Structured adaptive grid generation using algebraic methods
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, Bharat K.; Roger, R. P.; Chan, Stephen C.
1993-01-01
The accuracy of the numerical algorithm depends not only on the formal order of approximation but also on the distribution of grid points in the computational domain. Grid adaptation is a procedure which allows optimal grid redistribution as the solution progresses. It offers the prospect of accurate flow field simulations without the use of an excessively timely, computationally expensive, grid. Grid adaptive schemes are divided into two basic categories: differential and algebraic. The differential method is based on a variational approach where a function which contains a measure of grid smoothness, orthogonality and volume variation is minimized by using a variational principle. This approach provided a solid mathematical basis for the adaptive method, but the Euler-Lagrange equations must be solved in addition to the original governing equations. On the other hand, the algebraic method requires much less computational effort, but the grid may not be smooth. The algebraic techniques are based on devising an algorithm where the grid movement is governed by estimates of the local error in the numerical solution. This is achieved by requiring the points in the large error regions to attract other points and points in the low error region to repel other points. The development of a fast, efficient, and robust algebraic adaptive algorithm for structured flow simulation applications is presented. This development is accomplished in a three step process. The first step is to define an adaptive weighting mesh (distribution mesh) on the basis of the equidistribution law applied to the flow field solution. The second, and probably the most crucial step, is to redistribute grid points in the computational domain according to the aforementioned weighting mesh. The third and the last step is to reevaluate the flow property by an appropriate search/interpolate scheme at the new grid locations. The adaptive weighting mesh provides the information on the desired concentration
An Adaptive Unstructured Grid Method by Grid Subdivision, Local Remeshing, and Grid Movement
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
1999-01-01
An unstructured grid adaptation technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The approach is based on a combination of grid subdivision, local remeshing, and grid movement. For solution adaptive grids, the surface triangulation is locally refined by grid subdivision, and the tetrahedral grid in the field is partially remeshed at locations of dominant flow features. A grid redistribution strategy is employed for geometric adaptation of volume grids to moving or deforming surfaces. The method is automatic and fast and is designed for modular coupling with different solvers. Several steady state test cases with different inviscid flow features were tested for grid/solution adaptation. In all cases, the dominant flow features, such as shocks and vortices, were accurately and efficiently predicted with the present approach. A new and robust method of moving tetrahedral "viscous" grids is also presented and demonstrated on a three-dimensional example.
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.
Comparing Anisotropic Output-Based Grid Adaptation Methods by Decomposition
NASA Technical Reports Server (NTRS)
Park, Michael A.; Loseille, Adrien; Krakos, Joshua A.; Michal, Todd
2015-01-01
Anisotropic grid adaptation is examined by decomposing the steps of flow solution, ad- joint solution, error estimation, metric construction, and simplex grid adaptation. Multiple implementations of each of these steps are evaluated by comparison to each other and expected analytic results when available. For example, grids are adapted to analytic metric fields and grid measures are computed to illustrate the properties of multiple independent implementations of grid adaptation mechanics. Different implementations of each step in the adaptation process can be evaluated in a system where the other components of the adaptive cycle are fixed. Detailed examination of these properties allows comparison of different methods to identify the current state of the art and where further development should be targeted.
Variational method for adaptive grid generation
Brackbill, J.U.
1983-01-01
A variational method for generating adaptive meshes is described. Functionals measuring smoothness, skewness, orientation, and the Jacobian are minimized to generate a mapping from a rectilinear domain in natural coordinate to an arbitrary domain in physical coordinates. From the mapping, a mesh is easily constructed. In using the method to adaptively zone computational problems, as few as one third the number of mesh points are required in each coordinate direction compared with a uniformly zoned mesh.
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.
An adaptive grid method for computing time accurate solutions on structured grids
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Smith, Robert E.; Eiseman, Peter R.
1991-01-01
The solution method consists of three parts: a grid movement scheme; an unsteady Euler equation solver; and a temporal coupling routine that links the dynamic grid to the Euler solver. The grid movement scheme is an algebraic method containing grid controls that generate a smooth grid that resolves the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling is performed with a grid prediction correction procedure that is simple to implement and provides a grid that does not lag the solution in time. The adaptive solution method is tested by computing the unsteady inviscid solutions for a one dimensional shock tube and a two dimensional shock vortex iteraction.
Stability and error estimation for Component Adaptive Grid methods
NASA Technical Reports Server (NTRS)
Oliger, Joseph; Zhu, Xiaolei
1994-01-01
Component adaptive grid (CAG) methods for solving hyperbolic partial differential equations (PDE's) are discussed in this paper. Applying recent stability results for a class of numerical methods on uniform grids. The convergence of these methods for linear problems on component adaptive grids is established here. Furthermore, the computational error can be estimated on CAG's using the stability results. Using these estimates, the error can be controlled on CAG's. Thus, the solution can be computed efficiently on CAG's within a given error tolerance. Computational results for time dependent linear problems in one and two space dimensions are presented.
Efficient Unstructured Grid Adaptation Methods for Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Campbell, Richard L.; Carter, Melissa B.; Deere, Karen A.; Waithe, Kenrick A.
2008-01-01
This paper examines the use of two grid adaptation methods to improve the accuracy of the near-to-mid field pressure signature prediction of supersonic aircraft computed using the USM3D unstructured grid flow solver. The first method (ADV) is an interactive adaptation process that uses grid movement rather than enrichment to more accurately resolve the expansion and compression waves. The second method (SSGRID) uses an a priori adaptation approach to stretch and shear the original unstructured grid to align the grid with the pressure waves and reduce the cell count required to achieve an accurate signature prediction at a given distance from the vehicle. Both methods initially create negative volume cells that are repaired in a module in the ADV code. While both approaches provide significant improvements in the near field signature (< 3 body lengths) relative to a baseline grid without increasing the number of grid points, only the SSGRID approach allows the details of the signature to be accurately computed at mid-field distances (3-10 body lengths) for direct use with mid-field-to-ground boom propagation codes.
ICASE/LaRC Workshop on Adaptive Grid Methods
NASA Technical Reports Server (NTRS)
South, Jerry C., Jr. (Editor); Thomas, James L. (Editor); Vanrosendale, John (Editor)
1995-01-01
Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field.
Vortical Flow Prediction Using an Adaptive Unstructured Grid Method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2003-01-01
A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving practical vortical flow problems. The first test case concerns vortex flow over a simple 65 delta wing with different values of leading-edge radius. Although the geometry is quite simple, it poses a challenging problem for computing vortices originating from blunt leading edges. The second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the wind-tunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.
Vortical Flow Prediction Using an Adaptive Unstructured Grid Method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2001-01-01
A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving practical vortical flow problems. The first test case concerns vortex flow over a simple 65deg delta wing with different values of leading-edge bluntness, and the second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the windtunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.
On Accuracy of Adaptive Grid Methods for Captured Shocks
NASA Technical Reports Server (NTRS)
Yamaleev, Nail K.; Carpenter, Mark H.
2002-01-01
The accuracy of two grid adaptation strategies, grid redistribution and local grid refinement, is examined by solving the 2-D Euler equations for the supersonic steady flow around a cylinder. Second- and fourth-order linear finite difference shock-capturing schemes, based on the Lax-Friedrichs flux splitting, are used to discretize the governing equations. The grid refinement study shows that for the second-order scheme, neither grid adaptation strategy improves the numerical solution accuracy compared to that calculated on a uniform grid with the same number of grid points. For the fourth-order scheme, the dominant first-order error component is reduced by the grid adaptation, while the design-order error component drastically increases because of the grid nonuniformity. As a result, both grid adaptation techniques improve the numerical solution accuracy only on the coarsest mesh or on very fine grids that are seldom found in practical applications because of the computational cost involved. Similar error behavior has been obtained for the pressure integral across the shock. A simple analysis shows that both grid adaptation strategies are not without penalties in the numerical solution accuracy. Based on these results, a new grid adaptation criterion for captured shocks is proposed.
Parallel architectures for iterative methods on adaptive, block structured grids
NASA Technical Reports Server (NTRS)
Gannon, D.; Vanrosendale, J.
1983-01-01
A parallel computer architecture well suited to the solution of partial differential equations in complicated geometries is proposed. Algorithms for partial differential equations contain a great deal of parallelism. But this parallelism can be difficult to exploit, particularly on complex problems. One approach to extraction of this parallelism is the use of special purpose architectures tuned to a given problem class. The architecture proposed here is tuned to boundary value problems on complex domains. An adaptive elliptic algorithm which maps effectively onto the proposed architecture is considered in detail. Two levels of parallelism are exploited by the proposed architecture. First, by making use of the freedom one has in grid generation, one can construct grids which are locally regular, permitting a one to one mapping of grids to systolic style processor arrays, at least over small regions. All local parallelism can be extracted by this approach. Second, though there may be a regular global structure to the grids constructed, there will be parallelism at this level. One approach to finding and exploiting this parallelism is to use an architecture having a number of processor clusters connected by a switching network. The use of such a network creates a highly flexible architecture which automatically configures to the problem being solved.
A wavelet-optimized, very high order adaptive grid and order numerical method
NASA Technical Reports Server (NTRS)
Jameson, Leland
1996-01-01
Differencing operators of arbitrarily high order can be constructed by interpolating a polynomial through a set of data followed by differentiation of this polynomial and finally evaluation of the polynomial at the point where a derivative approximation is desired. Furthermore, the interpolating polynomial can be constructed from algebraic, trigonometric, or, perhaps exponential polynomials. This paper begins with a comparison of such differencing operator construction. Next, the issue of proper grids for high order polynomials is addressed. Finally, an adaptive numerical method is introduced which adapts the numerical grid and the order of the differencing operator depending on the data. The numerical grid adaptation is performed on a Chebyshev grid. That is, at each level of refinement the grid is a Chebvshev grid and this grid is refined locally based on wavelet analysis.
A time-accurate adaptive grid method and the numerical simulation of a shock-vortex interaction
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Eiseman, Peter R.
1990-01-01
A time accurate, general purpose, adaptive grid method is developed that is suitable for multidimensional steady and unsteady numerical simulations. The grid point movement is performed in a manner that generates smooth grids which resolve the severe solution gradients and the sharp transitions in the solution gradients. The temporal coupling of the adaptive grid and the PDE solver is performed with a grid prediction correction method that is simple to implement and ensures the time accuracy of the grid. Time accurate solutions of the 2-D Euler equations for an unsteady shock vortex interaction demonstrate the ability of the adaptive method to accurately adapt the grid to multiple solution features.
An adaptive grid method for computing the high speed 3D viscous flow about a re-entry vehicle
NASA Technical Reports Server (NTRS)
Bockelie, Michael J.; Smith, Robert E.
1992-01-01
An algebraic solution adaptive grid generation method that allows adapting the grid in all three coordinate directions is presented. Techniques are described that maintain the integrity of the original vehicle definition for grid point movement on the vehicle surface and that avoid grid cross over in the boundary layer portion of the grid lying next to the vehicle surface. The adaptive method is tested by computing the Mach 6 hypersonic three dimensional viscous flow about a proposed Martian entry vehicle.
A self-adaptive-grid method with application to airfoil flow
NASA Technical Reports Server (NTRS)
Nakahashi, K.; Deiwert, G. S.
1985-01-01
A self-adaptive-grid method is described that is suitable for multidimensional steady and unsteady computations. Based on variational principles, a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error. User-specified parameters, denoting both maximum and minimum permissible grid spacings, are used to define the all-important constants, thereby minimizing the empiricism and making the method self-adaptive. Operator splitting and one-sided controls for orthogonality and smoothness are used to make the method practical, robust, and efficient. Examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions, as well as for a steady inviscid flow computation and a one-dimensional case. These examples illustrate the precise control the user has with the self-adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions.
Grid coupling mechanism in the semi-implicit adaptive Multi-Level Multi-Domain method
NASA Astrophysics Data System (ADS)
Innocenti, M. E.; Tronci, C.; Markidis, S.; Lapenta, G.
2016-05-01
The Multi-Level Multi-Domain (MLMD) method is a semi-implicit adaptive method for Particle-In-Cell plasma simulations. It has been demonstrated in the past in simulations of Maxwellian plasmas, electrostatic and electromagnetic instabilities, plasma expansion in vacuum, magnetic reconnection [1, 2, 3]. In multiple occasions, it has been commented on the coupling between the coarse and the refined grid solutions. The coupling mechanism itself, however, has never been explored in depth. Here, we investigate the theoretical bases of grid coupling in the MLMD system. We obtain an evolution law for the electric field solution in the overlap area of the MLMD system which highlights a dependance on the densities and currents from both the coarse and the refined grid, rather than from the coarse grid alone: grid coupling is obtained via densities and currents.
A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection
Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.; Burkardt, John V.
2015-06-24
This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
The use of the spectral method within the fast adaptive composite grid method
McKay, S.M.
1994-12-31
The use of efficient algorithms for the solution of partial differential equations has been sought for many years. The fast adaptive composite grid (FAC) method combines an efficient algorithm with high accuracy to obtain low cost solutions to partial differential equations. The FAC method achieves fast solution by combining solutions on different grids with varying discretizations and using multigrid like techniques to find fast solution. Recently, the continuous FAC (CFAC) method has been developed which utilizes an analytic solution within a subdomain to iterate to a solution of the problem. This has been shown to achieve excellent results when the analytic solution can be found. The CFAC method will be extended to allow solvers which construct a function for the solution, e.g., spectral and finite element methods. In this discussion, the spectral methods will be used to provide a fast, accurate solution to the partial differential equation. As spectral methods are more accurate than finite difference methods, the ensuing accuracy from this hybrid method outside of the subdomain will be investigated.
Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme
NASA Astrophysics Data System (ADS)
Yabe, Takashi; Mizoe, Hiroki; Takizawa, Kenji; Moriki, Hiroshi; Im, Hyo-Nam; Ogata, Youichi
2004-02-01
A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.
NASA Astrophysics Data System (ADS)
Sheng, Qin; Sun, Hai-wei
2016-11-01
This study concerns the asymptotic stability of an eikonal, or ray, transformation based Peaceman-Rachford splitting method for solving the paraxial Helmholtz equation with high wave numbers. Arbitrary nonuniform grids are considered in transverse and beam propagation directions. The differential equation targeted has been used for modeling propagations of high intensity laser pulses over a long distance without diffractions. Self-focusing of high intensity beams may be balanced with the de-focusing effect of created ionized plasma channel in the situation, and applications of grid adaptations are frequently essential. It is shown rigorously that the fully discretized oscillation-free decomposition method on arbitrary adaptive grids is asymptotically stable with a stability index one. Simulation experiments are carried out to illustrate our concern and conclusions.
NASA Astrophysics Data System (ADS)
Commerçon, B.; Debout, V.; Teyssier, R.
2014-03-01
Context. Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. Aims: We present a new method for implicit adaptive time-stepping on adaptive mesh-refinement grids. We implement it in the radiation-hydrodynamics solver we designed for the RAMSES code for astrophysical purposes and, more particularly, for protostellar collapse. Methods: We briefly recall the radiation-hydrodynamics equations and the adaptive time-stepping methodology used for hydrodynamical solvers. We then introduce the different types of boundary conditions (Dirichlet, Neumann, and Robin) that are used at the interface between levels and present our implementation of the new method in the RAMSES code. The method is tested against classical diffusion and radiation-hydrodynamics tests, after which we present an application for protostellar collapse. Results: We show that using Dirichlet boundary conditions at level interfaces is a good compromise between robustness and accuracy and that it can be used in structure formation calculations. The gain in computational time over our former unique time step method ranges from factors of 5 to 50 depending on the level of adaptive time-stepping and on the problem. We successfully compare the old and new methods for protostellar collapse calculations that involve highly non linear physics. Conclusions: We have developed a simple but robust method for adaptive time-stepping of implicit scheme on adaptive mesh-refinement grids. It can be applied to a wide variety of physical problems that involve diffusion processes.
Adaptive integral method with fast Gaussian gridding for solving combined field integral equations
NASA Astrophysics Data System (ADS)
Bakır, O.; Baǧ; Cı, H.; Michielssen, E.
Fast Gaussian gridding (FGG), a recently proposed nonuniform fast Fourier transform algorithm, is used to reduce the memory requirements of the adaptive integral method (AIM) for accelerating the method of moments-based solution of combined field integral equations pertinent to the analysis of scattering from three-dimensional perfect electrically conducting surfaces. Numerical results that demonstrate the efficiency and accuracy of the AIM-FGG hybrid in comparison to an AIM-accelerated solver, which uses moment matching to project surface sources onto an auxiliary grid, are presented.
Vortical Flow Prediction using an Adaptive Unstructured Grid Method. Chapter 11
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2009-01-01
A computational fluid dynamics (CFD) method has been employed to compute vortical flows around slender wing/body configurations. The emphasis of the paper is on the effectiveness of an adaptive grid procedure in "capturing" concentrated vortices generated at sharp edges or flow separation lines of lifting surfaces flying at high angles of attack. The method is based on a tetrahedral unstructured grid technology developed at the NASA Langley Research Center. Two steady-state, subsonic, inviscid and Navier-Stokes flow test cases are presented to demonstrate the applicability of the method for solving vortical flow problems. The first test case concerns vortex flow over a simple 65 delta wing with different values of leading-edge radius. Although the geometry is quite simple, it poses a challenging problem for computing vortices originating from blunt leading edges. The second case is that of a more complex fighter configuration. The superiority of the adapted solutions in capturing the vortex flow structure over the conventional unadapted results is demonstrated by comparisons with the wind-tunnel experimental data. The study shows that numerical prediction of vortical flows is highly sensitive to the local grid resolution and that the implementation of grid adaptation is essential when applying CFD methods to such complicated flow problems.
A three-dimensional adaptive grid method. [for computational fluid dynamics
NASA Technical Reports Server (NTRS)
Nakahashi, K.; Deiwert, G. S.
1985-01-01
A three-dimensional solution-adaptive-grid scheme is described which is suitable for complex fluid flows. This method, using tension and torsion spring analogies, was previously developed and successfully applied for two-dimensional flows. In the present work, a collection of three-dimensional flow fields are used to demonstrate the feasibility and versatility of this concept to include an added dimension. Flow fields considered include: (1) supersonic flow past an aerodynamic afterbody with a propulsive jet at incidence to the free stream, (2) supersonic flow past a blunt fin mounted on a solid wall, and (3) supersonic flow over a bump. In addition to generating three-dimensional solution-adapted grids, the method can also be used effectively as an initial grid generator. The utility of the method lies in: (1) optimum distribution of discrete grid points, (2) improvement of accuracy, (3) improved computational efficiency, (4) minimization of data base sizes, and (5) simplified three-dimensional grid generation.
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.
LAPS Grid generation and adaptation
NASA Astrophysics Data System (ADS)
Pagliantini, Cecilia; Delzanno, Gia Luca; Guo, Zehua; Srinivasan, Bhuvana; Tang, Xianzhu; Chacon, Luis
2011-10-01
LAPS uses a common-data framework in which a general purpose grid generation and adaptation package in toroidal and simply connected domains is implemented. The initial focus is on implementing the Winslow/Laplace-Beltrami method for generating non-overlapping block structured grids. This is to be followed by a grid adaptation scheme based on Monge-Kantorovich optimal transport method [Delzanno et al., J. Comput. Phys,227 (2008), 9841-9864], that equidistributes application-specified error. As an initial set of applications, we will lay out grids for an axisymmetric mirror, a field reversed configuration, and an entire poloidal cross section of a tokamak plasma reconstructed from a CMOD experimental shot. These grids will then be used for computing the plasma equilibrium and transport in accompanying presentations. A key issue for Monge-Kantorovich grid optimization is the choice of error or monitor function for equi-distribution. We will compare the Operator Recovery Error Source Detector (ORESD) [Lapenta, Int. J. Num. Meth. Eng,59 (2004) 2065-2087], the Tau method and a strategy based on the grid coarsening [Zhang et al., AIAA J,39 (2001) 1706-1715] to find an ``optimal'' grid. Work supported by DOE OFES.
