; Luke, Edward; Ben Haj Ali, Amine
2016-12-01
A robust Mesh-Mover Algorithm (MMA) approach is designed to adapt meshes of moving boundaries problems. A new methodology is developed from the best combination of well-known algorithms in order to preserve the quality of initial meshes. In most situations, MMAs distribute mesh deformation while preserving a good mesh quality. However, invalid meshes are generated when the motion is complex and/or involves multiple bodies. After studying a few MMA limitations, we propose the following approach: use the Inverse Distance Weighting (IDW) function to produce the displacement field, then apply the Geometric Element Transformation Method (GETMe) smoothing algorithms to improve the resulting mesh quality, and use an untangler to revert negative elements. The proposed approach has been proven efficient to adapt meshes for various realistic aerodynamic motions: a symmetric wing that has suffered large tip bending and twisting and the high-lift components of a swept wing that has moved to different flight stages. Finally, the fluid flow problem has been solved on meshes that have moved and they have produced results close to experimental ones. However, for situations where moving boundaries are too close to each other, more improvements need to be made or other approaches should be taken, such as an overset grid method.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
A comparison of tetrahedral mesh improvement techniques
Freitag, L.A.; Ollivier-Gooch, C.
1996-12-01
Automatic mesh generation and adaptive refinement methods for complex three-dimensional domains have proven to be very successful tools for the efficient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more difficult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face-swapping techniques that change local connectivity and optimization-based mesh smoothing methods that adjust grid point location. The authors consider several criteria for each of these two methods and compare the quality of several meshes obtained by using different combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly effective in eliminating very small and very large angles. The highest quality meshes are obtained by using a combination of swapping and smoothing techniques.
Performance of an artificial absorber for truncating FEM meshes
NASA Astrophysics Data System (ADS)
Gong, Jian; Volakis, John L.
1995-01-01
We investigate the effectiveness of an artificial absorber for truncating finite element (FE) meshes. Specifically, we present the implementation of a novel mesh truncation approach using a perfectly matched anisotropic absorber for waveguides and stripline circuits. This truncation scheme is useful in many applications, including antennas, scattering, and microwave circuits.
Automated hexahedral meshing of anatomic structures using deformable registration.
Grosland, Nicole M; Bafna, Ritesh; Magnotta, Vincent A
2009-02-01
This work introduces a novel method of automating the process of patient-specific finite element (FE) model development using a mapped mesh technique. The objective is to map a predefined mesh (template) of high quality directly onto a new bony surface (target) definition, thereby yielding a similar mesh with minimal user interaction. To bring the template mesh into correspondence with the target surface, a deformable registration technique based on the FE method has been adopted. The procedure has been made hierarchical allowing several levels of mesh refinement to be used, thus reducing the time required to achieve a solution. Our initial efforts have focused on the phalanx bones of the human hand. Mesh quality metrics, such as element volume and distortion were evaluated. Furthermore, the distance between the target surface and the final mapped mesh were measured. The results have satisfactorily proven the applicability of the proposed method.
3D-Meshes aus medizinischen Volumendaten
NASA Astrophysics Data System (ADS)
Zelzer, Sascha; Meinzer, Hans-Peter
Diese Arbeit beschreibt eine template-basierte Methode zur Erzeugung von adaptiven Hexaeder-Meshes aus Volumendaten, welche komplizierte konkave Strukturen aufweisen können. Es wird ein vollständiger Satz von Templates generiert der es erlaubt, die Ränder konkaver Regionen feiner zu zerlegen als angrenzende Bereiche und somit die Gesamtzahl an Hexaeder verringert. Der Algorithmus arbeitet mit beliebigen gelabelten Volumendaten und erzeugt ein adaptives, konformes, reines Hexaeder-Mesh.