A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection
Zhang, Guannan; Webster, Clayton G; Gunzburger, Max D; Burkardt, John V
2014-03-01
This work proposes and analyzes a hyper-spherical adaptive hi- erarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the the- oretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a func- tion representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smooth- ness of the hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity anal- yses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.
A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection
Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.; Burkardt, John V.
2015-06-24
This study proposes and analyzes a hyperspherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hypersurface of an N-dimensional discontinuous quantity of interest, by virtue of a hyperspherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyperspherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of the hypersurface, the newmore » technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. In addition, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less
Parallel level-set methods on adaptive tree-based grids
NASA Astrophysics Data System (ADS)
Mirzadeh, Mohammad; Guittet, Arthur; Burstedde, Carsten; Gibou, Frederic
2016-10-01
We present scalable algorithms for the level-set method on dynamic, adaptive Quadtree and Octree Cartesian grids. The algorithms are fully parallelized and implemented using the MPI standard and the open-source p4est library. We solve the level set equation with a semi-Lagrangian method which, similar to its serial implementation, is free of any time-step restrictions. This is achieved by introducing a scalable global interpolation scheme on adaptive tree-based grids. Moreover, we present a simple parallel reinitialization scheme using the pseudo-time transient formulation. Both parallel algorithms scale on the Stampede supercomputer, where we are currently using up to 4096 CPU cores, the limit of our current account. Finally, a relevant application of the algorithms is presented in modeling a crystallization phenomenon by solving a Stefan problem, illustrating a level of detail that would be impossible to achieve without a parallel adaptive strategy. We believe that the algorithms presented in this article will be of interest and useful to researchers working with the level-set framework and modeling multi-scale physics in general.
NASA Astrophysics Data System (ADS)
Niccolini, G.; Alcolea, J.
Solving the radiative transfer problem is a common problematic to may fields in astrophysics. With the increasing angular resolution of spatial or ground-based telescopes (VLTI, HST) but also with the next decade instruments (NGST, ALMA, ...), astrophysical objects reveal and will certainly reveal complex spatial structures. Consequently, it is necessary to develop numerical tools being able to solve the radiative transfer equation in three dimensions in order to model and interpret these observations. I present a 3D radiative transfer program, using a new method for the construction of an adaptive spatial grid, based on the Monte Claro method. With the help of this tools, one can solve the continuum radiative transfer problem (e.g. a dusty medium), computes the temperature structure of the considered medium and obtain the flux of the object (SED and images).
Practical improvements of multi-grid iteration for adaptive mesh refinement method
NASA Astrophysics Data System (ADS)
Miyashita, Hisashi; Yamada, Yoshiyuki
2005-03-01
Adaptive mesh refinement(AMR) is a powerful tool to efficiently solve multi-scaled problems. However, the vanilla AMR method has a well-known critical demerit, i.e., it cannot be applied to non-local problems. Although multi-grid iteration (MGI) can be regarded as a good remedy for a non-local problem such as the Poisson equation, we observed fundamental difficulties in applying the MGI technique in AMR to realistic problems under complicated mesh layouts because it does not converge or it requires too many iterations even if it does converge. To cope with the problem, when updating the next approximation in the MGI process, we calculate the precise total corrections that are relatively accurate to the current residual by introducing a new iteration for such a total correction. This procedure greatly accelerates the MGI convergence speed especially under complicated mesh layouts.
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.
The fundamentals of adaptive grid movement
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.
1990-01-01
Basic grid point movement schemes are studied. The schemes are referred to as adaptive grids. Weight functions and equidistribution in one dimension are treated. The specification of coefficients in the linear weight, attraction to a given grid or a curve, and evolutionary forces are considered. Curve by curve and finite volume methods are described. The temporal coupling of partial differential equations solvers and grid generators was discussed.
An adaptive grid with directional control
NASA Technical Reports Server (NTRS)
Brackbill, J. U.
1993-01-01
An adaptive grid generator for adaptive node movement is here derived by combining a variational formulation of Winslow's (1981) variable-diffusion method with a directional control functional. By applying harmonic-function theory, it becomes possible to define conditions under which there exist unique solutions of the resulting elliptic equations. The results obtained for the grid generator's application to the complex problem posed by the fluid instability-driven magnetic field reconnection demonstrate one-tenth the computational cost of either a Eulerian grid or an adaptive grid without directional control.
Algebraic grid adaptation method using non-uniform rational B-spline surface modeling
NASA Technical Reports Server (NTRS)
Yang, Jiann-Cherng; Soni, B. K.
1992-01-01
An algebraic adaptive grid system based on equidistribution law and utilized by the Non-Uniform Rational B-Spline (NURBS) surface for redistribution is presented. A weight function, utilizing a properly weighted boolean sum of various flow field characteristics is developed. Computational examples are presented to demonstrate the success of this technique.
NASA Technical Reports Server (NTRS)
Banks, D. W.; Hafez, M. M.
1996-01-01
Grid adaptation for structured meshes is the art of using information from an existing, but poorly resolved, solution to automatically redistribute the grid points in such a way as to improve the resolution in regions of high error, and thus the quality of the solution. This involves: (1) generate a grid vis some standard algorithm, (2) calculate a solution on this grid, (3) adapt the grid to this solution, (4) recalculate the solution on this adapted grid, and (5) repeat steps 3 and 4 to satisfaction. Steps 3 and 4 can be repeated until some 'optimal' grid is converged to but typically this is not worth the effort and just two or three repeat calculations are necessary. They also may be repeated every 5-10 time steps for unsteady calculations.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.
2000-01-01
Preliminary verification and validation of an efficient Euler solver for adaptively refined Cartesian meshes with embedded boundaries is presented. The parallel, multilevel method makes use of a new on-the-fly parallel domain decomposition strategy based upon the use of space-filling curves, and automatically generates a sequence of coarse meshes for processing by the multigrid smoother. The coarse mesh generation algorithm produces grids which completely cover the computational domain at every level in the mesh hierarchy. A series of examples on realistically complex three-dimensional configurations demonstrate that this new coarsening algorithm reliably achieves mesh coarsening ratios in excess of 7 on adaptively refined meshes. Numerical investigations of the scheme's local truncation error demonstrate an achieved order of accuracy between 1.82 and 1.88. Convergence results for the multigrid scheme are presented for both subsonic and transonic test cases and demonstrate W-cycle multigrid convergence rates between 0.84 and 0.94. Preliminary parallel scalability tests on both simple wing and complex complete aircraft geometries shows a computational speedup of 52 on 64 processors using the run-time mesh partitioner.
NASA Technical Reports Server (NTRS)
Aftosmis, M. J.; Berger, M. J.; Adomavicius, G.; Nixon, David (Technical Monitor)
1998-01-01
The work presents a new method for on-the-fly domain decomposition technique for mapping grids and solution algorithms to parallel machines, and is applicable to both shared-memory and message-passing architectures. It will be demonstrated on the Cray T3E, HP Exemplar, and SGI Origin 2000. Computing time has been secured on all these platforms. The decomposition technique is an outgrowth of techniques used in computational physics for simulations of N-body problems and the event horizons of black holes, and has not been previously used by the CFD community. Since the technique offers on-the-fly partitioning, it offers a substantial increase in flexibility for computing in heterogeneous environments, where the number of available processors may not be known at the time of job submission. In addition, since it is dynamic it permits the job to be repartitioned without global communication in cases where additional processors become available after the simulation has begun, or in cases where dynamic mesh adaptation changes the mesh size during the course of a simulation. The platform for this partitioning strategy is a completely new Cartesian Euler solver tarcreted at parallel machines which may be used in conjunction with Ames' "Cart3D" arbitrary geometry simulation package.
Kallinderis, Yannis; Vitsas, Panagiotis A.; Menounou, Penelope
2012-07-15
A low-order flow/acoustics interaction method for the prediction of sound propagation and diffraction in unsteady subsonic compressible flow using adaptive 3-D hybrid grids is investigated. The total field is decomposed into the flow field described by the Euler equations, and the acoustics part described by the Nonlinear Perturbation Equations. The method is shown capable of predicting monopole sound propagation, while employment of acoustics-guided adapted grid refinement improves the accuracy of capturing the acoustic field. Interaction of sound with solid boundaries is also examined in terms of reflection, and diffraction. Sound propagation through an unsteady flow field is examined using static and dynamic flow/acoustics coupling demonstrating the importance of the latter.
Grid adaptation using chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1994-01-01
The objective of this paper is to perform grid adaptation using composite overlapping meshes in regions of large gradient to accurately capture the salient features during computation. The chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using trilinear interpolation. Application to the Euler equations for shock reflections and to shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well-resolved.
Grid adaptation using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
Grid adaption using Chimera composite overlapping meshes
NASA Technical Reports Server (NTRS)
Kao, Kai-Hsiung; Liou, Meng-Sing; Chow, Chuen-Yen
1993-01-01
The objective of this paper is to perform grid adaptation using composite over-lapping meshes in regions of large gradient to capture the salient features accurately during computation. The Chimera grid scheme, a multiple overset mesh technique, is used in combination with a Navier-Stokes solver. The numerical solution is first converged to a steady state based on an initial coarse mesh. Solution-adaptive enhancement is then performed by using a secondary fine grid system which oversets on top of the base grid in the high-gradient region, but without requiring the mesh boundaries to join in any special way. Communications through boundary interfaces between those separated grids are carried out using tri-linear interpolation. Applications to the Euler equations for shock reflections and to a shock wave/boundary layer interaction problem are tested. With the present method, the salient features are well resolved.
On the use of adaptive moving grid methods in combustion problems
Hyman, J.M.; Larrouturou, B.
1986-01-01
The investigators have presented the reasons and advantages of adaptively moving the mesh points for the solution of time-dependent PDEs (partial differential equations) systems developing sharp gradients, and more specifically for combustion problems. Several available adaptive dynamic rezone methods have been briefly reviewed, and the effectiveness of these algorithms for combustion problems has been illustrated by the numerical solution of a simple flame propagation problem. 29 refs., 7 figs.
Near-Body Grid Adaption for Overset Grids
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2016-01-01
A solution adaption capability for curvilinear near-body grids has been implemented in the OVERFLOW overset grid computational fluid dynamics code. The approach follows closely that used for the Cartesian off-body grids, but inserts refined grids in the computational space of original near-body grids. Refined curvilinear grids are generated using parametric cubic interpolation, with one-sided biasing based on curvature and stretching ratio of the original grid. Sensor functions, grid marking, and solution interpolation tasks are implemented in the same fashion as for off-body grids. A goal-oriented procedure, based on largest error first, is included for controlling growth rate and maximum size of the adapted grid system. The adaption process is almost entirely parallelized using MPI, resulting in a capability suitable for viscous, moving body simulations. Two- and three-dimensional examples are presented.
Barnette, Daniel W.
2002-01-01
The present invention provides a method of grid generation that uses the geometry of the problem space and the governing relations to generate a grid. The method can generate a grid with minimized discretization errors, and with minimal user interaction. The method of the present invention comprises assigning grid cell locations so that, when the governing relations are discretized using the grid, at least some of the discretization errors are substantially zero. Conventional grid generation is driven by the problem space geometry; grid generation according to the present invention is driven by problem space geometry and by governing relations. The present invention accordingly can provide two significant benefits: more efficient and accurate modeling since discretization errors are minimized, and reduced cost grid generation since less human interaction is required.
The fluid dynamic approach to equidistribution methods for grid generation and adaptation
Delzanno, Gian Luca; Finn, John M
2009-01-01
The equidistribution methods based on L{sub p} Monge-Kantorovich optimization [Finn and Delzanno, submitted to SISC, 2009] and on the deformation [Moser, 1965; Dacorogna and Moser, 1990, Liao and Anderson, 1992] method are analyzed primarily in the context of grid generation. It is shown that the first class of methods can be obtained from a fluid dynamic formulation based on time-dependent equations for the mass density and the momentum density, arising from a variational principle. In this context, deformation methods arise from a fluid formulation by making a specific assumption on the time evolution of the density (but with some degree of freedom for the momentum density). In general, deformation methods do not arise from a variational principle. However, it is possible to prescribe an optimal deformation method, related to L{sub 1} Monge-Kantorovich optimization, by making a further assumption on the momentum density. Some applications of the L{sub p} fluid dynamic formulation to imaging are also explored.
Adaptive EAGLE dynamic solution adaptation and grid quality enhancement
NASA Technical Reports Server (NTRS)
Luong, Phu Vinh; Thompson, J. F.; Gatlin, B.; Mastin, C. W.; Kim, H. J.
1992-01-01
In the effort described here, the elliptic grid generation procedure in the EAGLE grid code was separated from the main code into a subroutine, and a new subroutine which evaluates several grid quality measures at each grid point was added. The elliptic grid routine can now be called, either by a computational fluid dynamics (CFD) code to generate a new adaptive grid based on flow variables and quality measures through multiple adaptation, or by the EAGLE main code to generate a grid based on quality measure variables through static adaptation. Arrays of flow variables can be read into the EAGLE grid code for use in static adaptation as well. These major changes in the EAGLE adaptive grid system make it easier to convert any CFD code that operates on a block-structured grid (or single-block grid) into a multiple adaptive code.
Dynamic Load Balancing for Adaptive Unstructured Grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Saini, Subhash (Technical Monitor)
1998-01-01
Dynamic mesh adaptation on unstructured grids is a powerful tool for computing unsteady three-dimensional problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture phenomena of interest, such procedures make standard computational methods more cost effective. Highly refined meshes are required to accurately capture shock waves, contact discontinuities, vortices, and shear layers in fluid flow problems. Adaptive meshes have also proved to be useful in several other areas of computational science and engineering like computer vision and graphics, semiconductor device modeling, and structural mechanics. Local mesh adaptation provides the opportunity to obtain solutions that are comparable to those obtained on globally-refined grids but at a much lower cost. Additional information is contained in the original extended abstract.
Interactive solution-adaptive grid generation
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Henderson, Todd L.
1992-01-01
TURBO-AD is an interactive solution-adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution-adaptive grid generation technique into a single interactive solution-adaptive grid generation package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties that had been encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on a unit square in the parametric domain, and the new adapted grid in the parametric domain is then mapped back to the physical domain. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using control sources obtained from flow properties. Then a new modified grid is generated from the adapted control net. This solution-adaptive grid generation process is efficient because the number of control points is much less than the number of grid points and the generation of a new grid from the adapted control net is an efficient algebraic process. TURBO-AD provides the user with both local and global grid controls.
Zhang, Guannan; Webster, Clayton G; Gunzburger, Max D
2012-09-01
Although Bayesian analysis has become vital to the quantification of prediction uncertainty in groundwater modeling, its application has been hindered due to the computational cost associated with numerous model executions needed for exploring the posterior probability density function (PPDF) of model parameters. This is particularly the case when the PPDF is estimated using Markov Chain Monte Carlo (MCMC) sampling. In this study, we develop a new approach that improves computational efficiency of Bayesian inference by constructing a surrogate system based on an adaptive sparse-grid high-order stochastic collocation (aSG-hSC) method. Unlike previous works using first-order hierarchical basis, we utilize a compactly supported higher-order hierar- chical basis to construct the surrogate system, resulting in a significant reduction in the number of computational simulations required. In addition, we use hierarchical surplus as an error indi- cator to determine adaptive sparse grids. This allows local refinement in the uncertain domain and/or anisotropic detection with respect to the random model parameters, which further improves computational efficiency. Finally, we incorporate a global optimization technique and propose an iterative algorithm for building the surrogate system for the PPDF with multiple significant modes. Once the surrogate system is determined, the PPDF can be evaluated by sampling the surrogate system directly with very little computational cost. The developed method is evaluated first using a simple analytical density function with multiple modes and then using two synthetic groundwater reactive transport models. The groundwater models represent different levels of complexity; the first example involves coupled linear reactions and the second example simulates nonlinear ura- nium surface complexation. The results show that the aSG-hSC is an effective and efficient tool for Bayesian inference in groundwater modeling in comparison with conventional
Interactive solution-adaptive grid generation procedure
NASA Technical Reports Server (NTRS)
Henderson, Todd L.; Choo, Yung K.; Lee, Ki D.
1992-01-01
TURBO-AD is an interactive solution adaptive grid generation program under development. The program combines an interactive algebraic grid generation technique and a solution adaptive grid generation technique into a single interactive package. The control point form uses a sparse collection of control points to algebraically generate a field grid. This technique provides local grid control capability and is well suited to interactive work due to its speed and efficiency. A mapping from the physical domain to a parametric domain was used to improve difficulties encountered near outwardly concave boundaries in the control point technique. Therefore, all grid modifications are performed on the unit square in the parametric domain, and the new adapted grid is then mapped back to the physical domain. The grid adaption is achieved by adapting the control points to a numerical solution in the parametric domain using control sources obtained from the flow properties. Then a new modified grid is generated from the adapted control net. This process is efficient because the number of control points is much less than the number of grid points and the generation of the grid is an efficient algebraic process. TURBO-AD provides the user with both local and global controls.
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.
Myocardial Strain Imaging with High-Performance Adaptive Dynamic Grid Interpolation Method
NASA Astrophysics Data System (ADS)
Shuhui Bu,; Makoto Yamakawa,; Tsuyoshi Shiina,
2010-07-01
The accurate assessment of local myocardial strain is important for diagnosing ischemic heart diseases because decreased myocardial motion often appears in the early stage. Calculating the spatial derivation of displacement is a necessary step in the strain calculation, but the numerical calculation is extremely sensitive to noise. Commonly used smoothing methods are the moving-average and median filters; however, these methods have a trade-off between spatial resolution and accuracy. A novel smoothing/fitting method is proposed for overcoming this problem. In this method, the detected displacement vectors are discretized at mesh nodes, and virtual springs are connected between adjacent nodes. By controlling the elasticity of the virtual springs, misdetected displacements are fitted without the above problem. Further improvements can be achieved by applying a Kalman filter for position tracking, and then calculating the strain from the accumulated displacement vectors. From the simulation results, we conclude that the proposed method improves the accuracy and spatial resolution of the strain images.
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
2006-01-01
A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.
Topology and grid adaption for high-speed flow computations
NASA Technical Reports Server (NTRS)
Abolhassani, Jamshid S.; Tiwari, Surendra N.
1989-01-01
This study investigates the effects of grid topology and grid adaptation on numerical solutions of the Navier-Stokes equations. In the first part of this study, a general procedure is presented for computation of high-speed flow over complex three-dimensional configurations. The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and a Reynolds number of 2,000,000. The O-type and H-type grids have been used for this study, and the results are compared together and with other theoretical and experimental results. The results demonstrate that while the H-type grid is suitable for the leading and trailing edges, a more accurate solution can be obtained for the middle part of the wing with an O-type grid. In the second part of this study, methods of grid adaption are reviewed and a method is developed with the capability of adapting to several variables. This method is based on a variational approach and is an algebraic method. Also, the method has been formulated in such a way that there is no need for any matrix inversion. This method is used in conjunction with the calculation of hypersonic flow over a blunt-nose body. A movie has been produced which shows simultaneously the transient behavior of the solution and the grid adaption.
Three-dimensional Navier-Stokes calculations using solution-adapted grids
NASA Technical Reports Server (NTRS)
Henderson, T. L.; Huang, W.; Lee, K. D.; Choo, Y. K.
1993-01-01
A three-dimensional solution-adaptive grid generation technique is presented. The adaptation technique redistributes grid points to improve the accuracy of a flow solution without increasing the number of grid points. It is applicable to structured grids with a multiblock topology. The method uses a numerical mapping and potential theory to modify the initial grid distribution based on the properties of the flow solution on the initial grid. The technique is demonstrated with two examples - a transonic finite wing and a supersonic blunt fin. The advantages are shown by comparing flow solutions on the adapted grids with those on the initial grids.
Spectral methods on arbitrary grids
NASA Technical Reports Server (NTRS)
Carpenter, Mark H.; Gottlieb, David
1995-01-01
Stable and spectrally accurate numerical methods are constructed on arbitrary grids for partial differential equations. These new methods are equivalent to conventional spectral methods but do not rely on specific grid distributions. Specifically, we show how to implement Legendre Galerkin, Legendre collocation, and Laguerre Galerkin methodology on arbitrary grids.
Unstructured grid methods for compressible flows
NASA Technical Reports Server (NTRS)
Morgan, K.; Peraire, J.; Peiro, J.
1992-01-01
The implementation of the finite element method on unstructured triangular grids is described and the development of centered finite element schemes for the solution of the compressible Euler equation on general triangular and tetrahedral grids is discussed. Explicit and implicit Lax-Wendroff type methods and a method based upon the use of explicit multistep timestepping are considered. In the latter case, the convergence behavior of the method is accelerated by the incorporation of a fully unstructured multigrid procedure. The advancing front method for generating unstructured grids of triangles and tetrahedra is described and the application of adaptive mesh techniques to both steady and transient flow analysis is illustrated.
Adaptive refinement tools for tetrahedral unstructured grids
NASA Technical Reports Server (NTRS)
Pao, S. Paul (Inventor); Abdol-Hamid, Khaled S. (Inventor)
2011-01-01
An exemplary embodiment providing one or more improvements includes software which is robust, efficient, and has a very fast run time for user directed grid enrichment and flow solution adaptive grid refinement. All user selectable options (e.g., the choice of functions, the choice of thresholds, etc.), other than a pre-marked cell list, can be entered on the command line. The ease of application is an asset for flow physics research and preliminary design CFD analysis where fast grid modification is often needed to deal with unanticipated development of flow details.
An adaptive grid algorithm for one-dimensional nonlinear equations
NASA Technical Reports Server (NTRS)
Gutierrez, William E.; Hills, Richard G.
1990-01-01
Richards' equation, which models the flow of liquid through unsaturated porous media, is highly nonlinear and difficult to solve. Step gradients in the field variables require the use of fine grids and small time step sizes. The numerical instabilities caused by the nonlinearities often require the use of iterative methods such as Picard or Newton interation. These difficulties result in large CPU requirements in solving Richards equation. With this in mind, adaptive and multigrid methods are investigated for use with nonlinear equations such as Richards' equation. Attention is focused on one-dimensional transient problems. To investigate the use of multigrid and adaptive grid methods, a series of problems are studied. First, a multigrid program is developed and used to solve an ordinary differential equation, demonstrating the efficiency with which low and high frequency errors are smoothed out. The multigrid algorithm and an adaptive grid algorithm is used to solve one-dimensional transient partial differential equations, such as the diffusive and convective-diffusion equations. The performance of these programs are compared to that of the Gauss-Seidel and tridiagonal methods. The adaptive and multigrid schemes outperformed the Gauss-Seidel algorithm, but were not as fast as the tridiagonal method. The adaptive grid scheme solved the problems slightly faster than the multigrid method. To solve nonlinear problems, Picard iterations are introduced into the adaptive grid and tridiagonal methods. Burgers' equation is used as a test problem for the two algorithms. Both methods obtain solutions of comparable accuracy for similar time increments. For the Burgers' equation, the adaptive grid method finds the solution approximately three times faster than the tridiagonal method. Finally, both schemes are used to solve the water content formulation of the Richards' equation. For this problem, the adaptive grid method obtains a more accurate solution in fewer work units and
Adaptive grid generation in a patient-specific cerebral aneurysm
NASA Astrophysics Data System (ADS)
Hodis, Simona; Kallmes, David F.; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
Adaptive grid generation in a patient-specific cerebral aneurysm.
Hodis, Simona; Kallmes, David F; Dragomir-Daescu, Dan
2013-11-01
Adapting grid density to flow behavior provides the advantage of increasing solution accuracy while decreasing the number of grid elements in the simulation domain, therefore reducing the computational time. One method for grid adaptation requires successive refinement of grid density based on observed solution behavior until the numerical errors between successive grids are negligible. However, such an approach is time consuming and it is often neglected by the researchers. We present a technique to calculate the grid size distribution of an adaptive grid for computational fluid dynamics (CFD) simulations in a complex cerebral aneurysm geometry based on the kinematic curvature and torsion calculated from the velocity field. The relationship between the kinematic characteristics of the flow and the element size of the adaptive grid leads to a mathematical equation to calculate the grid size in different regions of the flow. The adaptive grid density is obtained such that it captures the more complex details of the flow with locally smaller grid size, while less complex flow characteristics are calculated on locally larger grid size. The current study shows that kinematic curvature and torsion calculated from the velocity field in a cerebral aneurysm can be used to find the locations of complex flow where the computational grid needs to be refined in order to obtain an accurate solution. We found that the complexity of the flow can be adequately described by velocity and vorticity and the angle between the two vectors. For example, inside the aneurysm bleb, at the bifurcation, and at the major arterial turns the element size in the lumen needs to be less than 10% of the artery radius, while at the boundary layer, the element size should be smaller than 1% of the artery radius, for accurate results within a 0.5% relative approximation error. This technique of quantifying flow complexity and adaptive remeshing has the potential to improve results accuracy and reduce
SAGE: The Self-Adaptive Grid Code. 3
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1999-01-01
The multi-dimensional self-adaptive grid code, SAGE, is an important tool in the field of computational fluid dynamics (CFD). It provides an efficient method to improve the accuracy of flow solutions while simultaneously reducing computer processing time. Briefly, SAGE enhances an initial computational grid by redistributing the mesh points into more appropriate locations. The movement of these points is driven by an equal-error-distribution algorithm that utilizes the relationship between high flow gradients and excessive solution errors. The method also provides a balance between clustering points in the high gradient regions and maintaining the smoothness and continuity of the adapted grid, The latest version, Version 3, includes the ability to change the boundaries of a given grid to more efficiently enclose flow structures and provides alternative redistribution algorithms.
Adaptive hybrid prismatic-tetrahedral grids for viscous flows
NASA Technical Reports Server (NTRS)
Kallinderis, Yannis; Khawaja, Aly; Mcmorris, Harlan
1995-01-01
The paper presents generation of adaptive hybrid prismatic/tetrahedral grids for complex 3-D geometries including multi-body domains. The prisms cover the region close to each body's surface, while tetrahedra are created elsewhere. Two developments are presented for hybrid grid generation around complex 3-D geometries. The first is a new octree/advancing front type of method for generation of the tetrahedra of the hybrid mesh. The main feature of the present advancing front tetrahedra generator that is different from previous such methods is that it does not require the creation of a background mesh by the user for the determination of the grid-spacing and stretching parameters. These are determined via an automatically generated octree. The second development is an Automatic Receding Method (ARM) for treating the narrow gaps in between different bodies in a multiply-connected domain. This method is applied to a two-element wing case. A hybrid grid adaptation scheme that employs both h-refinement and redistribution strategies is developed to provide optimum meshes for viscous flow computations. Grid refinement is a dual adaptation scheme that couples division of tetrahedra, as well as 2-D directional division of prisms.
Grid crusher apparatus and method
McDaniels, J.D. Jr.
1994-01-11
A grid crusher apparatus and method are provided for a nuclear fuel rod consolidation system. Spacer grids are crushed within a basket which is then placed in a storage canister. The grid crusher apparatus has a ram assembly and a basket driving mechanism. The ram assembly has a sleeve ram and a central ram. The sleeve ram surrounds the central ram which is longitudinally movable within the sleeve ram. The central ram protrudes from the sleeve ram at a ram contact end and is retractable upon application of a preselected force to the central ram so that the central ram is flush with the sleeve ram at the ram contact end. The basket driving mechanism is configured to move the basket containing a spacer grid towards the ram contact end so that the spacer grid is crushed within the basket. The spacer grid is crushed by the combination of successive forces from the central ram and the sleeve ram, respectively. Essentially, the central portion of the spacer grid is crushed first, and then the remaining outer portion of the spacer grid is crushed to complete the crushing action of the spacer grid. The foregoing process is repeated for other spacer grids until the basket reaches a predetermined allowable capacity, and then the basket is stored in a storage canister. 11 figs.
A Grid Sourcing and Adaptation Study Using Unstructured Grids for Supersonic Boom Prediction
NASA Technical Reports Server (NTRS)
Carter, Melissa B.; Deere, Karen A.
2008-01-01
NASA created the Supersonics Project as part of the NASA Fundamental Aeronautics Program to advance technology that will make a supersonic flight over land viable. Computational flow solvers have lacked the ability to accurately predict sonic boom from the near to far field. The focus of this investigation was to establish gridding and adaptation techniques to predict near-to-mid-field (<10 body lengths below the aircraft) boom signatures at supersonic speeds using the USM3D unstructured grid flow solver. The study began by examining sources along the body the aircraft, far field sourcing and far field boundaries. The study then examined several techniques for grid adaptation. During the course of the study, volume sourcing was introduced as a new way to source grids using the grid generation code VGRID. Two different methods of using the volume sources were examined. The first method, based on manual insertion of the numerous volume sources, made great improvements in the prediction capability of USM3D for boom signatures. The second method (SSGRID), which uses an a priori adaptation approach to stretch and shear the original unstructured grid to align the grid and pressure waves, showed similar results with a more automated approach. Due to SSGRID s results and ease of use, the rest of the study focused on developing a best practice using SSGRID. The best practice created by this study for boom predictions using the CFD code USM3D involved: 1) creating a small cylindrical outer boundary either 1 or 2 body lengths in diameter (depending on how far below the aircraft the boom prediction is required), 2) using a single volume source under the aircraft, and 3) using SSGRID to stretch and shear the grid to the desired length.
The multidimensional Self-Adaptive Grid code, SAGE, version 2
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1995-01-01
This new report on Version 2 of the SAGE code includes all the information in the original publication plus all upgrades and changes to the SAGE code since that time. The two most significant upgrades are the inclusion of a finite-volume option and the ability to adapt and manipulate zonal-matching multiple-grid files. In addition, the original SAGE code has been upgraded to Version 1.1 and includes all options mentioned in this report, with the exception of the multiple grid option and its associated features. Since Version 2 is a larger and more complex code, it is suggested (but not required) that Version 1.1 be used for single-grid applications. This document contains all the information required to run both versions of SAGE. The formulation of the adaption method is described in the first section of this document. The second section is presented in the form of a user guide that explains the input and execution of the code. The third section provides many examples. Successful application of the SAGE code in both two and three dimensions for the solution of various flow problems has proven the code to be robust, portable, and simple to use. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for complex grid structures. Modifications to the method and the simple but extensive input options make this a flexible and user-friendly code. The SAGE code can accommodate two-dimensional and three-dimensional, finite-difference and finite-volume, single grid, and zonal-matching multiple grid flow problems.
The use of solution adaptive grids in solving partial differential equations
NASA Technical Reports Server (NTRS)
Anderson, D. A.; Rai, M. M.
1982-01-01
The grid point distribution used in solving a partial differential equation using a numerical method has a substantial influence on the quality of the solution. An adaptive grid which adjusts as the solution changes provides the best results when the number of grid points available for use during the calculation is fixed. Basic concepts used in generating and applying adaptive grids are reviewed in this paper, and examples illustrating applications of these concepts are presented.
Hierarchy-Direction Selective Approach for Locally Adaptive Sparse Grids
Stoyanov, Miroslav K
2013-09-01
We consider the problem of multidimensional adaptive hierarchical interpolation. We use sparse grids points and functions that are induced from a one dimensional hierarchical rule via tensor products. The classical locally adaptive sparse grid algorithm uses an isotropic refinement from the coarser to the denser levels of the hierarchy. However, the multidimensional hierarchy provides a more complex structure that allows for various anisotropic and hierarchy selective refinement techniques. We consider the more advanced refinement techniques and apply them to a number of simple test functions chosen to demonstrate the various advantages and disadvantages of each method. While there is no refinement scheme that is optimal for all functions, the fully adaptive family-direction-selective technique is usually more stable and requires fewer samples.
Efficient Load Balancing and Data Remapping for Adaptive Grid Calculations
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak
1997-01-01
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 to dynamically balance the processor workloads with a global view. This paper presents, for the first time, 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. Previous results indicated that mesh repartitioning and data remapping are potential bottlenecks for performing large-scale scientific calculations. We resolve these issues and demonstrate that our framework remains viable on a large number of processors.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Technical Reports Server (NTRS)
Chen, S. C.
1988-01-01
This report describes a numerical method for generating 3-D grids for general configurations. The basic method involves the solution of a set of quasi-linear elliptic partial differential equations via pointwise relaxation with a local relaxation factor. It allows specification of the grid spacing off the boundary surfaces and the grid orthogonality at the boundary surfaces. It includes adaptive mechanisms to improve smoothness, orthogonality, and flow resolution in the grid interior.
Techniques for grid manipulation and adaptation. [computational fluid dynamics
NASA Technical Reports Server (NTRS)
Choo, Yung K.; Eisemann, Peter R.; Lee, Ki D.
1992-01-01
Two approaches have been taken to provide systematic grid manipulation for improved grid quality. One is the control point form (CPF) of algebraic grid generation. It provides explicit control of the physical grid shape and grid spacing through the movement of the control points. It works well in the interactive computer graphics environment and hence can be a good candidate for integration with other emerging technologies. The other approach is grid adaptation using a numerical mapping between the physical space and a parametric space. Grid adaptation is achieved by modifying the mapping functions through the effects of grid control sources. The adaptation process can be repeated in a cyclic manner if satisfactory results are not achieved after a single application.
Unstructured viscous flow solution using adaptive hybrid grids
NASA Technical Reports Server (NTRS)
Galle, Martin
1995-01-01
A three dimensional finite volume scheme based on hybrid grids containing both tetrahedral and hexahedral cells is presented. The application to hybrid grids offers the possibility to combine the flexibility of tetrahedral meshes with the accuracy of hexahedral grids. An algorithm to compute a dual mesh for the entire computational domain was developed. The dual mesh technique guarantees conservation in the whole flow field even at interfaces between hexahedral and tetrahedral domains and enables the employment of an accurate upwind flow solver. The hybrid mesh can be adapted to the solution by dividing cells in areas of insufficient resolution. The method is tested on different viscous and inviscid cases for hypersonic, transonic and subsonic flows.
Adapting Grids For Computing Two-Dimensional Flows
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1992-01-01
SAGE2D is two-dimensional implementation of Self Adaptive Grid Evolution computer program that intelligently redistributes initial grid points on basis of initial flow-field solution. Grids modified according to initial computed flows enabling recomputation at greater accuracy. Written in FORTRAN 77.
Unstructured Adaptive Grid Computations on an Array of SMPs
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Pramanick, Ira; Sohn, Andrew; Simon, Horst D.
1996-01-01
Dynamic load balancing is necessary for parallel adaptive methods to solve unsteady CFD problems on unstructured grids. We have presented such a dynamic load balancing framework called JOVE, in this paper. Results on a four-POWERnode POWER CHALLENGEarray demonstrated that load balancing gives significant performance improvements over no load balancing for such adaptive computations. The parallel speedup of JOVE, implemented using MPI on the POWER CHALLENCEarray, was significant, being as high as 31 for 32 processors. An implementation of JOVE that exploits 'an array of SMPS' architecture was also studied; this hybrid JOVE outperformed flat JOVE by up to 28% on the meshes and adaption models tested. With large, realistic meshes and actual flow-solver and adaption phases incorporated into JOVE, hybrid JOVE can be expected to yield significant advantage over flat JOVE, especially as the number of processors is increased, thus demonstrating the scalability of an array of SMPs architecture.
A Solution Adaptive Technique Using Tetrahedral Unstructured Grids
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2000-01-01
An adaptive unstructured grid refinement technique has been developed and successfully applied to several three dimensional inviscid flow test cases. The method is based on a combination of surface mesh subdivision and local remeshing of the volume grid Simple functions of flow quantities are employed to detect dominant features of the flowfield The method is designed for modular coupling with various error/feature analyzers and flow solvers. Several steady-state, inviscid flow test cases are presented to demonstrate the applicability of the method for solving practical three-dimensional problems. In all cases, accurate solutions featuring complex, nonlinear flow phenomena such as shock waves and vortices have been generated automatically and efficiently.
Load Balancing Unstructured Adaptive Grids for CFD Problems
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Oliker, Leonid
1996-01-01
Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. A dynamic load balancing method is presented that balances the workload across all processors with a global view. After each parallel tetrahedral mesh adaption, the method first determines if the new mesh is sufficiently unbalanced to warrant a repartitioning. If so, the adapted mesh is repartitioned, with new partitions assigned to processors so that the redistribution cost is minimized. The new partitions are accepted only if the remapping cost is compensated by the improved load balance. Results indicate that this strategy is effective for large-scale scientific computations on distributed-memory multiprocessors.
The multidimensional self-adaptive grid code, SAGE
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1992-01-01
This report describes the multidimensional self-adaptive grid code SAGE. A two-dimensional version of this code was described in an earlier report by the authors. The formulation of the multidimensional version is described in the first section of this document. The second section is presented in the form of a user guide that explains the input and execution of the code and provides many examples. Successful application of the SAGE code in both two and three dimensions for the solution of various flow problems has proven the code to be robust, portable, and simple to use. Although the basic formulation follows the method of Nakahashi and Deiwert, many modifications have been made to facilitate the use of the self-adaptive grid method for complex grid structures. Modifications to the method and the simplified input options make this a flexible and user-friendly code. The new SAGE code can accommodate both two-dimensional and three-dimensional flow problems.
Cartesian Off-Body Grid Adaption for Viscous Time- Accurate Flow Simulation
NASA Technical Reports Server (NTRS)
Buning, Pieter G.; Pulliam, Thomas H.
2011-01-01
An improved solution adaption capability has been implemented in the OVERFLOW overset grid CFD code. Building on the Cartesian off-body approach inherent in OVERFLOW and the original adaptive refinement method developed by Meakin, the new scheme provides for automated creation of multiple levels of finer Cartesian grids. Refinement can be based on the undivided second-difference of the flow solution variables, or on a specific flow quantity such as vorticity. Coupled with load-balancing and an inmemory solution interpolation procedure, the adaption process provides very good performance for time-accurate simulations on parallel compute platforms. A method of using refined, thin body-fitted grids combined with adaption in the off-body grids is presented, which maximizes the part of the domain subject to adaption. Two- and three-dimensional examples are used to illustrate the effectiveness and performance of the adaption scheme.
Multilevel methods for elliptic problems on unstructured grids
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Go, Susie; Zikatanov, Ludmil
1997-01-01
Multilevel methods on unstructured grids for elliptic problems are reviewed. The advantages of these techniques are the flexible approximation of the boundaries of complicated physical domains and the ability to adapt the grid to the resolution of fine scaled structures. Multilevel methods, which include multigrid methods and domain decomposition methods, depend on the correct splitting of appropriate finite element spaces. The standard splittings used in the structured grid case cannot be directly extended to unstructured grids due to their requirement for a hierarchical grid structure. Issues related to the application of multilevel methods to unstructured grids are discussed, including how the coarse spaces and transfer operators are defined and how different types of boundary conditions are treated. An obvious way to generate a coarse mesh is to regrid the physical domain several times. Several alternatives are proposed and discussed: node nested coarse spaces, agglomerated coarse spaces and algebraically generated coarse spaces.
OMEGA: The operational multiscale environment model with grid adaptivity
Bacon, D.P.
1995-07-01
This review talk describes the OMEGA code, used for weather simulation and the modeling of aerosol transport through the atmosphere. Omega employs a 3D mesh of wedge shaped elements (triangles when viewed from above) that adapt with time. Because wedges are laid out in layers of triangular elements, the scheme can utilize structured storage and differencing techniques along the elevation coordinate, and is thus a hybrid of structured and unstructured methods. The utility of adaptive gridding in this moded, near geographic features such as coastlines, where material properties change discontinuously, is illustrated. Temporal adaptivity was used additionally to track moving internal fronts, such as clouds of aerosol contaminants. The author also discusses limitations specific to this problem, including manipulation of huge data bases and fixed turn-around times. In practice, the latter requires a carefully tuned optimization between accuracy and computation speed.
Solving Fluid Flow Problems on Moving and Adaptive Overlapping Grids
Henshaw, W
2005-07-28
Solution of fluid dynamics problems on overlapping grids will be discussed. An overlapping grid consists of a set of structured component grids that cover a domain and overlap where they meet. Overlapping grids provide an effective approach for developing efficient and accurate approximations for complex, possibly moving geometry. Topics to be addressed include the reactive Euler equations, the incompressible Navier-Stokes equations and elliptic equations solved with a multigrid algorithm. Recent developments coupling moving grids and adaptive mesh refinement and preliminary parallel results will also be presented.