Kupczik, Kornelius; Lev-Tov Chattah, Netta
2014-01-01
In several primate groups enamel is reduced or absent from the lingual (tongue) side of the mandibular incisor crowns akin to other placental and marsupial mammalian groups such as rodents, lagomorphs and wombats. Here we investigate the presumed adaptation of crowns with unilateral enamel to the incision of tough foods in cercopithecines, an Old World monkey subfamily, using a simulation approach. We developed and validated a finite element model of the lower central incisor of the rhesus macaque (Macaca mulatta) with labial enamel only to compute three-dimensional displacements and maximum principal stresses on the crown subjected to compressive loads varying in orientation. Moreover, we developed a model of a macaque incisor with enamel present on both labial and lingual aspects, thus resembling the ancestral condition found in the sister taxon, the leaf-eating colobines. The results showed that, concomitant with experimental results, the cercopithecine crown with unilateral enamel bends predominantly towards the inside of the mouth, while displacements decreased when both labial and lingual enamel are present. Importantly, the cercopithecine incisor crown experienced lower maximum principal stress on the lingual side compared to the incisor with enamel on the lingual and labial aspects under non-axial loads directed either towards the inside or outside of the mouth. These findings suggest that cercopithecine mandibular incisors are adapted to a wide range of ingestive behaviours compared to colobines. We conclude that the evolutionary loss of lingual enamel in cercopithecines has conferred a safeguard against crown failure under a loading regime assumed for the ingestion (peeling, scraping) of tough-skinned fruits. PMID:24831704
Kupczik, Kornelius; Lev-Tov Chattah, Netta
2014-01-01
In several primate groups enamel is reduced or absent from the lingual (tongue) side of the mandibular incisor crowns akin to other placental and marsupial mammalian groups such as rodents, lagomorphs and wombats. Here we investigate the presumed adaptation of crowns with unilateral enamel to the incision of tough foods in cercopithecines, an Old World monkey subfamily, using a simulation approach. We developed and validated a finite element model of the lower central incisor of the rhesus macaque (Macaca mulatta) with labial enamel only to compute three-dimensional displacements and maximum principal stresses on the crown subjected to compressive loads varying in orientation. Moreover, we developed a model of a macaque incisor with enamel present on both labial and lingual aspects, thus resembling the ancestral condition found in the sister taxon, the leaf-eating colobines. The results showed that, concomitant with experimental results, the cercopithecine crown with unilateral enamel bends predominantly towards the inside of the mouth, while displacements decreased when both labial and lingual enamel are present. Importantly, the cercopithecine incisor crown experienced lower maximum principal stress on the lingual side compared to the incisor with enamel on the lingual and labial aspects under non-axial loads directed either towards the inside or outside of the mouth. These findings suggest that cercopithecine mandibular incisors are adapted to a wide range of ingestive behaviours compared to colobines. We conclude that the evolutionary loss of lingual enamel in cercopithecines has conferred a safeguard against crown failure under a loading regime assumed for the ingestion (peeling, scraping) of tough-skinned fruits.
GeoClawSed: A Model with Finite Volume and Adaptive Refinement Method for Tsunami Sediment Transport
NASA Astrophysics Data System (ADS)
Tang, H.; Weiss, R.
2015-12-01
The shallow-water and advection-diffusion equations are commonly used for tsunami sediment-transport modeling. GeoClawSed is based on GeoClaw and adds a bed updating and avalanching scheme to the two-dimensional coupled system combining the shallow- water and advection-diffusion equations, which is a set of hyperbolic integral conservation laws. The modeling system consists of three coupled model components: (1) the shallow-water equations for hydrodynamics; (2) advection-diffusion equation for sediment transport; and (3) an equation for morphodynamics. For the hydrodynamic part, the finite-volume wave propagation methods (high resolution Godunov-type methods) are applied to the shallow-water equations. The well-known Riemann solver in GeoClaw is capable of dealing with diverse flow regimes present during tsunami flows. For the sediment-transport part, the advection-diffusion equation is employed to calculate the distribution of sediment in the water column. In the fully-coupled version, the advection-diffusion equation is also included in the Riemann solver. The Van Leer method is applied for calculating sediment flux in each direction. The bed updating and avalanching scheme (morphodynamics) is used for updating topography during tsunami wave propagation. Adaptive refinement method is extended to hydrodynamic part, sediment transport model and topography. GeoClawSed can evolve different resolution and accurately capture discontinuities in both flow dynamic and sediment transport. Together, GeoClawSed is designed for modeling tsunami propagation, inundation, sediment transport as well as topography change. Finally, GeoClawSed is applied for studying marine and terrestrial deposit distribution after tsunami wave. Keywords: Tsunami; Sediment Transport; Shallow Water Equations; Advection-Diffusion Equation; Adaptive Refinement Method
Piras, P; Sansalone, G; Teresi, L; Kotsakis, T; Colangelo, P; Loy, A
2012-07-01
The shape and mechanical performance in Talpidae humeri were studied by means of Geometric Morphometrics and Finite Element Analysis, including both extinct and extant taxa. The aim of this study was to test whether the ability to dig, quantified by humerus mechanical performance, was characterized by convergent or parallel adaptations in different clades of complex tunnel digger within Talpidae, that is, Talpinae+Condylura (monophyletic) and some complex tunnel diggers not belonging to this clade. Our results suggest that the pattern underlying Talpidae humerus evolution is evolutionary parallelism. However, this insight changed to true convergence when we tested an alternative phylogeny based on molecular data, with Condylura moved to a more basal phylogenetic position. Shape and performance analyses, as well as specific comparative methods, provided strong evidence that the ability to dig complex tunnels reached a functional optimum in distantly related taxa. This was also confirmed by the lower phenotypic variance in complex tunnel digger taxa, compared to non-complex tunnel diggers. Evolutionary rates of phenotypic change showed a smooth deceleration in correspondence with the most recent common ancestor of the Talpinae+Condylura clade.
Unstructured Mesh Methods for the Simulation of Hypersonic Flows
NASA Technical Reports Server (NTRS)
Peraire, Jaime; Bibb, K. L. (Technical Monitor)
2001-01-01
This report describes the research work undertaken at the Massachusetts Institute of Technology. The aim of this research is to identify effective algorithms and methodologies for the efficient and routine solution of hypersonic viscous flows about re-entry vehicles. For over ten years we have received support from NASA to develop unstructured mesh methods for Computational Fluid Dynamics. As a result of this effort a methodology based on the use, of unstructured adapted meshes of tetrahedra and finite volume flow solvers has been developed. A number of gridding algorithms flow solvers, and adaptive strategies have been proposed. The most successful algorithms developed from the basis of the unstructured mesh system FELISA. The FELISA system has been extensively for the analysis of transonic and hypersonic flows about complete vehicle configurations. The system is highly automatic and allows for the routine aerodynamic analysis of complex configurations starting from CAD data. The code has been parallelized and utilizes efficient solution algorithms. For hypersonic flows, a version of the, code which incorporates real gas effects, has been produced. One of the latest developments before the start of this grant was to extend the system to include viscous effects. This required the development of viscous generators, capable of generating the anisotropic grids required to represent boundary layers, and viscous flow solvers. In figures I and 2, we show some sample hypersonic viscous computations using the developed viscous generators and solvers. Although these initial results were encouraging, it became apparent that in order to develop a fully functional capability for viscous flows, several advances in gridding, solution accuracy, robustness and efficiency were required. As part of this research we have developed: 1) automatic meshing techniques and the corresponding computer codes have been delivered to NASA and implemented into the GridEx system, 2) a finite
Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement
Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; ...
2013-12-10
A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examplesmore » highlighting the mesh adaptivity of this method are also provided.« less
Interpolation methods and the accuracy of lattice-Boltzmann mesh refinement
Guzik, Stephen M.; Weisgraber, Todd H.; Colella, Phillip; Alder, Berni J.
2013-12-10
A lattice-Boltzmann model to solve the equivalent of the Navier-Stokes equations on adap- tively refined grids is presented. A method for transferring information across interfaces between different grid resolutions was developed following established techniques for finite- volume representations. This new approach relies on a space-time interpolation and solving constrained least-squares problems to ensure conservation. The effectiveness of this method at maintaining the second order accuracy of lattice-Boltzmann is demonstrated through a series of benchmark simulations and detailed mesh refinement studies. These results exhibit smaller solution errors and improved convergence when compared with similar approaches relying only on spatial interpolation. Examples highlighting the mesh adaptivity of this method are also provided.
An ADER-WENO Finite Volume AMR code for Astrophysics
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.; Hidalgo, A.; Balsara, D.
2014-09-01
A high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions is presented. A high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method, while a high order spatial accuracy is obtained through a WENO reconstruction. Thanks to the one-step nature of the underlying scheme, the resulting algorithm can be efficiently imported within an AMR framework on space-time adaptive meshes. We provide convincing evidence that the presented high order AMR scheme behaves better than traditional second order AMR methods. Tests are shown of the new scheme for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations and the equations of ideal magnetohydrodynamics. The proposed scheme is likely to become a useful tool in several astrophysical scenarios.
An assessment of the adaptive unstructured tetrahedral grid, Euler Flow Solver Code FELISA
NASA Technical Reports Server (NTRS)
Djomehri, M. Jahed; Erickson, Larry L.
1994-01-01
A three-dimensional solution-adaptive Euler flow solver for unstructured tetrahedral meshes is assessed, and the accuracy and efficiency of the method for predicting sonic boom pressure signatures about simple generic models are demonstrated. Comparison of computational and wind tunnel data and enhancement of numerical solutions by means of grid adaptivity are discussed. The mesh generation is based on the advancing front technique. The FELISA code consists of two solvers, the Taylor-Galerkin and the Runge-Kutta-Galerkin schemes, both of which are spacially discretized by the usual Galerkin weighted residual finite-element methods but with different explicit time-marching schemes to steady state. The solution-adaptive grid procedure is based on either remeshing or mesh refinement techniques. An alternative geometry adaptive procedure is also incorporated.
A Finite Element Method for Simulation of Compressible Cavitating Flows
NASA Astrophysics Data System (ADS)
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.