Cosmos++: Relativistic Magnetohydrodynamics on Unstructured Grids with Local Adaptive Refinement
Anninos, P; Fragile, P C; Salmonson, J D
2005-05-06
A new code and methodology are introduced for solving the fully general relativistic magnetohydrodynamic (GRMHD) equations using time-explicit, finite-volume discretization. The code has options for solving the GRMHD equations using traditional artificial-viscosity (AV) or non-oscillatory central difference (NOCD) methods, or a new extended AV (eAV) scheme using artificial-viscosity together with a dual energy-flux-conserving formulation. The dual energy approach allows for accurate modeling of highly relativistic flows at boost factors well beyond what has been achieved to date by standard artificial viscosity methods. it provides the benefit of Godunov methods in capturing high Lorentz boosted flows but without complicated Riemann solvers, and the advantages of traditional artificial viscosity methods in their speed and flexibility. Additionally, the GRMHD equations are solved on an unstructured grid that supports local adaptive mesh refinement using a fully threated oct-tree (in three dimensions) network to traverse the grid hierarchy across levels and immediate neighbors. A number of tests are presented to demonstrate robustness of the numerical algorithms and adaptive mesh framework over a wide spectrum of problems, boosts, and astrophysical applications, including relativistic shock tubes, shock collisions, magnetosonic shocks, Alfven wave propagation, blast waves, magnetized Bondi flow, and the magneto-rotational instability in Kerr black hole spacetimes.
SIMULATION OF DISPERSION OF A POWER PLANT PLUME USING AN ADAPTIVE GRID ALGORITHM
A new dynamic adaptive grid algorithm has been developed for use in air quality modeling. This algorithm uses a higher order numerical scheme?the piecewise parabolic method (PPM)?for computing advective solution fields; a weight function capable of promoting grid node clustering ...
Multiprocessor computer overset grid method and apparatus
Barnette, Daniel W.; Ober, Curtis C.
2003-01-01
A multiprocessor computer overset grid method and apparatus comprises associating points in each overset grid with processors and using mapped interpolation transformations to communicate intermediate values between processors assigned base and target points of the interpolation transformations. The method allows a multiprocessor computer to operate with effective load balance on overset grid applications.
Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems
NASA Technical Reports Server (NTRS)
Steinthorsson, Erlendur; Modiano, David; Colella, Phillip
1995-01-01
To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.
Adaptive mesh refinement in curvilinear body-fitted grid systems
NASA Astrophysics Data System (ADS)
Steinthorsson, Erlendur; Modiano, David; Colella, Phillip
1995-10-01
To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.
Simulation of the dispersion of nuclear contamination using an adaptive Eulerian grid model.
Lagzi, I; Kármán, D; Turányi, T; Tomlin, A S; Haszpra, L
2004-01-01
Application of an Eulerian model using layered adaptive unstructured grids coupled to a meso-scale meteorological model is presented for modelling the dispersion of nuclear contamination following the accidental release from a single but strong source to the atmosphere. The model automatically places a finer resolution grid, adaptively in time, in regions were high spatial numerical error is expected. The high-resolution grid region follows the movement of the contaminated air over time. Using this method, grid resolutions of the order of 6 km can be achieved in a computationally effective way. The concept is illustrated by the simulation of hypothetical nuclear accidents at the Paks NPP, in Central Hungary. The paper demonstrates that the adaptive model can achieve accuracy comparable to that of a high-resolution Eulerian model using significantly less grid points and computer simulation time. PMID:15149762
Adaptive sparse grid expansions of the vibrational Hamiltonian.
Strobusch, D; Scheurer, Ch
2014-02-21
The vibrational Hamiltonian involves two high dimensional operators, the kinetic energy operator (KEO), and the potential energy surface (PES). Both must be approximated for systems involving more than a few atoms. Adaptive approximation schemes are not only superior to truncated Taylor or many-body expansions (MBE), they also allow for error estimates, and thus operators of predefined precision. To this end, modified sparse grids (SG) are developed that can be combined with adaptive MBEs. This MBE/SG hybrid approach yields a unified, fully adaptive representation of the KEO and the PES. Refinement criteria, based on the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, are presented. The combination of the adaptive MBE/SG approach and the VSCF plus VCI methods yields a black box like procedure to compute accurate vibrational spectra. This is demonstrated on a test set of molecules, comprising water, formaldehyde, methanimine, and ethylene. The test set is first employed to prove convergence for semi-empirical PM3-PESs and subsequently to compute accurate vibrational spectra from CCSD(T)-PESs that agree well with experimental values.
Adaptive sparse grid expansions of the vibrational Hamiltonian
Strobusch, D.; Scheurer, Ch.
2014-02-21
The vibrational Hamiltonian involves two high dimensional operators, the kinetic energy operator (KEO), and the potential energy surface (PES). Both must be approximated for systems involving more than a few atoms. Adaptive approximation schemes are not only superior to truncated Taylor or many-body expansions (MBE), they also allow for error estimates, and thus operators of predefined precision. To this end, modified sparse grids (SG) are developed that can be combined with adaptive MBEs. This MBE/SG hybrid approach yields a unified, fully adaptive representation of the KEO and the PES. Refinement criteria, based on the vibrational self-consistent field (VSCF) and vibrational configuration interaction (VCI) methods, are presented. The combination of the adaptive MBE/SG approach and the VSCF plus VCI methods yields a black box like procedure to compute accurate vibrational spectra. This is demonstrated on a test set of molecules, comprising water, formaldehyde, methanimine, and ethylene. The test set is first employed to prove convergence for semi-empirical PM3-PESs and subsequently to compute accurate vibrational spectra from CCSD(T)-PESs that agree well with experimental values.
A fifth-order finite difference scheme for hyperbolic equations on block-adaptive curvilinear grids
NASA Astrophysics Data System (ADS)
Chen, Yuxi; Tóth, Gábor; Gombosi, Tamas I.
2016-01-01
We present a new fifth-order accurate finite difference method for hyperbolic equations on block-adaptive curvilinear grids. The scheme employs the 5th order accurate monotonicity preserving limiter MP5 to construct high order accurate face fluxes. The fifth-order accuracy of the spatial derivatives is ensured by a flux correction step. The method is generalized to curvilinear grids with a free-stream preserving discretization. It is also extended to block-adaptive grids using carefully designed ghost cell interpolation algorithms. Only three layers of ghost cells are required, and the grid blocks can be as small as 6 × 6 × 6 cells. Dynamic grid refinement and coarsening are also fifth-order accurate. All interpolation algorithms employ a general limiter based on the principles of the MP5 limiter. The finite difference scheme is fully conservative on static uniform grids. Conservation is only maintained at the truncation error level at grid resolution changes and during grid adaptation, but our numerical tests indicate that the results are still very accurate. We demonstrate the capabilities of the new method on a number of numerical tests, including smooth but non-linear problems as well as simulations involving discontinuities.
A New Elliptical Grid Clustering Method
NASA Astrophysics Data System (ADS)
Guansheng, Zheng
A new base on grid clustering method is presented in this paper. This new method first does unsupervised learning on the high dimensions data. This paper proposed a grid-based approach to clustering. It maps the data onto a multi-dimensional space and applies a linear transformation to the feature space instead of to the objects themselves and then approach a grid-clustering method. Unlike the conventional methods, it uses a multidimensional hyper-eclipse grid cell. Some case studies and ideas how to use the algorithms are described. The experimental results show that EGC can discover abnormity shapes of clusters.
Adaptive gridding strategies for Free-Lagrangian calculations of low speed flows
NASA Astrophysics Data System (ADS)
Fritts, Martin J.
1988-01-01
Free-Lagrangian methods have been employed in two-dimensional simulations of the long-term evolution of fluid instabilities for low speed flows. For example, calculations of the Rayleigh-Taylor instability have proceeded through the inversion and mixing of two fluid layers and simulations of droplet deformations have continued well beyond droplet shattering. The freedom to choose grid connections permits several important benefits for these calculations. 1. Mass conservation is enforced for all individual fluid elements. 2. Vertex movement is always Lagrangian. 3. Grid adjustments can be made automatically, with no user intervention. 4. Grid connections may be selected to ensure accuracy in the difference equations. 5. Adaptive gridding schemes are local, adding and deleting vertices as dictated by local accuracy estimators. 6. Any geometric configuration may be easily gridded, for any vertex distribution on the boundaries or in the interior of the fluids. This paper will review some two-dimensional results, with the emphasis on the adaptive gridding algorithms and the accuracy of the resultant difference templates for the mathematical operators. The relation of the triangular mesh to the Voronoi mesh will be explored, particularly for the case when they are dual meshes. Three-dimensional algorithms for adaptive gridding will be presented which are exact analogues to the two-dimensional case. Gridding efficiencies will be discussed for several schemes.
NASA Technical Reports Server (NTRS)
Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.
1995-01-01
This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.
Anisotropic Solution Adaptive Unstructured Grid Generation Using AFLR
NASA Technical Reports Server (NTRS)
Marcum, David L.
2007-01-01
An existing volume grid generation procedure, AFLR3, was successfully modified to generate anisotropic tetrahedral elements using a directional metric transformation defined at source nodes. The procedure can be coupled with a solver and an error estimator as part of an overall anisotropic solution adaptation methodology. It is suitable for use with an error estimator based on an adjoint, optimization, sensitivity derivative, or related approach. This offers many advantages, including more efficient point placement along with robust and efficient error estimation. It also serves as a framework for true grid optimization wherein error estimation and computational resources can be used as cost functions to determine the optimal point distribution. Within AFLR3 the metric transformation is implemented using a set of transformation vectors and associated aspect ratios. The modified overall procedure is presented along with details of the anisotropic transformation implementation. Multiple two-and three-dimensional examples are also presented that demonstrate the capability of the modified AFLR procedure to generate anisotropic elements using a set of source nodes with anisotropic transformation metrics. The example cases presented use moderate levels of anisotropy and result in usable element quality. Future testing with various flow solvers and methods for obtaining transformation metric information is needed to determine practical limits and evaluate the efficacy of the overall approach.
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.
NASA Technical Reports Server (NTRS)
Brislawn, Kristi D.; Brown, David L.; Chesshire, Geoffrey S.; Saltzman, Jeffrey S.
1995-01-01
Adaptive mesh refinement (AMR) in conjunction with higher-order upwind finite-difference methods have been used effectively on a variety of problems in two and three dimensions. In this paper we introduce an approach for resolving problems that involve complex geometries in which resolution of boundary geometry is important. The complex geometry is represented by using the method of overlapping grids, while local resolution is obtained by refining each component grid with the AMR algorithm, appropriately generalized for this situation. The CMPGRD algorithm introduced by Chesshire and Henshaw is used to automatically generate the overlapping grid structure for the underlying mesh.
FLAG: A multi-dimensional adaptive free-Lagrange code for fully unstructured grids
Burton, D.E.; Miller, D.S.; Palmer, T.
1995-07-01
The authors describe FLAG, a 3D adaptive free-Lagrange method for unstructured grids. The grid elements were 3D polygons, which move with the flow, and are refined or reconnected as necessary to achieve uniform accuracy. The authors stressed that they were able to construct a 3D hydro version of this code in 3 months, using an object-oriented FORTRAN approach.
Self-Avoiding Walks Over Adaptive Triangular Grids
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1999-01-01
Space-filling curves is a popular approach based on a geometric embedding for linearizing computational meshes. We present a new O(n log n) combinatorial algorithm for constructing a self avoiding walk through a two dimensional mesh containing n triangles. We show that for hierarchical adaptive meshes, the algorithm can be locally adapted and easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the runtime partitioning and load balancing of adaptive unstructured grids.
NASA Technical Reports Server (NTRS)
Nakamura, S.
1983-01-01
The effects of truncation error on the numerical solution of transonic flows using the full potential equation are studied. The effects of adapting grid point distributions to various solution aspects including shock waves is also discussed. A conclusion is that a rapid change of grid spacing is damaging to the accuracy of the flow solution. Therefore, in a solution adaptive grid application an optimal grid is obtained as a tradeoff between the amount of grid refinement and the rate of grid stretching.
Visualizing 3D Turbulence On Temporally Adaptive Wavelet Collocation Grids
NASA Astrophysics Data System (ADS)
Goldstein, D. E.; Kadlec, B. J.; Yuen, D. A.; Erlebacher, G.
2005-12-01
Today there is an explosion in data from high-resolution computations of nonlinear phenomena in many fields, including the geo- and environmental sciences. The efficient storage and subsequent visualization of these large data sets is a trade off in storage costs versus data quality. New dynamically adaptive simulation methodologies promise significant computational cost savings and have the added benefit of producing results on adapted grids that significantly reduce storage and data manipulation costs. Yet, with these adaptive simulation methodologies come new challenges in the visualization of temporally adaptive data sets. In this work turbulence data sets from Stochastic Coherent Adaptive Large Eddy Simulations (SCALES) are visualized with the open source tool ParaView, as a challenging case study. SCALES simulations use a temporally adaptive collocation grid defined by wavelet threshold filtering to resolve the most energetic coherent structures in a turbulence field. A subgrid scale model is used to account for the effect of unresolved subgrid scale modes. The results from the SCALES simulations are saved on a thresholded dyadic wavelet collocation grid, which by its nature does not include cell information. Paraview is an open source visualization package developed by KitWare(tm) that is based on the widely used VTK graphics toolkit. The efficient generation of cell information, required with current ParaView data formats, is explored using custom algorithms and VTK toolkit routines. Adaptive 3d visualizations using isosurfaces and volume visualizations are compared with non-adaptive visualizations. To explore the localized multiscale structures in the turbulent data sets the wavelet coefficients are also visualized allowing visualization of energy contained in local physical regions as well as in local wave number space.
An adaptive grid-based all hexahedral meshing algorithm based on 2-refinement.
Edgel, Jared; Benzley, Steven E.; Owen, Steven James
2010-08-01
Most adaptive mesh generation algorithms employ a 3-refinement method. This method, although easy to employ, provides a mesh that is often too coarse in some areas and over refined in other areas. Because this method generates 27 new hexes in place of a single hex, there is little control on mesh density. This paper presents an adaptive all-hexahedral grid-based meshing algorithm that employs a 2-refinement method. 2-refinement is based on dividing the hex to be refined into eight new hexes. This method allows a greater control on mesh density when compared to a 3-refinement procedure. This adaptive all-hexahedral meshing algorithm provides a mesh that is efficient for analysis by providing a high element density in specific locations and a reduced mesh density in other areas. In addition, this tool can be effectively used for inside-out hexahedral grid based schemes, using Cartesian structured grids for the base mesh, which have shown great promise in accommodating automatic all-hexahedral algorithms. This adaptive all-hexahedral grid-based meshing algorithm employs a 2-refinement insertion method. This allows greater control on mesh density when compared to 3-refinement methods. This algorithm uses a two layer transition zone to increase element quality and keeps transitions from lower to higher mesh densities smooth. Templates were introduced to allow both convex and concave refinement.
Digital breast tomosynthesis reconstruction with an adaptive voxel grid
NASA Astrophysics Data System (ADS)
Claus, Bernhard; Chan, Heang-Ping
2014-03-01
In digital breast tomosynthesis (DBT) volume datasets are typically reconstructed with an anisotropic voxel size, where the in-plane voxel size usually reflects the detector pixel size (e.g., 0.1 mm), and the slice separation is generally between 0.5-1.0 mm. Increasing the tomographic angle is expected to give better 3D image quality; however, the slice spacing in the reconstruction should be reduced, otherwise one may risk losing fine-scale image detail (e.g., small microcalcifications). An alternative strategy consists of reconstructing on an adaptive voxel grid, where the voxel height at each location is adapted based on the backprojected data at this location, with the goal to improve image quality for microcalcifications. In this paper we present an approach for generating such an adaptive voxel grid. This approach is based on an initial reconstruction step that is performed at a finer slice-spacing combined with a selection of an "optimal" height for each voxel. This initial step is followed by a (potentially iterative) reconstruction acting now on the adaptive grid only.
A new method for gridding DNA microarrays.
Charalambous, Christoforos C; Matsopoulos, George K
2013-10-01
In this paper, a new methodological scheme for the gridding of DNA microarrays is proposed. The scheme composes of a series of processes applied sequentially. Each DNA microarray image is pre-processed to remove any noise and the center of each spot is detected using a template matching algorithm. Then, an initial gridding is automatically placed on the DNA microarray image by 'building' rectangular pyramids around the detected spots' centers. The gridlines "move" between the pyramids, horizontally and vertically, forming this initial grid. Furthermore, a refinement process is applied composing of a five-step approach in order to correct gridding imperfections caused by its initial placement, both in non-spot cases and in more than one spot enclosure cases. The proposed gridding scheme is applied on DNA microarray images under known transformations and on real-world DNA data. Its performance is compared against the projection pursuit method, which is often used due to its speed and simplicity, as well as against a state-of-the-art method, the Optimal Multi-level Thresholding Gridding (OMTG). According to the obtained results, the proposed gridding scheme outperforms both methods, qualitatively and quantitatively.
Solution adaptive grids applied to low Reynolds number flow
NASA Astrophysics Data System (ADS)
de With, G.; Holdø, A. E.; Huld, T. A.
2003-08-01
A numerical study has been undertaken to investigate the use of a solution adaptive grid for flow around a cylinder in the laminar flow regime. The main purpose of this work is twofold. The first aim is to investigate the suitability of a grid adaptation algorithm and the reduction in mesh size that can be obtained. Secondly, the uniform asymmetric flow structures are ideal to validate the mesh structures due to mesh refinement and consequently the selected refinement criteria. The refinement variable used in this work is a product of the rate of strain and the mesh cell size, and contains two variables Cm and Cstr which determine the order of each term. By altering the order of either one of these terms the refinement behaviour can be modified.
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.
On the dynamics of some grid adaption schemes
NASA Technical Reports Server (NTRS)
Sweby, Peter K.; Yee, Helen C.
1994-01-01
The dynamics of a one-parameter family of mesh equidistribution schemes coupled with finite difference discretisations of linear and nonlinear convection-diffusion model equations is studied numerically. It is shown that, when time marched to steady state, the grid adaption not only influences the stability and convergence rate of the overall scheme, but can also introduce spurious dynamics to the numerical solution procedure.
Adaptive Algebraic Multigrid Methods
Brezina, M; Falgout, R; MacLachlan, S; Manteuffel, T; McCormick, S; Ruge, J
2004-04-09
Our ability to simulate physical processes numerically is constrained by our ability to solve the resulting linear systems, prompting substantial research into the development of multiscale iterative methods capable of solving these linear systems with an optimal amount of effort. Overcoming the limitations of geometric multigrid methods to simple geometries and differential equations, algebraic multigrid methods construct the multigrid hierarchy based only on the given matrix. While this allows for efficient black-box solution of the linear systems associated with discretizations of many elliptic differential equations, it also results in a lack of robustness due to assumptions made on the near-null spaces of these matrices. This paper introduces an extension to algebraic multigrid methods that removes the need to make such assumptions by utilizing an adaptive process. The principles which guide the adaptivity are highlighted, as well as their application to algebraic multigrid solution of certain symmetric positive-definite linear systems.
SIMULATION OF DISPERSION OF A POWER PLANT PLUME USING AN ADAPTIVE GRID ALGORITHM. (R827028)
A new dynamic adaptive grid algorithm has been developed for use in air quality modeling. This algorithm uses a higher order numerical scheme––the piecewise parabolic method (PPM)––for computing advective solution fields; a weight function capable o...
A geometry-based adaptive unstructured grid generation algorithm for complex geological media
NASA Astrophysics Data System (ADS)
Bahrainian, Seyed Saied; Dezfuli, Alireza Daneh
2014-07-01
In this paper a novel unstructured grid generation algorithm is presented that considers the effect of geological features and well locations in grid resolution. The proposed grid generation algorithm presents a strategy for definition and construction of an initial grid based on the geological model, geometry adaptation of geological features, and grid resolution control. The algorithm is applied to seismotectonic map of the Masjed-i-Soleiman reservoir. Comparison of grid results with the “Triangle” program shows a more suitable permeability contrast. Immiscible two-phase flow solutions are presented for a fractured porous media test case using different grid resolutions. Adapted grid on the fracture geometry gave identical results with that of a fine grid. The adapted grid employed 88.2% less CPU time when compared to the solutions obtained by the fine grid.
Generalized Monge-Kantorovich optimization for grid generation and adaptation in LP
Delzanno, G L; Finn, J M
2009-01-01
The Monge-Kantorovich grid generation and adaptation scheme of is generalized from a variational principle based on L{sub 2} to a variational principle based on L{sub p}. A generalized Monge-Ampere (MA) equation is derived and its properties are discussed. Results for p > 1 are obtained and compared in terms of the quality of the resulting grid. We conclude that for the grid generation application, the formulation based on L{sub p} for p close to unity leads to serious problems associated with the boundary. Results for 1.5 {approx}< p {approx}< 2.5 are quite good, but there is a fairly narrow range around p = 2 where the results are close to optimal with respect to grid distortion. Furthermore, the Newton-Krylov methods used to solve the generalized MA equation perform best for p = 2.
INITIAL APPL;ICATION OF THE ADAPTIVE GRID AIR POLLUTION MODEL
The paper discusses an adaptive-grid algorithm used in air pollution models. The algorithm reduces errors related to insufficient grid resolution by automatically refining the grid scales in regions of high interest. Meanwhile the grid scales are coarsened in other parts of the d...
Self-Avoiding Walks over Adaptive Triangular Grids
NASA Technical Reports Server (NTRS)
Heber, Gerd; Biswas, Rupak; Gao, Guang R.; Saini, Subhash (Technical Monitor)
1998-01-01
In this paper, we present a new approach to constructing a "self-avoiding" walk through a triangular mesh. Unlike the popular approach of visiting mesh elements using space-filling curves which is based on a geometric embedding, our approach is combinatorial in the sense that it uses the mesh connectivity only. We present an algorithm for constructing a self-avoiding walk which can be applied to any unstructured triangular mesh. The complexity of the algorithm is O(n x log(n)), where n is the number of triangles in the mesh. We show that for hierarchical adaptive meshes, the algorithm can be easily parallelized by taking advantage of the regularity of the refinement rules. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.
A transonic rectangular grid embedded panel method
NASA Technical Reports Server (NTRS)
Johnson, F. T.; Bussoletti, J. E.; James, R. M.; Young, D. P.; Woo, A. C.
1982-01-01
A method is presented that has the potential for solving transonic flow problems about the same complex aircraft configurations currently being analyzed by subsonic panel methods. This method does not require the generation of surface fitted grids. Instead it uses rectangular grids and subgrids together with embedded surface panels on which boundary conditions are imposed. Both the Euler and full potential equations are considered. The method of least squares is used to reduce the solution of these equations to the solution of a sequence of Poisson problems. The Poisson problems are solved using fast Fourier transforms and panel influence coefficient techniques. The overall method is still in its infancy but some two dimensional results are shown illustrating various key features.
An adaptive grid refinement strategy for the simulation of negative streamers
Montijn, C. . E-mail: carolynne.montijn@cwi.nl; Hundsdorfer, W. . E-mail: willem.hundsdorfer@cwi.nl; Ebert, U. . E-mail: ute.ebert@cwi.nl
2006-12-10
The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers.
An adaptive grid for graph-based segmentation in retinal OCT
Lang, Andrew; Carass, Aaron; Calabresi, Peter A.; Ying, Howard S.; Prince, Jerry L.
2016-01-01
Graph-based methods for retinal layer segmentation have proven to be popular due to their efficiency and accuracy. These methods build a graph with nodes at each voxel location and use edges connecting nodes to encode the hard constraints of each layer’s thickness and smoothness. In this work, we explore deforming the regular voxel grid to allow adjacent vertices in the graph to more closely follow the natural curvature of the retina. This deformed grid is constructed by fixing node locations based on a regression model of each layer’s thickness relative to the overall retina thickness, thus we generate a subject specific grid. Graph vertices are not at voxel locations, which allows for control over the resolution that the graph represents. By incorporating soft constraints between adjacent nodes, segmentation on this grid will favor smoothly varying surfaces consistent with the shape of the retina. Our final segmentation method then follows our previous work. Boundary probabilities are estimated using a random forest classifier followed by an optimal graph search algorithm on the new adaptive grid to produce a final segmentation. Our method is shown to produce a more consistent segmentation with an overall accuracy of 3.38 μm across all boundaries.
Parallel, grid-adaptive approaches for relativistic hydro and magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Keppens, R.; Meliani, Z.; van Marle, A. J.; Delmont, P.; Vlasis, A.; van der Holst, B.
2012-02-01
Relativistic hydro and magnetohydrodynamics provide continuum fluid descriptions for gas and plasma dynamics throughout the visible universe. We present an overview of state-of-the-art modeling in special relativistic regimes, targeting strong shock-dominated flows with speeds approaching the speed of light. Significant progress in its numerical modeling emerged in the last two decades, and we highlight specifically the need for grid-adaptive, shock-capturing treatments found in several contemporary codes in active use and development. Our discussion highlights one such code, MPI-AMRVAC (Message-Passing Interface-Adaptive Mesh Refinement Versatile Advection Code), but includes generic strategies for allowing massively parallel, block-tree adaptive simulations in any dimensionality. We provide implementation details reflecting the underlying data structures as used in MPI-AMRVAC. Parallelization strategies and scaling efficiencies are discussed for representative applications, along with guidelines for data formats suitable for parallel I/O. Refinement strategies available in MPI-AMRVAC are presented, which cover error estimators in use in many modern AMR frameworks. A test suite for relativistic hydro and magnetohydrodynamics is provided, chosen to cover all aspects encountered in high-resolution, shock-governed astrophysical applications. This test suite provides ample examples highlighting the advantages of AMR in relativistic flow problems.
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.
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.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2004-01-28
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. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Hydrodynamics
Anderson, R W; Pember, R B; Elliott, N S
2002-10-19
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. The novel components of the combined ALE-AMR method hinge upon the integration of traditional AMR techniques with both staggered grid Lagrangian operators as well as elliptic relaxation operators on moving, deforming mesh hierarchies. Numerical examples demonstrate the utility of the method in performing detailed three-dimensional shock-driven instability calculations.
A parallel dynamic load balancing algorithm for 3-D adaptive unstructured grids
NASA Technical Reports Server (NTRS)
Vidwans, A.; Kallinderis, Y.; Venkatakrishnan, V.
1993-01-01
Adaptive local grid refinement and coarsening results in unequal distribution of workload among the processors of a parallel system. A novel method for balancing the load in cases of dynamically changing tetrahedral grids is developed. The approach employs local exchange of cells among processors in order to redistribute the load equally. An important part of the load balancing algorithm is the method employed by a processor to determine which cells within its subdomain are to be exchanged. Two such methods are presented and compared. The strategy for load balancing is based on the Divide-and-Conquer approach which leads to an efficient parallel algorithm. This method is implemented on a distributed-memory MIMD system.
Adaptive 3D single-block grids for the computation of viscous flows around wings
Hagmeijer, R.; Kok, J.C.
1996-12-31
A robust algorithm for the adaption of a 3D single-block structured grid suitable for the computation of viscous flows around a wing is presented and demonstrated by application to the ONERA M6 wing. The effects of grid adaption on the flow solution and accuracy improvements is analyzed. Reynolds number variations are studied.
Parallel adaptive wavelet collocation method for PDEs
Nejadmalayeri, Alireza; Vezolainen, Alexei; Brown-Dymkoski, Eric; Vasilyev, Oleg V.
2015-10-01
A parallel adaptive wavelet collocation method for solving a large class of Partial Differential Equations is presented. The parallelization is achieved by developing an asynchronous parallel wavelet transform, which allows one to perform parallel wavelet transform and derivative calculations with only one data synchronization at the highest level of resolution. The data are stored using tree-like structure with tree roots starting at a priori defined level of resolution. Both static and dynamic domain partitioning approaches are developed. For the dynamic domain partitioning, trees are considered to be the minimum quanta of data to be migrated between the processes. This allows fully automated and efficient handling of non-simply connected partitioning of a computational domain. Dynamic load balancing is achieved via domain repartitioning during the grid adaptation step and reassigning trees to the appropriate processes to ensure approximately the same number of grid points on each process. The parallel efficiency of the approach is discussed based on parallel adaptive wavelet-based Coherent Vortex Simulations of homogeneous turbulence with linear forcing at effective non-adaptive resolutions up to 2048{sup 3} using as many as 2048 CPU cores.
FUN3D Grid Refinement and Adaptation Studies for the Ares Launch Vehicle
NASA Technical Reports Server (NTRS)
Bartels, Robert E.; Vasta, Veer; Carlson, Jan-Renee; Park, Mike; Mineck, Raymond E.
2010-01-01
This paper presents grid refinement and adaptation studies performed in conjunction with computational aeroelastic analyses of the Ares crew launch vehicle (CLV). The unstructured grids used in this analysis were created with GridTool and VGRID while the adaptation was performed using the Computational Fluid Dynamic (CFD) code FUN3D with a feature based adaptation software tool. GridTool was developed by ViGYAN, Inc. while the last three software suites were developed by NASA Langley Research Center. The feature based adaptation software used here operates by aligning control volumes with shock and Mach line structures and by refining/de-refining where necessary. It does not redistribute node points on the surface. This paper assesses the sensitivity of the complex flow field about a launch vehicle to grid refinement. It also assesses the potential of feature based grid adaptation to improve the accuracy of CFD analysis for a complex launch vehicle configuration. The feature based adaptation shows the potential to improve the resolution of shocks and shear layers. Further development of the capability to adapt the boundary layer and surface grids of a tetrahedral grid is required for significant improvements in modeling the flow field.
Analysis of a Major Electric Grid -- Stability and Adaptive Protection
NASA Astrophysics Data System (ADS)
Alanzi, Sultan
Protective systems of the electric grid are designed to detect and mitigate the effects of faults and other disturbances that may occur. Distance relays are used extensively for the detection of faults on transmission lines. Out-of-step relays are used for generator protection to detect loss of synchronism conditions that result from disturbances on the electric grid. Also, when a disturbance occurs and generators may tend to lose synchronism with each other, it is beneficial to separate the overall system into several independent systems that can remain stable. Unfortunately there have been cases, such as the 2003 Northeast blackout where the operation of protective relays, namely the zone 3 distance relay used for transmission line protection, contributed to the cascading effect of the blackout. It is the objective of this dissertation to propose adaptive relays for both distance protection of transmission lines and out-of-step protection of generators. By being adaptive, the relays are made aware of the system operating conditions and can adjust its settings accordingly. Inputs to the adaptive logic can come from system or environmental conditions. As a result of this effort, a new distance relay operating characteristic is proposed, referred to as a mushroom relay, which is a combination of a quadrilateral relay and a Mho relay. Also, a new criterion for determining if a power swing following a disturbance is stable or unstable is proposed. Distance protection of transmission lines is very important when discussing system responses to faults and disturbances. Distance relays are very common worldwide and although they offer great protection, there are limitations that need to be addressed. Parallel line operations (infeed effect) and the loadability limits are among the limitations that lead to improper response of relays. An Adaptive Distance Relays (ADR) offer great benefits to the protection scheme as their settings can be changed in accordance with prefault
Analysis of a Major Electric Grid -- Stability and Adaptive Protection
NASA Astrophysics Data System (ADS)
Alanzi, Sultan
Protective systems of the electric grid are designed to detect and mitigate the effects of faults and other disturbances that may occur. Distance relays are used extensively for the detection of faults on transmission lines. Out-of-step relays are used for generator protection to detect loss of synchronism conditions that result from disturbances on the electric grid. Also, when a disturbance occurs and generators may tend to lose synchronism with each other, it is beneficial to separate the overall system into several independent systems that can remain stable. Unfortunately there have been cases, such as the 2003 Northeast blackout where the operation of protective relays, namely the zone 3 distance relay used for transmission line protection, contributed to the cascading effect of the blackout. It is the objective of this dissertation to propose adaptive relays for both distance protection of transmission lines and out-of-step protection of generators. By being adaptive, the relays are made aware of the system operating conditions and can adjust its settings accordingly. Inputs to the adaptive logic can come from system or environmental conditions. As a result of this effort, a new distance relay operating characteristic is proposed, referred to as a mushroom relay, which is a combination of a quadrilateral relay and a Mho relay. Also, a new criterion for determining if a power swing following a disturbance is stable or unstable is proposed. Distance protection of transmission lines is very important when discussing system responses to faults and disturbances. Distance relays are very common worldwide and although they offer great protection, there are limitations that need to be addressed. Parallel line operations (infeed effect) and the loadability limits are among the limitations that lead to improper response of relays. An Adaptive Distance Relays (ADR) offer great benefits to the protection scheme as their settings can be changed in accordance with prefault
Adaptive data management in the ARC Grid middleware
NASA Astrophysics Data System (ADS)
Cameron, D.; Gholami, A.; Karpenko, D.; Konstantinov, A.
2011-12-01
The Advanced Resource Connector (ARC) Grid middleware was designed almost 10 years ago, and has proven to be an attractive distributed computing solution and successful in adapting to new data management and storage technologies. However, with an ever-increasing user base and scale of resources to manage, along with the introduction of more advanced data transfer protocols, some limitations in the current architecture have become apparent. The simple first-in first-out approach to data transfer leads to bottlenecks in the system, as does the built-in assumption that all data is immediately available from remote data storage. We present an entirely new data management architecture for ARC which aims to alleviate these problems, by introducing a three-layer structure. The top layer accepts incoming requests for data transfer and directs them to the middle layer, which schedules individual transfers and negotiates with various intermediate catalog and storage systems until the physical file is ready to be transferred. The lower layer performs all operations which use large amounts of bandwidth, i.e. the physical data transfer. Using such a layered structure allows more efficient use of the available bandwidth as well as enabling late-binding of jobs to data transfer slots based on a priority system. Here we describe in full detail the design and implementation of the new system.
Grid and basis adaptive polynomial chaos techniques for sensitivity and uncertainty analysis
Perkó, Zoltán Gilli, Luca Lathouwers, Danny Kloosterman, Jan Leen
2014-03-01
The demand for accurate and computationally affordable sensitivity and uncertainty techniques is constantly on the rise and has become especially pressing in the nuclear field with the shift to Best Estimate Plus Uncertainty methodologies in the licensing of nuclear installations. Besides traditional, already well developed methods – such as first order perturbation theory or Monte Carlo sampling – Polynomial Chaos Expansion (PCE) has been given a growing emphasis in recent years due to its simple application and good performance. This paper presents new developments of the research done at TU Delft on such Polynomial Chaos (PC) techniques. Our work is focused on the Non-Intrusive Spectral Projection (NISP) approach and adaptive methods for building the PCE of responses of interest. Recent efforts resulted in a new adaptive sparse grid algorithm designed for estimating the PC coefficients. The algorithm is based on Gerstner's procedure for calculating multi-dimensional integrals but proves to be computationally significantly cheaper, while at the same it retains a similar accuracy as the original method. More importantly the issue of basis adaptivity has been investigated and two techniques have been implemented for constructing the sparse PCE of quantities of interest. Not using the traditional full PC basis set leads to further reduction in computational time since the high order grids necessary for accurately estimating the near zero expansion coefficients of polynomial basis vectors not needed in the PCE can be excluded from the calculation. Moreover the sparse PC representation of the response is easier to handle when used for sensitivity analysis or uncertainty propagation due to the smaller number of basis vectors. The developed grid and basis adaptive methods have been implemented in Matlab as the Fully Adaptive Non-Intrusive Spectral Projection (FANISP) algorithm and were tested on four analytical problems. These show consistent good performance both
On Efficient Parallel Implementation of Moving Body Overset Grid Methods
NASA Technical Reports Server (NTRS)
Wissink, Andrew M.; Meakin, Robert L.; Warmbrodt, William (Technical Monitor)
1997-01-01
An investigation into the parallel performance of moving-body overset grid methods will be presented. Parallel versions of the OVERFLOW flow solver, DCF3D domain connectivity software, and SIXDO six-degree-of-freedom routine are coupled with an automatic load balance routine and tested for 3D Navier-Stokes calculations on the IBM SP2. The primary source of parallel inefficiency in moving and problems are the domain connectivity costs with DCF 3D. Although this algorithm constitutes a relatively low fraction of the total solution cost (e.g. 10-20%) in calculations on serial machines, the consequently cause a significant degradation in the overall parallel performance. The paper will highlight some approaches for improving the scalability of DCF3D. The paper will present results of a proposed new load balancing scheme that seeks more equal distribution of the inter-grid boundary points in order to more evenly load balance the donor search costs associated with DCF3D. Some preliminary results will also be given from a new solution-adaption algorithm coupled with OVERFLOW which incorporates overset cartesian grids with various levels of refinement. The measured parallel performance from a descending delta-wing configuration and a generic store-separation from a wing/pylon case will be presented.
Automated Grid Disruption Response System: Robust Adaptive Topology Control (RATC)
2012-03-01
GENI Project: The RATC research team is using topology control as a mechanism to improve system operations and manage disruptions within the electric grid. The grid is subject to interruption from cascading faults caused by extreme operating conditions, malicious external attacks, and intermittent electricity generation from renewable energy sources. The RATC system is capable of detecting, classifying, and responding to grid disturbances by reconfiguring the grid in order to maintain economically efficient operations while guaranteeing reliability. The RATC system would help prevent future power outages, which account for roughly $80 billion in losses for businesses and consumers each year. Minimizing the time it takes for the grid to respond to expensive interruptions will also make it easier to integrate intermittent renewable energy sources into the grid.
Three-dimensional solution-adaptive grid generation of composite configurations
NASA Astrophysics Data System (ADS)
Tu, Yen
A solution adaptive grid generation procedure is developed and applied to 3-D inviscid transonic fluid flow around complex geometries using a composite block grid structure. The adaptation is based upon control functions in an elliptic grid generation system. The control function is constructed in a manner such that a proper grid network can be generated as a fluid flow solution is evolving. The grid network is boundary conforming for accurate representation of boundary conditions. The procedure implemented allows orthodonality at boundaries for more accurate computations, while smoothness is implicit in the elliptic equations. The approach allows multiple block grid systems to be constructed to treat complex configurations as well. The solution adaptive computational procedure was accomplished by coupling the elliptic grid generation technique with an implicit, finite volume, upwind Euler flow solver. In simulating trasonic fluid flow around finned body of revolution and a multiple store configuration, the grid systems adapt to pressure gradients in the flow field. Results obtained show that the technique is capable of generating grid networks proper for the simulations of complex aerodynamic configurations.
Aeroacoustic Simulation of Nose Landing Gear on Adaptive Unstructured Grids With FUN3D
NASA Technical Reports Server (NTRS)
Vatsa, Veer N.; Khorrami, Mehdi R.; Park, Michael A.; Lockhard, David P.
2013-01-01
Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D, developed at NASA Langley Research center, is used to compute the unsteady flow field for this configuration. Starting with a coarse grid, a series of successively finer grids were generated using the adaptive gridding methodology available in the FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. In general, the correlation with the experimental data improves with grid refinement. A similar trend is observed for sound pressure levels obtained by using these CFD solutions as input to a FfowcsWilliams-Hawkings noise propagation code to compute the farfield noise levels. In general, the numerical solutions obtained on adapted grids compare well with the hand-tuned enriched fine grid solutions and experimental data. In addition, the grid adaption strategy discussed here simplifies the grid generation process, and results in improved computational efficiency of CFD simulations.
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
Adaptive numerical methods for partial differential equations
Cololla, P.
1995-07-01
This review describes a structured approach to adaptivity. The Automated Mesh Refinement (ARM) algorithms developed by M Berger are described, touching on hyperbolic and parabolic applications. Adaptivity is achieved by overlaying finer grids only in areas flagged by a generalized error criterion. The author discusses some of the issues involved in abutting disparate-resolution grids, and demonstrates that suitable algorithms exist for dissipative as well as hyperbolic systems.
Multiple Coarse Grid Multigrid Methods for Solving Elliptic Problems
NASA Technical Reports Server (NTRS)
Xiao, Shengyou; Young, David
1996-01-01
In this paper we describe some classes of multigrid methods for solving large linear systems arising in the solution by finite difference methods of certain boundary value problems involving Poisson's equation on rectangular regions. If parallel computing systems are used, then with standard multigrid methods many of the processors will be idle when one is working at the coarsest grid levels. We describe the use of Multiple Coarse Grid MultiGrid (MCGMG) methods. Here one first constructs a periodic set of equations corresponding to the given system. One then constructs a set of coarse grids such that for each grid corresponding to the grid size h there are four grids corresponding to the grid size 2*h. Multigrid operations such as restriction of residuals and interpolation of corrections are done in parallel at each grid level. For suitable choices of the multigrid operators the MCGMG method is equivalent to the Parallel Superconvergent MultiGrid (PSMG) method of Frederickson and McBryan. The convergence properties of MCGMG methods can be accurately analyzed using spectral methods.
Block-structured adaptive meshes and reduced grids for atmospheric general circulation models.
Jablonowski, Christiane; Oehmke, Robert C; Stout, Quentin F
2009-11-28
Adaptive mesh refinement techniques offer a flexible framework for future variable-resolution climate and weather models since they can focus their computational mesh on certain geographical areas or atmospheric events. Adaptive meshes can also be used to coarsen a latitude-longitude grid in polar regions. This allows for the so-called reduced grid setups. A spherical, block-structured adaptive grid technique is applied to the Lin-Rood finite-volume dynamical core for weather and climate research. This hydrostatic dynamics package is based on a conservative and monotonic finite-volume discretization in flux form with vertically floating Lagrangian layers. The adaptive dynamical core is built upon a flexible latitude-longitude computational grid and tested in two- and three-dimensional model configurations. The discussion is focused on static mesh adaptations and reduced grids. The two-dimensional shallow water setup serves as an ideal testbed and allows the use of shallow water test cases like the advection of a cosine bell, moving vortices, a steady-state flow, the Rossby-Haurwitz wave or cross-polar flows. It is shown that reduced grid configurations are viable candidates for pure advection applications but should be used moderately in nonlinear simulations. In addition, static grid adaptations can be successfully used to resolve three-dimensional baroclinic waves in the storm-track region.
TWO-GRID METHODS FOR MAXWELL EIGENVALUE PROBLEMS
ZHOU, J.; HU, X.; ZHONG, L.; SHU, S.; CHEN, L.
2015-01-01
Two new two-grid algorithms are proposed for solving the Maxwell eigenvalue problem. The new methods are based on the two-grid methodology recently proposed by Xu and Zhou [Math. Comp., 70 (2001), pp. 17–25] and further developed by Hu and Cheng [Math. Comp., 80 (2011), pp. 1287–1301] for elliptic eigenvalue problems. The new two-grid schemes reduce the solution of the Maxwell eigenvalue problem on a fine grid to one linear indefinite Maxwell equation on the same fine grid and an original eigenvalue problem on a much coarser grid. The new schemes, therefore, save total computational cost. The error estimates reveals that the two-grid methods maintain asymptotically optimal accuracy, and the numerical experiments presented confirm the theoretical results. PMID:26190866
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALE method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
Bo, Wurigen; Shashkov, Mikhail
2015-07-21
We present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35], [34] and [6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. Furthermore, in the standard ReALEmore » method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way.« less
Carving and adaptive drainage enforcement of grid digital elevation models
NASA Astrophysics Data System (ADS)
Soille, Pierre; Vogt, Jürgen; Colombo, Roberto
2003-12-01
An effective and widely used method for removing spurious pits in digital elevation models consists of filling them until they overflow. However, this method sometimes creates large flat regions which in turn pose a problem for the determination of accurate flow directions. In this study, we propose to suppress each pit by creating a descending path from it to the nearest point having a lower elevation value. This is achieved by carving, i.e., lowering, the terrain elevations along the detected path. Carving paths are identified through a flooding simulation starting from the river outlets. The proposed approach allows for adaptive drainage enforcement whereby river networks coming from other data sources are imposed to the digital elevation model only in places where the automatic river network extraction deviates substantially from the known networks. An improvement to methods for routing flow over flat regions is also introduced. Detailed results are presented over test areas of the Danube basin.
Grid adaption based on modified anisotropic diffusion equations formulated in the parametic domain
Hagmeijer, R.
1994-11-01
A new grid-adaption algorithm for problems in computational fluid dynamics is presented. The basic equations are derived from a variational problem formulated in the parametric domain of the mapping that defines the existing grid. Modification of the basic equations provides desirable properties in boundary layers. The resulting modified anisotropic diffusion equations are solved for the computational coordinates as functions of the parametric coordinates and these functions are numerically inverted. Numerical examples show that the algorithm is robust, that shocks and boundary layers are well-resolved on the adapted grid, and that the flow solution becomes a globally smooth function of the computational coordinates.
NASA Astrophysics Data System (ADS)
Zeng, Xiankui; Ye, Ming; Burkardt, John; Wu, Jichun; Wang, Dong; Zhu, Xiaobin
2016-04-01
Sparse grid (SG) stochastic collocation methods have been recently used to build accurate but cheap-to-run surrogates for groundwater models to reduce the computational burden of Bayesian uncertainty analysis. The surrogates can be built for either a log-likelihood function or state variables such as hydraulic head and solute concentration. Using a synthetic groundwater flow model, this study evaluates the log-likelihood and head surrogates in terms of the computational cost of building them, the accuracy of the surrogates, and the accuracy of the distributions of model parameters and predictions obtained using the surrogates. The head surrogates outperform the log-likelihood surrogates for the following four reasons: (1) the shape of the head response surface is smoother than that of the log-likelihood response surface in parameter space, (2) the head variation is smaller than the log-likelihood variation in parameter space, (3) the interpolation error of the head surrogates does not accumulate to be larger than the interpolation error of the log-likelihood surrogates, and (4) the model simulations needed for building one head surrogate can be recycled for building others. For both log-likelihood and head surrogates, adaptive sparse grids are built using two indicators: absolute error and relative error. The adaptive head surrogates are insensitive to the error indicators, because the ratio between the two indicators is hydraulic head, which has small variation in the parameter space. The adaptive log-likelihood surrogates based on the relative error indicators outperform those based on the absolute error indicators, because adaptation based on the relative error indicator puts more sparse-grid nodes in the areas in the parameter space where the log-likelihood is high. While our numerical study suggests building state-variable surrogates and using the relative error indicator for building log-likelihood surrogates, selecting appropriate type of surrogates and
An Efficient Means of Adaptive Refinement Within Systems of Overset Grids
NASA Technical Reports Server (NTRS)
Meakin, Robert L.
1996-01-01
An efficient means of adaptive refinement within systems of overset grids is presented. Problem domains are segregated into near-body and off-body fields. Near-body fields are discretized via overlapping body-fitted grids that extend only a short distance from body surfaces. Off-body fields are discretized via systems of overlapping uniform Cartesian grids of varying levels of refinement. a novel off-body grid generation and management scheme provides the mechanism for carrying out adaptive refinement of off-body flow dynamics and solid body motion. The scheme allows for very efficient use of memory resources, and flow solvers and domain connectivity routines that can exploit the structure inherent to uniform Cartesian grids.
An Efficient Grid Generation Method for Arbitrary Domains
NASA Astrophysics Data System (ADS)
Orme, Melissa; Huang, Changzheng
1997-11-01
This paper describes an efficient grid generation method for arbitrary or multiply connected domains. Our method, essentially based on the edge swapping techniques, combines the advantages of the Delaunay triangulation method and the advancing front method. The latter two methods are in popular use nowadays. But both suffer some limitations. Delaunay method generates high quality grid but grid may cut across the boundary in concave regions. Advancing front method works for general domain but may encounter difficulties where fronts have to be merged. The current method garantees the boundary integrity and attains the nice Delaunay features into the domain. This is achieved by carefully documenting the grid information so that each edge is readily identified to be inside or outside the domain; and (2) continuously swapping out those bad edges that destroy the Delaunay properties. The computer program built on this method allows users to control the grid density distribution by specifying typical grid sizes on a few chosen points. Interesting examples are demonstrated here. One of them is a circular domain with three letters APS inside. (see figure 1 and figure 2 ). Given a grid size for APS and another size for the circle, the program automatically generates a smooth triangular grid regardless of the complex multiply connected geometry.
CHARACTERIZATION OF DISCONTINUITIES IN HIGH-DIMENSIONAL STOCHASTIC PROBLEMS ON ADAPTIVE SPARSE GRIDS
Jakeman, John D; Archibald, Richard K; Xiu, Dongbin
2011-01-01
In this paper we present a set of efficient algorithms for detection and identification of discontinuities in high dimensional space. The method is based on extension of polynomial annihilation for edge detection in low dimensions. Compared to the earlier work, the present method poses significant improvements for high dimensional problems. The core of the algorithms relies on adaptive refinement of sparse grids. It is demonstrated that in the commonly encountered cases where a discontinuity resides on a small subset of the dimensions, the present method becomes optimal , in the sense that the total number of points required for function evaluations depends linearly on the dimensionality of the space. The details of the algorithms will be presented and various numerical examples are utilized to demonstrate the efficacy of the method.
Method For Model-Reference Adaptive Control
NASA Technical Reports Server (NTRS)
Seraji, Homayoun
1990-01-01
Relatively simple method of model-reference adaptive control (MRAC) developed from two prior classes of MRAC techniques: signal-synthesis method and parameter-adaption method. Incorporated into unified theory, which yields more general adaptation scheme.
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.
Spatial grid services for adaptive spatial query optimization
NASA Astrophysics Data System (ADS)
Gao, Bingbo; Xie, Chuanjie; Sheng, Wentao
2008-10-01
Spatial information sharing and integration has now become an important issue of Geographical Information Science (GIS). Web Service technologies provide a easy and standard way to share spatial resources over network, and grid technologies which aim at sharing resources such as data, storage, and computational powers can help the sharing go deeper. However, the dynamic characteristic of grid brings complexity to spatial query optimization which is more stressed in GIS domain because spatial operations are both CPU intensive and data intensive. To address this problem, a new grid framework is employed to provide standard spatial services which can also manage and report their state information to the coordinator which is responsible for distributed spatial query optimization.
Emergent Adaptive Noise Reduction from Communal Cooperation of Sensor Grid
NASA Technical Reports Server (NTRS)
Jones, Kennie H.; Jones, Michael G.; Nark, Douglas M.; Lodding, Kenneth N.
2010-01-01
In the last decade, the realization of small, inexpensive, and powerful devices with sensors, computers, and wireless communication has promised the development of massive sized sensor networks with dense deployments over large areas capable of high fidelity situational assessments. However, most management models have been based on centralized control and research has concentrated on methods for passing data from sensor devices to the central controller. Most implementations have been small but, as it is not scalable, this methodology is insufficient for massive deployments. Here, a specific application of a large sensor network for adaptive noise reduction demonstrates a new paradigm where communities of sensor/computer devices assess local conditions and make local decisions from which emerges a global behaviour. This approach obviates many of the problems of centralized control as it is not prone to single point of failure and is more scalable, efficient, robust, and fault tolerant
Adaptive grid embedding for the two-dimensional flux-split Euler equations. M.S. Thesis
NASA Technical Reports Server (NTRS)
Warren, Gary Patrick
1990-01-01
A numerical algorithm is presented for solving the 2-D flux-split Euler equations using a multigrid method with adaptive grid embedding. The method uses an unstructured data set along with a system of pointers for communication on the irregularly shaped grid topologies. An explicit two-stage time advancement scheme is implemented. A multigrid algorithm is used to provide grid level communication and to accelerate the convergence of the solution to steady state. Results are presented for a subcritical airfoil and a transonic airfoil with 3 levels of adaptation. Comparisons are made with a structured upwind Euler code which uses the same flux integration techniques of the present algorithm. Good agreement is obtained with converged surface pressure coefficients. The lift coefficients of the adaptive code are within 2 1/2 percent of the structured code for the sub-critical case and within 4 1/2 percent of the structured code for the transonic case using approximately one-third the number of grid points.
Milne, R.B.
1995-12-01
This thesis describes a new method for the numerical solution of partial differential equations of the parabolic type on an adaptively refined mesh in two or more spatial dimensions. The method is motivated and developed in the context of the level set formulation for the curvature dependent propagation of surfaces in three dimensions. In that setting, it realizes the multiple advantages of decreased computational effort, localized accuracy enhancement, and compatibility with problems containing a range of length scales.
Scenario generation for stochastic optimization problems via the sparse grid method
Chen, Michael; Mehrotra, Sanjay; Papp, David
2015-04-19
We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid method can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.
NASA Technical Reports Server (NTRS)
Park, Michael A.; Krakos, Joshua A.; Michal, Todd; Loseille, Adrien; Alonso, Juan J.
2016-01-01
Unstructured grid adaptation is a powerful tool to control discretization error for Computational Fluid Dynamics (CFD). It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provides a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity continue to be significant bottlenecks in the CFD work flow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to diffuse grid adaptation technology into production CFD work flows.
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.
Elastic finite-difference method for irregular grids
Oprsal, I.; Zahradnik, J.
1999-01-01
Finite-difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low-velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero-valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fulfills the free-surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
3D magnetospheric parallel hybrid multi-grid method applied to planet-plasma interactions
NASA Astrophysics Data System (ADS)
Leclercq, L.; Modolo, R.; Leblanc, F.; Hess, S.; Mancini, M.
2016-03-01
We present a new method to exploit multiple refinement levels within a 3D parallel hybrid model, developed to study planet-plasma interactions. This model is based on the hybrid formalism: ions are kinetically treated whereas electrons are considered as a inertia-less fluid. Generally, ions are represented by numerical particles whose size equals the volume of the cells. Particles that leave a coarse grid subsequently entering a refined region are split into particles whose volume corresponds to the volume of the refined cells. The number of refined particles created from a coarse particle depends on the grid refinement rate. In order to conserve velocity distribution functions and to avoid calculations of average velocities, particles are not coalesced. Moreover, to ensure the constancy of particles' shape function sizes, the hybrid method is adapted to allow refined particles to move within a coarse region. Another innovation of this approach is the method developed to compute grid moments at interfaces between two refinement levels. Indeed, the hybrid method is adapted to accurately account for the special grid structure at the interfaces, avoiding any overlapping grid considerations. Some fundamental test runs were performed to validate our approach (e.g. quiet plasma flow, Alfven wave propagation). Lastly, we also show a planetary application of the model, simulating the interaction between Jupiter's moon Ganymede and the Jovian plasma.
Adaptive reconnection-based arbitrary Lagrangian Eulerian method
NASA Astrophysics Data System (ADS)
Bo, Wurigen; Shashkov, Mikhail
2015-10-01
eW present a new adaptive Arbitrary Lagrangian Eulerian (ALE) method. This method is based on the reconnection-based ALE (ReALE) methodology of Refs. [35,34,6]. The main elements in a standard ReALE method are: an explicit Lagrangian phase on an arbitrary polygonal (in 2D) mesh in which the solution and positions of grid nodes are updated; a rezoning phase in which a new grid is defined by changing the connectivity (using Voronoi tessellation) but not the number of cells; and a remapping phase in which the Lagrangian solution is transferred onto the new grid. In the standard ReALE method, the rezoned mesh is smoothed by using one or several steps toward centroidal Voronoi tessellation, but it is not adapted to the solution in any way. In the current paper we present a new adaptive ReALE method, A-ReALE, that is based on the following design principles. First, a monitor function (or error indicator) based on the Hessian of some flow parameter(s) is utilized. Second, an equi-distribution principle for the monitor function is used as a criterion for adapting the mesh. Third, a centroidal Voronoi tessellation is used to adapt the mesh. Fourth, we scale the monitor function to avoid very small and large cells and then smooth it to permit the use of theoretical results related to weighted centroidal Voronoi tessellation. In the A-ReALE method, both number of cells and their locations are allowed to change at the rezone stage on each time step. The number of generators at each time step is chosen to guarantee the required spatial resolution in regions where monitor function reaches its maximum value. We present all details required for implementation of new adaptive A-ReALE method and demonstrate its performance in comparison with standard ReALE method on series of numerical examples.
Comparison of local grid refinement methods for MODFLOW
Mehl, S.; Hill, M.C.; Leake, S.A.
2006-01-01
Many ground water modeling efforts use a finite-difference method to solve the ground water flow equation, and many of these models require a relatively fine-grid discretization to accurately represent the selected process in limited areas of interest. Use of a fine grid over the entire domain can be computationally prohibitive; using a variably spaced grid can lead to cells with a large aspect ratio and refinement in areas where detail is not needed. One solution is to use local-grid refinement (LGR) whereby the grid is only refined in the area of interest. This work reviews some LGR methods and identifies advantages and drawbacks in test cases using MODFLOW-2000. The first test case is two dimensional and heterogeneous; the second is three dimensional and includes interaction with a meandering river. Results include simulations using a uniform fine grid, a variably spaced grid, a traditional method of LGR without feedback, and a new shared node method with feedback. Discrepancies from the solution obtained with the uniform fine grid are investigated. For the models tested, the traditional one-way coupled approaches produced discrepancies in head up to 6.8% and discrepancies in cell-to-cell fluxes up to 7.1%, while the new method has head and cell-to-cell flux discrepancies of 0.089% and 0.14%, respectively. Additional results highlight the accuracy, flexibility, and CPU time trade-off of these methods and demonstrate how the new method can be successfully implemented to model surface water-ground water interactions. Copyright ?? 2006 The Author(s).
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.
Adapting implicit methods to parallel processors
Reeves, L.; McMillin, B.; Okunbor, D.; Riggins, D.
1994-12-31
When numerically solving many types of partial differential equations, it is advantageous to use implicit methods because of their better stability and more flexible parameter choice, (e.g. larger time steps). However, since implicit methods usually require simultaneous knowledge of the entire computational domain, these methods axe difficult to implement directly on distributed memory parallel processors. This leads to infrequent use of implicit methods on parallel/distributed systems. The usual implementation of implicit methods is inefficient due to the nature of parallel systems where it is common to take the computational domain and distribute the grid points over the processors so as to maintain a relatively even workload per processor. This creates a problem at the locations in the domain where adjacent points are not on the same processor. In order for the values at these points to be calculated, messages have to be exchanged between the corresponding processors. Without special adaptation, this will result in idle processors during part of the computation, and as the number of idle processors increases, the lower the effective speed improvement by using a parallel processor.
Parallel Implementation of an Adaptive Scheme for 3D Unstructured Grids on the SP2
NASA Technical Reports Server (NTRS)
Oliker, Leonid; Biswas, Rupak; Strawn, Roger C.
1996-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing unsteady flows that require local grid modifications to efficiently resolve solution features. For this work, we consider an edge-based adaption scheme that has shown good single-processor performance on the C90. We report on our experience parallelizing this code for the SP2. Results show a 47.OX speedup on 64 processors when 10% of the mesh is randomly refined. Performance deteriorates to 7.7X when the same number of edges are refined in a highly-localized region. This is because almost all mesh adaption is confined to a single processor. However, this problem can be remedied by repartitioning the mesh immediately after targeting edges for refinement but before the actual adaption takes place. With this change, the speedup improves dramatically to 43.6X.
Parallel implementation of an adaptive scheme for 3D unstructured grids on the SP2
NASA Technical Reports Server (NTRS)
Strawn, Roger C.; Oliker, Leonid; Biswas, Rupak
1996-01-01
Dynamic mesh adaption on unstructured grids is a powerful tool for computing unsteady flows that require local grid modifications to efficiently resolve solution features. For this work, we consider an edge-based adaption scheme that has shown good single-processor performance on the C90. We report on our experience parallelizing this code for the SP2. Results show a 47.0X speedup on 64 processors when 10 percent of the mesh is randomly refined. Performance deteriorates to 7.7X when the same number of edges are refined in a highly-localized region. This is because almost all the mesh adaption is confined to a single processor. However, this problem can be remedied by repartitioning the mesh immediately after targeting edges for refinement but before the actual adaption takes place. With this change, the speedup improves dramatically to 43.6X.
Son, Sang-Kil
2011-03-01
We introduce a new numerical grid-based method on unstructured grids in the three-dimensional real-space to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a discrete Laplacian operator based on Voronoi cells and their natural neighbors, featuring high adaptivity and simplicity. To resolve multicenter Coulomb singularity in all-electron calculations of polyatomic molecules, this method utilizes highly adaptive molecular grids which consist of spherical atomic grids. It provides accurate and efficient solutions for the Schroedinger equation and the Poisson equation with the all-electron Coulomb potentials regardless of the coordinate system and the molecular symmetry. For numerical examples, we assess accuracy of the VFD method for electronic structures of one-electron polyatomic systems, and apply the method to the density-functional theory for many-electron polyatomic molecules.
Supersampling method for efficient grid-based electronic structure calculations
NASA Astrophysics Data System (ADS)
Ryu, Seongok; Choi, Sunghwan; Hong, Kwangwoo; Kim, Woo Youn
2016-03-01
The egg-box effect, the spurious variation of energy and force due to the discretization of continuous space, is an inherent vexing problem in grid-based electronic structure calculations. Its effective suppression allowing for large grid spacing is thus crucial for accurate and efficient computations. We here report that the supersampling method drastically alleviates it by eliminating the rapidly varying part of a target function along both radial and angular directions. In particular, the use of the sinc filtering function performs best because as an ideal low pass filter it clearly cuts out the high frequency region beyond allowed by a given grid spacing.
Grid-Adapted FUN3D Computations for the Second High Lift Prediction Workshop
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Rumsey, C. L.; Park, M. A.
2014-01-01
Contributions of the unstructured Reynolds-averaged Navier-Stokes code FUN3D to the 2nd AIAA CFD High Lift Prediction Workshop are described, and detailed comparisons are made with experimental data. Using workshop-supplied grids, results for the clean wing configuration are compared with results from the structured code CFL3D Using the same turbulence model, both codes compare reasonably well in terms of total forces and moments, and the maximum lift is similarly over-predicted for both codes compared to experiment. By including more representative geometry features such as slat and flap brackets and slat pressure tube bundles, FUN3D captures the general effects of the Reynolds number variation, but under-predicts maximum lift on workshop-supplied grids in comparison with the experimental data, due to excessive separation. However, when output-based, off-body grid adaptation in FUN3D is employed, results improve considerably. In particular, when the geometry includes both brackets and the pressure tube bundles, grid adaptation results in a more accurate prediction of lift near stall in comparison with the wind-tunnel data. Furthermore, a rotation-corrected turbulence model shows improved pressure predictions on the outboard span when using adapted grids.
Robust Optimal Adaptive Control Method with Large Adaptive Gain
NASA Technical Reports Server (NTRS)
Nguyen, Nhan T.
2009-01-01
In the presence of large uncertainties, a control system needs to be able to adapt rapidly to regain performance. Fast adaptation is referred to the implementation of adaptive control with a large adaptive gain to reduce the tracking error rapidly. However, a large adaptive gain can lead to high-frequency oscillations which can adversely affect robustness of an adaptive control law. A new adaptive control modification is presented that can achieve robust adaptation with a large adaptive gain without incurring high-frequency oscillations as with the standard model-reference adaptive control. The modification is based on the minimization of the Y2 norm of the tracking error, which is formulated as an optimal control problem. The optimality condition is used to derive the modification using the gradient method. The optimal control modification results in a stable adaptation and allows a large adaptive gain to be used for better tracking while providing sufficient stability robustness. Simulations were conducted for a damaged generic transport aircraft with both standard adaptive control and the adaptive optimal control modification technique. The results demonstrate the effectiveness of the proposed modification in tracking a reference model while maintaining a sufficient time delay margin.
Preliminary Benchmarking of Plinian Eruption Simulations Using an Adaptive Grid Eulerian Technique
NASA Astrophysics Data System (ADS)
Peterson, A. H.; Ogden, D. E.; Wohletz, K. H.; Gisler, G.; Glatzmaier, G. A.
2005-12-01
The SAGE (SAIC Adaptive Grid Eulerian) code is an Eulerian hydrodynamics numerical technique employing adaptive mesh refinement at each cycle for every cell in 1-, 2-, and 3-D grids. It is primarily designed to solve high deformation flow of multiple materials and thus provides important capabilities for simulating volcanic eruption phenomena. Its multimaterial equation of state libraries includes a comprehensive coverage of water from solid ice through two-phase liquid and vapor to supercritical states approaching the Hugoniot, and extremely important aspect for simulating volcanic gases in general. In development are strength and failure rules that model non-Newtonian fluid/solid deformation. Because of the low effective sound speeds of eruptive mixtures, the facts that SAGE uses a piecewise, linear, multi-material, Gudonov numerical method to resolve shocks with second-order precision and exactly conserves mass, momentum, and energy, are a highly desirable attributes. Although this code has been previously used to simulate a volcanic eruption (i.e., eruption through a crater lake at Ruapehu volcano by Morrissey and Gisler), we are embarking in an effort to benchmark the code with CFDLib, a well-validated arbitrary Lagrangian-Eulerian code developed at Los Alamos National Laboratory. Through this effort we expect to better understand the strengths and weaknesses, the limitations, and provide direction for important enhancement of SAGE, and potentially provide the volcanological community with a powerful alternative to numerical codes currently available. At this point in our benchmarking, we demonstrate some results for fluid convection within a chamber and fluid jetting through a conduit.
Application of a solution adaptive grid scheme, SAGE, to complex three-dimensional flows
NASA Technical Reports Server (NTRS)
Davies, Carol B.; Venkatapathy, Ethiraj
1991-01-01
A new three-dimensional (3D) adaptive grid code based on the algebraic, solution-adaptive scheme of Nakahashi and Deiwert is developed and applied to a variety of problems. The new computer code, SAGE, is an extension of the same-named two-dimensional (2D) solution-adaptive program that has already proven to be a powerful tool in computational fluid dynamics applications. The new code has been applied to a range of complex three-dimensional, supersonic and hypersonic flows. Examples discussed are a tandem-slot fuel injector, the hypersonic forebody of the Aeroassist Flight Experiment (AFE), the 3D base flow behind the AFE, the supersonic flow around a 3D swept ramp and a generic, hypersonic, 3D nozzle-plume flow. The associated adapted grids and the solution enhancements resulting from the grid adaption are presented for these cases. Three-dimensional adaption is more complex than its 2D counterpart, and the complexities unique to the 3D problems are discussed.
Multigrid-based grid-adaptive solution of the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Michelsen, Jess
A finite volume scheme for solution of the incompressible Navier-Stokes equations in two dimensions and axisymmetry is described. Solutions are obtained on nonorthogonal, solution adaptive BFC grids, based on the Brackbill-Saltzman generator. Adaptivity is achieved by the use of a single control function based on the local kinetic energy production. Nonstaggered allocation of pressure and Cartesian velocity components avoids the introduction of curvature terms associated with the use of a grid-direction vector-base. A special interpolation of the pressure correction equation in the SIMPLE algorithm ensures firm coupling between velocity and pressure field. Steady-state solutions are accelerated by a full approximation multigrid scheme working on the decoupled grid-flow problem, while an algebraic multigrid scheme is employed for the pressure correction equation.
Automatic off-body overset adaptive Cartesian mesh method based on an octree approach
Peron, Stephanie; Benoit, Christophe
2013-01-01
This paper describes a method for generating adaptive structured Cartesian grids within a near-body/off-body mesh partitioning framework for the flow simulation around complex geometries. The off-body Cartesian mesh generation derives from an octree structure, assuming each octree leaf node defines a structured Cartesian block. This enables one to take into account the large scale discrepancies in terms of resolution between the different bodies involved in the simulation, with minimum memory requirements. Two different conversions from the octree to Cartesian grids are proposed: the first one generates Adaptive Mesh Refinement (AMR) type grid systems, and the second one generates abutting or minimally overlapping Cartesian grid set. We also introduce an algorithm to control the number of points at each adaptation, that automatically determines relevant values of the refinement indicator driving the grid refinement and coarsening. An application to a wing tip vortex computation assesses the capability of the method to capture accurately the flow features.
Lattice Boltzmann method on unstructured grids: further developments.
Ubertini, S; Bella, G; Succi, S
2003-07-01
We discuss further developments of the finite-volume lattice Boltzmann formulation on unstructured grids. It is shown that the method tolerates significant grid distortions without showing any appreciable numerical viscosity effects at second order in the mesh size. A theoretical argument of plausibility for such a property is presented. In addition, a set of boundary conditions which permit to handle flows with open boundaries is also introduced and numerically demonstrated for the case of channel flows and driven cavity flows. PMID:12935281
White Light Schlieren Optics Using Bacteriorhodopsin as an Adaptive Image Grid
NASA Technical Reports Server (NTRS)
Peale, Robert; Ruffin, Boh; Donahue, Jeff; Barrett, Carolyn
1996-01-01
A Schlieren apparatus using a bacteriorhodopsin film as an adaptive image grid with white light illumination is demonstrated for the first time. The time dependent spectral properties of the film are characterized. Potential applications include a single-ended Schlieren system for leak detection.
SIMULATION OF A REACTING POLLUTANT PUFF USING AN ADAPTIVE GRID ALGORITHM
A new dynamic solution adaptive grid algorithm DSAGA-PPM, has been developed for use in air quality modeling. In this paper, this algorithm is described and evaluated with a test problem. Cone-shaped distributions of various chemical species undergoing chemical reactions are rota...
Some aspects of adaptive grid technology related to boundary and interior layers
NASA Astrophysics Data System (ADS)
Carey, Graham F.; Anderson, M.; Carnes, B.; Kirk, B.
2004-04-01
We consider the use of adaptive mesh strategies for solution of problems exhibiting boundary and interior layer solutions. As the presence of these layer structures suggests, reliable and accurate solution of this class of problems using finite difference, finite volume or finite element schemes requires grading the mesh into the layers and due attention to the associated algorithms. When the nature and structure of the layer is known, mesh grading can be achieved during the grid generation by specifying an appropriate grading function. However, in many applications the location and nature of the layer behavior is not known in advance. Consequently, adaptive mesh techniques that employ feedback from intermediate grid solutions are an appealing approach. In this paper, we provide a brief overview of the main adaptive grid strategies in the context of problems with layers. Associated error indicators that guide the refinement feedback control/grid optimization process are also covered and there is a brief commentary on the supporting data structure requirements. Some current issues concerning the use of stabilization in conjunction with adaptive mesh refinement (AMR), the question of "pollution effects" in computation of local error indicators, the influence of nonlinearities and the design of meshes for targeted optimization of specific quantities are considered. The application of AMR for layer problems is illustrated by means of case studies from semiconductor device transport (drift diffusion), nonlinear reaction-diffusion, layers due to surface capillary effects, and shockwaves in compressible gas dynamics.
A Cartesian grid embedded boundary method for Poisson`s equation on irregular domains
Johansen, H.; Colella, P.
1997-01-31
The authors present a numerical method for solving Poisson`s equation, with variable coefficients and Dirichlet boundary conditions, on two-dimensional regions. The approach uses a finite-volume discretization, which embeds the domain in a regular Cartesian grid. They treat the solution as a cell-centered quantity, even when those centers are outside the domain. Cells that contain a portion of the domain boundary use conservation differencing of second-order accurate fluxes, on each cell volume. The calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes. This allows them to use multi-grid iterations with a simple point relaxation strategy. They have combined this with an adaptive mesh refinement (AMR) procedure. They provide evidence that the algorithm is second-order accurate on various exact solutions, and compare the adaptive and non-adaptive calculations.
A method for generating volumetric fault zone grids for pillar gridded reservoir models
NASA Astrophysics Data System (ADS)
Qu, Dongfang; Røe, Per; Tveranger, Jan
2015-08-01
The internal structure and petrophysical property distribution of fault zones are commonly exceedingly complex compared to the surrounding host rock from which they are derived. This in turn produces highly complex fluid flow patterns which affect petroleum migration and trapping as well as reservoir behavior during production and injection. Detailed rendering and forecasting of fluid flow inside fault zones require high-resolution, explicit models of fault zone structure and properties. A fundamental requirement for achieving this is the ability to create volumetric grids in which modeling of fault zone structures and properties can be performed. Answering this need, a method for generating volumetric fault zone grids which can be seamlessly integrated into existing standard reservoir modeling tools is presented. The algorithm has been tested on a wide range of fault configurations of varying complexity, providing flexible modeling grids which in turn can be populated with fault zone structures and properties.
A HYBRID SOLAR WIND MODEL OF THE CESE+HLL METHOD WITH A YIN-YANG OVERSET GRID AND AN AMR GRID
Feng Xueshang; Zhang Shaohua; Xiang Changqing; Yang Liping; Jiang Chaowei; Wu, S. T.
2011-06-10
A hybrid three-dimensional (3D) MHD model for solar wind study is proposed in the present paper with combined grid systems and solvers. The computational domain from the Sun to Earth space is decomposed into the near-Sun and off-Sun domains, which are respectively constructed with a Yin-Yang overset grid system and a Cartesian adaptive mesh refinement (AMR) grid system and coupled with a domain connection interface in the overlapping region between the near-Sun and off-Sun domains. The space-time conservation element and solution element method is used in the near-Sun domain, while the Harten-Lax-Leer method is employed in the off-Sun domain. The Yin-Yang overset grid can avoid well-known singularity and polar grid convergence problems and its body-fitting property helps achieve high-quality resolution near the solar surface. The block structured AMR Cartesian grid can automatically capture far-field plasma flow features, such as heliospheric current sheets and shock waves, and at the same time, it can save significant computational resources compared to the uniformly structured Cartesian grid. A numerical study of the solar wind structure for Carrington rotation 2069 shows that the newly developed hybrid MHD solar wind model successfully produces many realistic features of the background solar wind, in both the solar corona and interplanetary space, by comparisons with multiple solar and interplanetary observations.
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
Sjogreen, B; Yee, H C
2007-12-12
Flows containing steady or nearly steady strong shocks in parts of the flow field, and unsteady turbulence with shocklets on other parts of the flow field are difficult to capture accurately and efficiently employing the same numerical scheme even under the multiblock grid or adaptive grid refinement framework. On one hand, sixth-order or higher shock-capturing methods are appropriate for unsteady turbulence with shocklets. On the other hand, lower order shock-capturing methods are more effective for strong steady shocks in terms of convergence. In order to minimize the shortcomings of low order and high order shock-capturing schemes for the subject flows, a multi-block overlapping grid with different orders of accuracy on different blocks is proposed. Test cases to illustrate the performance of the new solver are included.
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Pernice, M.; Johnson, C.R.; Smith, P.J.; Fogelson, A.
1998-12-10
OAK-B135 Final Report: Symposium on Adaptive Methods for Partial Differential Equations. Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
A general hybrid radiation transport scheme for star formation simulations on an adaptive grid
Klassen, Mikhail; Pudritz, Ralph E.; Kuiper, Rolf; Peters, Thomas; Banerjee, Robi; Buntemeyer, Lars
2014-12-10
Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate method for solving the radiation transfer problem. We describe the implementation of a hybrid radiation transport scheme in the adaptive grid-based FLASH general magnetohydrodyanmics code. The hybrid scheme splits the radiative transport problem into a raytracing step and a diffusion step. The raytracer captures the first absorption event, as stars irradiate their environments, while the evolution of the diffuse component of the radiation field is handled by a flux-limited diffusion solver. We demonstrate the accuracy of our method through a variety of benchmark tests including the irradiation of a static disk, subcritical and supercritical radiative shocks, and thermal energy equilibration. We also demonstrate the capability of our method for casting shadows and calculating gas and dust temperatures in the presence of multiple stellar sources. Our method enables radiation-hydrodynamic studies of young stellar objects, protostellar disks, and clustered star formation in magnetized, filamentary environments.
A General Hybrid Radiation Transport Scheme for Star Formation Simulations on an Adaptive Grid
NASA Astrophysics Data System (ADS)
Klassen, Mikhail; Kuiper, Rolf; Pudritz, Ralph E.; Peters, Thomas; Banerjee, Robi; Buntemeyer, Lars
2014-12-01
Radiation feedback plays a crucial role in the process of star formation. In order to simulate the thermodynamic evolution of disks, filaments, and the molecular gas surrounding clusters of young stars, we require an efficient and accurate method for solving the radiation transfer problem. We describe the implementation of a hybrid radiation transport scheme in the adaptive grid-based FLASH general magnetohydrodyanmics code. The hybrid scheme splits the radiative transport problem into a raytracing step and a diffusion step. The raytracer captures the first absorption event, as stars irradiate their environments, while the evolution of the diffuse component of the radiation field is handled by a flux-limited diffusion solver. We demonstrate the accuracy of our method through a variety of benchmark tests including the irradiation of a static disk, subcritical and supercritical radiative shocks, and thermal energy equilibration. We also demonstrate the capability of our method for casting shadows and calculating gas and dust temperatures in the presence of multiple stellar sources. Our method enables radiation-hydrodynamic studies of young stellar objects, protostellar disks, and clustered star formation in magnetized, filamentary environments.
Structure overset grid method and its applications to simulation of multi-body separation
NASA Astrophysics Data System (ADS)
Zhang, HaiRui; Fan, JingJing; Yuan, Wu; Zhang, WeiHua
2015-09-01
This paper proposes an automatic structure overset grid method, which utilizes the hole-surface optimization with one-step searching, wall-surface grid oversetting, and dynamic overset grid approaches to achieve the high adaptability of overset grids for complex multi-body aircrafts. Specifically, based on the automatic structure overset grids, the method first solves the coupling of Navier-Stokes (N-S) unsteady flow equation and 6DOF motion equation, and establishes the multi-body collision model. Then, the numerical simulation of unsteady flow for complex aircrafts' multi-body separation, the simulation of multi-body separating trajectory and the separation safety analysis are accomplished. Thus, the method can properly handle practical engineering problems including the wing/drop tank separation, aircraft/mount separation, and cluster bomb projection. Experiments show that our numerical results match well with experimental results, which demonstrates the effectiveness of our methods in solving the multi-body separation problem for aircrafts with complex shapes.
An adaptive discretization of compressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
Qiu, Linhai; Lu, Wenlong; Fedkiw, Ronald
2016-01-01
We present a novel method for simulating compressible flow on a multitude of Cartesian grids that can rotate and translate. Following previous work, we split the time integration into an explicit step for advection followed by an implicit solve for the pressure. A second order accurate flux based scheme is devised to handle advection on each moving Cartesian grid using an effective characteristic velocity that accounts for the grid motion. In order to avoid the stringent time step restriction imposed by very fine grids, we propose strategies that allow for a fluid velocity CFL number larger than 1. The stringent time step restriction related to the sound speed is alleviated by formulating an implicit linear system in order to find a pressure consistent with the equation of state. This implicit linear system crosses overlapping Cartesian grid boundaries by utilizing local Voronoi meshes to connect the various degrees of freedom obtaining a symmetric positive-definite system. Since a straightforward application of this technique contains an inherent central differencing which can result in spurious oscillations, we introduce a new high order diffusion term similar in spirit to ENO-LLF but solved for implicitly in order to avoid any associated time step restrictions. The method is conservative on each grid, as well as globally conservative on the background grid that contains all other grids. Moreover, a conservative interpolation operator is devised for conservatively remapping values in order to keep them consistent across different overlapping grids. Additionally, the method is extended to handle two-way solid fluid coupling in a monolithic fashion including cases (in the appendix) where solids in close proximity do not properly allow for grid based degrees of freedom in between them.
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.
Effect of Under-Resolved Grids on High Order Methods
NASA Technical Reports Server (NTRS)
Yee, H. C.; Sjoegreen, B.; Mansour, Nagi (Technical Monitor)
2001-01-01
There has been much discussion on verification and validation processes for establishing the credibility of CFD simulations. Since the early 1990s, many of the aeronautical and mechanical engineering related reference journals mandated that any accepted articles in numerical simulations (without known solutions to compared with) need to perform a minimum of one level of grid refinement and time step reduction. Due to the difficulty in analysis, the effect of under-resolved grids and the nonlinear behavior of available spatial discretizations, are scarcely discussed in the literature. Here, an under-resolved numerical simulation is one where the grid spacing being used is too coarse to resolve the smallest physically relevant scales of the chosen continuum governing equations that are of interest to the numerical modeler. With the advent of new developments in fourth-order or higher spatial schemes, it has become common to regard high order schemes as more accurate, reliable and require less grid points. The danger comes when one tries to perform computations with the coarsest grid possible while still hoping to maintain numerical results sufficiently accurate for complex flows, and especially, data-limited problems. On one hand, high order methods when applies to highly coupled multidimensional complex nonlinear problems might have different stability, convergence and reliability behavior than their well studied low order counterparts, especially for nonlinear schemes such as TVD, MUSCL with limiters, ENO, WENO and discrete Galerkin. On the other hand, high order methods involve more operation counts and systematic grid convergence study can be time consuming and prohibitively expansive. At the same time it is difficult to fully understand or categorize the different nonlinear behavior of finite discretizations, especially at the limits of under-resolution when different types of bifurcation phenomena might occur, depending on the combination of grid spacings, time
The development and application of the self-adaptive grid code, SAGE
NASA Technical Reports Server (NTRS)
Davies, Carol B.
1993-01-01
The multidimensional self-adaptive grid code, SAGE, has proven to be a flexible and useful tool in the solution of complex flow problems. Both 2- and 3-D examples given in this report show the code to be reliable and to substantially improve flowfield solutions. Since the adaptive procedure is a marching scheme the code is extremely fast and uses insignificant CPU time compared to the corresponding flow solver. The SAGE program is also machine and flow solver independent. Significant effort was made to simplify user interaction, though some parameters still need to be chosen with care. It is also difficult to tell when the adaption process has provided its best possible solution. This is particularly true if no experimental data are available or if there is a lack of theoretical understanding of the flow. Another difficulty occurs if local features are important but missing in the original grid; the adaption to this solution will not result in any improvement, and only grid refinement can result in an improved solution. These are complex issues that need to be explored within the context of each specific problem.
Simple method for model reference adaptive control
NASA Technical Reports Server (NTRS)
Seraji, H.
1989-01-01
A simple method is presented for combined signal synthesis and parameter adaptation within the framework of model reference adaptive control theory. The results are obtained using a simple derivation based on an improved Liapunov function.
An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.
2003-01-01
An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.
Scenario generation for stochastic optimization problems via the sparse grid method
Chen, Michael; Mehrotra, Sanjay; Papp, David
2015-04-19
We study the use of sparse grids in the scenario generation (or discretization) problem in stochastic programming problems where the uncertainty is modeled using a continuous multivariate distribution. We show that, under a regularity assumption on the random function involved, the sequence of optimal objective function values of the sparse grid approximations converges to the true optimal objective function values as the number of scenarios increases. The rate of convergence is also established. We treat separately the special case when the underlying distribution is an affine transform of a product of univariate distributions, and show how the sparse grid methodmore » can be adapted to the distribution by the use of quadrature formulas tailored to the distribution. We numerically compare the performance of the sparse grid method using different quadrature rules with classic quasi-Monte Carlo (QMC) methods, optimal rank-one lattice rules, and Monte Carlo (MC) scenario generation, using a series of utility maximization problems with up to 160 random variables. The results show that the sparse grid method is very efficient, especially if the integrand is sufficiently smooth. In such problems the sparse grid scenario generation method is found to need several orders of magnitude fewer scenarios than MC and QMC scenario generation to achieve the same accuracy. As a result, it is indicated that the method scales well with the dimension of the distribution--especially when the underlying distribution is an affine transform of a product of univariate distributions, in which case the method appears scalable to thousands of random variables.« less
NASA Astrophysics Data System (ADS)
Singh, B.; Goel, S.
2015-03-01
This paper presents a grid interfaced solar photovoltaic (SPV) energy system with a novel adaptive harmonic detection control for power quality improvement at ac mains under balanced as well as unbalanced and distorted supply conditions. The SPV energy system is capable of compensation of linear and nonlinear loads with the objectives of load balancing, harmonics elimination, power factor correction and terminal voltage regulation. The proposed control increases the utilization of PV infrastructure and brings down its effective cost due to its other benefits. The adaptive harmonic detection control algorithm is used to detect the fundamental active power component of load currents which are subsequently used for reference source currents estimation. An instantaneous symmetrical component theory is used to obtain instantaneous positive sequence point of common coupling (PCC) voltages which are used to derive inphase and quadrature phase voltage templates. The proposed grid interfaced PV energy system is modelled and simulated in MATLAB Simulink and its performance is verified under various operating conditions.
Grid-free simulation of diffusion using random walk methods
NASA Technical Reports Server (NTRS)
Ghoniem, A. F.; Sherman, F. S.
1985-01-01
The simulation of the diffusion of a continuum field by the random walk (RW) displacement of a set of particles is considered. Elements of the gradients of the diffusive concentration are transported by computational particles. It is demonstrated that, by the use of concentration gradients in the RW process, statistical errors are reduced and each realization of the numerical solution is a representation of the exact solution. The algorithm is grid-free, and the computational elements move to follow the gradients; hence, the algorithm is self-adaptive, and uniform resolution is achieved for all times.
Final Report: Symposium on Adaptive Methods for Partial Differential Equations
Pernice, Michael; Johnson, Christopher R.; Smith, Philip J.; Fogelson, Aaron
1998-12-08
Complex physical phenomena often include features that span a wide range of spatial and temporal scales. Accurate simulation of such phenomena can be difficult to obtain, and computations that are under-resolved can even exhibit spurious features. While it is possible to resolve small scale features by increasing the number of grid points, global grid refinement can quickly lead to problems that are intractable, even on the largest available computing facilities. These constraints are particularly severe for three dimensional problems that involve complex physics. One way to achieve the needed resolution is to refine the computational mesh locally, in only those regions where enhanced resolution is required. Adaptive solution methods concentrate computational effort in regions where it is most needed. These methods have been successfully applied to a wide variety of problems in computational science and engineering. Adaptive methods can be difficult to implement, prompting the development of tools and environments to facilitate their use. To ensure that the results of their efforts are useful, algorithm and tool developers must maintain close communication with application specialists. Conversely it remains difficult for application specialists who are unfamiliar with the methods to evaluate the trade-offs between the benefits of enhanced local resolution and the effort needed to implement an adaptive solution method.
NASA Astrophysics Data System (ADS)
Anderson, Robert; Pember, Richard; Elliott, Noah
2001-11-01
We present a method, ALE-AMR, for modeling unsteady compressible flow that combines a staggered grid arbitrary Lagrangian-Eulerian (ALE) scheme with structured local adaptive mesh refinement (AMR). The ALE method is a three step scheme on a staggered grid of quadrilateral cells: Lagrangian advance, mesh relaxation, and remap. The AMR scheme uses a mesh hierarchy that is dynamic in time and is composed of nested structured grids of varying resolution. The integration algorithm on the hierarchy is a recursive procedure in which the coarse grids are advanced a single time step, the fine grids are advanced to the same time, and the coarse and fine grid solutions are synchronized. The novel details of ALE-AMR are primarily motivated by the need to reconcile and extend AMR techniques typically employed for stationary rectangular meshes with cell-centered quantities to the moving quadrilateral meshes with staggered quantities used in the ALE scheme. Solutions of several test problems are discussed.
Jakeman, J.D. Wildey, T.
2015-01-01
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the physical discretization error and the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity of the sparse grid. Utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.
Development of the Finite Difference Time Domain Method on a Lebedev Grid for Anisotropic Materials
NASA Astrophysics Data System (ADS)
Nauta, Marcel D.
The finite-difference time-domain (FDTD) method is derived on a Lebedev grid, instead of the standard Yee grid, to better represent the constitutive relations in anisotropic materials. The Lebedev grid extends the Yee grid by approximating Maxwell's equations with tensor constitutive relations using only central differences. A dispersion relation with stability criteria is derived and it is proven that the Lebedev grid has a consistent calculus. An integral derivation of the update equations illustrates how to appropriately excite the grid. This approach is also used to derive the update equations at planar material interfaces and domain edge PEC. Lebedev grid results are compared with analytical and Yee grid solutions using an equal memory comparison. Numerical results show that the Lebedev grid suffers greater dispersion error but better represents material interfaces. Focus is given to generalizing the concepts that make the Yee grid robust for isotropic materials. Keywords: FDTD, anisotropic materials, Lebedev grid, collocated grids.
A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids.
Boschitsch, Alexander H; Fenley, Marcia O
2011-05-10
An adaptive Cartesian grid (ACG) concept is presented for the fast and robust numerical solution of the 3D Poisson-Boltzmann Equation (PBE) governing the electrostatic interactions of large-scale biomolecules and highly charged multi-biomolecular assemblies such as ribosomes and viruses. The ACG offers numerous advantages over competing grid topologies such as regular 3D lattices and unstructured grids. For very large biological molecules and multi-biomolecule assemblies, the total number of grid-points is several orders of magnitude less than that required in a conventional lattice grid used in the current PBE solvers thus allowing the end user to obtain accurate and stable nonlinear PBE solutions on a desktop computer. Compared to tetrahedral-based unstructured grids, ACG offers a simpler hierarchical grid structure, which is naturally suited to multigrid, relieves indirect addressing requirements and uses fewer neighboring nodes in the finite difference stencils. Construction of the ACG and determination of the dielectric/ionic maps are straightforward, fast and require minimal user intervention. Charge singularities are eliminated by reformulating the problem to produce the reaction field potential in the molecular interior and the total electrostatic potential in the exterior ionic solvent region. This approach minimizes grid-dependency and alleviates the need for fine grid spacing near atomic charge sites. The technical portion of this paper contains three parts. First, the ACG and its construction for general biomolecular geometries are described. Next, a discrete approximation to the PBE upon this mesh is derived. Finally, the overall solution procedure and multigrid implementation are summarized. Results obtained with the ACG-based PBE solver are presented for: (i) a low dielectric spherical cavity, containing interior point charges, embedded in a high dielectric ionic solvent - analytical solutions are available for this case, thus allowing rigorous
Multi-Dimensional Spectral Difference Method for Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
2005-01-01
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.
Adjoint-Based, Three-Dimensional Error Prediction and Grid Adaptation
NASA Technical Reports Server (NTRS)
Park, Michael A.
2002-01-01
Engineering computational fluid dynamics (CFD) analysis and design applications focus on output functions (e.g., lift, drag). Errors in these output functions are generally unknown and conservatively accurate solutions may be computed. Computable error estimates can offer the possibility to minimize computational work for a prescribed error tolerance. Such an estimate can be computed by solving the flow equations and the linear adjoint problem for the functional of interest. The computational mesh can be modified to minimize the uncertainty of a computed error estimate. This robust mesh-adaptation procedure automatically terminates when the simulation is within a user specified error tolerance. This procedure for estimating and adapting to error in a functional is demonstrated for three-dimensional Euler problems. An adaptive mesh procedure that links to a Computer Aided Design (CAD) surface representation is demonstrated for wing, wing-body, and extruded high lift airfoil configurations. The error estimation and adaptation procedure yielded corrected functions that are as accurate as functions calculated on uniformly refined grids with ten times as many grid points.
Guba, O.; Taylor, M. A.; Ullrich, P. A.; Overfelt, J. R.; Levy, M. N.
2014-06-25
We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable resolution grids using the shallow water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution dependent coefficient. For the spectral element method with variable resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity ismore » constructed so that for regions of uniform resolution it matches the traditional constant coefficient hyperviscsosity. With the tensor hyperviscosity the large scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications where long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less
Guba, O.; Taylor, M. A.; Ullrich, P. A.; Overfelt, J. R.; Levy, M. N.
2014-11-27
We evaluate the performance of the Community Atmosphere Model's (CAM) spectral element method on variable-resolution grids using the shallow-water equations in spherical geometry. We configure the method as it is used in CAM, with dissipation of grid scale variance, implemented using hyperviscosity. Hyperviscosity is highly scale selective and grid independent, but does require a resolution-dependent coefficient. For the spectral element method with variable-resolution grids and highly distorted elements, we obtain the best results if we introduce a tensor-based hyperviscosity with tensor coefficients tied to the eigenvalues of the local element metric tensor. The tensor hyperviscosity is constructed so that, formore » regions of uniform resolution, it matches the traditional constant-coefficient hyperviscosity. With the tensor hyperviscosity, the large-scale solution is almost completely unaffected by the presence of grid refinement. This later point is important for climate applications in which long term climatological averages can be imprinted by stationary inhomogeneities in the truncation error. We also evaluate the robustness of the approach with respect to grid quality by considering unstructured conforming quadrilateral grids generated with a well-known grid-generating toolkit and grids generated by SQuadGen, a new open source alternative which produces lower valence nodes.« less
Gutowski, William J.; Prusa, Joseph M.; Smolarkiewicz, Piotr K.
2012-05-08
This project had goals of advancing the performance capabilities of the numerical general circulation model EULAG and using it to produce a fully operational atmospheric global climate model (AGCM) that can employ either static or dynamic grid stretching for targeted phenomena. The resulting AGCM combined EULAG's advanced dynamics core with the "physics" of the NCAR Community Atmospheric Model (CAM). Effort discussed below shows how we improved model performance and tested both EULAG and the coupled CAM-EULAG in several ways to demonstrate the grid stretching and ability to simulate very well a wide range of scales, that is, multi-scale capability. We leveraged our effort through interaction with an international EULAG community that has collectively developed new features and applications of EULAG, which we exploited for our own work summarized here. Overall, the work contributed to over 40 peer-reviewed publications and over 70 conference/workshop/seminar presentations, many of them invited. 3a. EULAG Advances EULAG is a non-hydrostatic, parallel computational model for all-scale geophysical flows. EULAG's name derives from its two computational options: EULerian (flux form) or semi-LAGrangian (advective form). The model combines nonoscillatory forward-in-time (NFT) numerical algorithms with a robust elliptic Krylov solver. A signature feature of EULAG is that it is formulated in generalized time-dependent curvilinear coordinates. In particular, this enables grid adaptivity. In total, these features give EULAG novel advantages over many existing dynamical cores. For EULAG itself, numerical advances included refining boundary conditions and filters for optimizing model performance in polar regions. We also added flexibility to the model's underlying formulation, allowing it to work with the pseudo-compressible equation set of Durran in addition to EULAG's standard anelastic formulation. Work in collaboration with others also extended the demonstrated range of
Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel; Wang, Z. J.
2004-01-01
A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. A discussion on the Discontinuous Spectral Difference (SD) Method, locations of the unknowns and flux points and numerical results are also presented.
New iterative gridding algorithm using conjugate gradient method
NASA Astrophysics Data System (ADS)
Jiang, Xuguang; Thedens, Daniel
2004-05-01
Non-uniformly sampled data in MRI applications must be interpolated onto a regular Cartesian grid to perform fast image reconstruction using FFT. The conventional method for this is gridding, which requires a density compensation function (DCF). The calculation of DCF may be time-consuming, ambiguously defined, and may not be always reusable due to changes in k-space trajectories. A recently proposed reconstruction method that eliminates the requirement of DCF is block uniform resampling (BURS) which uses singular value decomposition (SVD). However, the SVD is still computationally intensive. In this work, we present a modified BURS algorithm using conjugate gradient method (CGM) in place of direct SVD calculation. Calculation of a block of grid point values in each iteration further reduces the computational load. The new method reduces the calculation complexity while maintaining a high-quality reconstruction result. For an n-by-n matrix, the time complexity per iteration is reduced from O(n*n*n) in SVD to O(n*n) in CGM. The time can be further reduced when we stop the iteration in CGM earlier according to the norm of the residual vector. Using this method, the quality of the reconstructed image improves compared to regularized BURS. The reduced time complexity and improved reconstruction result make the new algorithm promising in dealing with large-sized images and 3D images.
An overset grid method for the study of reflex tearing.
Maki, K L; Braun, R J; Driscoll, T A; King-Smith, P E
2008-09-01
We present an overset grid method to simulate the evolution of human tear film thickness subject to reflex tearing. The free-surface evolution is governed by a single fourth-order non-linear equation derived from lubrication theory with specified film thickness and volume flux at each end. The model arises from considering the limiting case where the surfactant is strongly affecting the surface tension. In numerical simulations, the overset grid is composed of fine boundary grids near the upper and lower eyelids to capture localized capillary thinning referred to as 'black lines' and a Cartesian grid covers the remaining domain. Numerical studies are performed on a non-linear test problem to confirm the accuracy and convergence of the scheme. The computations on the tear film model show qualitative agreement with in vivo tear film thickness measurements. Furthermore, the role of the black lines in the presence of tear supply from the lid margins, reflex tearing, was found to be more subtle than a barrier to tear fluid flow between the anterior of the eye and the meniscus at the lid margin. During reflex tearing, tears may flow through the region normally containing the black line and drift down over the cornea under the influence of gravity.
Overset Grid Methods for Multidisciplinary Applications in Rotorcraft Problems
NASA Technical Reports Server (NTRS)
Ahmad, J. U.; VanDalsem, William R. (Technical Monitor)
1996-01-01
A methodology for the coupling of an advanced computational fluid dynamics method based on an overset grid flow-solver and an advanced computational structural dynamics method based on a finite element analysis is presented. Various procedures for the fluid-structure interactions modeling along with their limitations are also discussed. The flight test data for the four-bladed UH-60A Blackhawk helicopter rotor is chosen for the validation of the results. Convergence and accuracy are tested by numerical experiments with a single-bladed rotor. A comparison of airload predictions with flight test data as well as with a rigid blade case is presented. Grid and interpolation related issues for this aeroelastic application are described.
NASA Technical Reports Server (NTRS)
Lytle, John K.; Harloff, Gary J.; Hsu, Andrew T.
1990-01-01
Previous calculations of jet-in-crossflow problems have been sensitive to the turbulence and artificial viscosity models and to the grid. Consequently, the eddy viscosity model in the PARC3D code was modified to consider the turbulent jet by switching from the Baldwin-Lomax (1978) model to an axisymmetric jet model. A modified artificial viscosity model has been utilized and evaluated in this study as well. The new model includes cell size scaling and a directional dependence in the coefficients. Computational results from PARC3D demonstrate the effects of the viscosity models on the pressure distribution fore and aft of the jet and the ability of the adaptive grid scheme to adjust to the three-dimensional gradients around the jet.
Jakeman, J. D.; Wildey, T.
2015-01-01
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this papermore » we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.« less
Jakeman, J. D.; Wildey, T.
2015-01-01
In this paper we present an algorithm for adaptive sparse grid approximations of quantities of interest computed from discretized partial differential equations. We use adjoint-based a posteriori error estimates of the interpolation error in the sparse grid to enhance the sparse grid approximation and to drive adaptivity. We show that utilizing these error estimates provides significantly more accurate functional values for random samples of the sparse grid approximation. We also demonstrate that alternative refinement strategies based upon a posteriori error estimates can lead to further increases in accuracy in the approximation over traditional hierarchical surplus based strategies. Throughout this paper we also provide and test a framework for balancing the physical discretization error with the stochastic interpolation error of the enhanced sparse grid approximation.
Moire and grid methods: a signal-processing approach
NASA Astrophysics Data System (ADS)
Surrel, Yves
1994-11-01
This presentation is a formulation of moire and grid methods with the vocabulary of signal processing. It addresses basically the case of in-plane geometrical moire, but, as is well known, any geometrical moire setup can be related to in-plane moire. We show that the moire phenomenon is not a measurement method by itself, but only a step in a process of information transmission by spatial frequency modulation. The distortion of a grid bonded onto the surface of a loaded specimen or structure will cause locally a modulation (Delta) F of the spatial frequency vector F of the grid. The modulation (Delta) F is linearly related to the strain and rotation tensors. An equivalent point of view is to consider the same phenomenon as a phase modulation, caused by the inverse displacements. In this approach, moire is presented merely as an analog means of frequency substraction. The interpretation of the classical fringe processing techniques -- temporal and spatial phase shifting, Fourier transform method -- is made, and some consequences of the zoom-in effect induced by the moire phenomenon are given.
Hydrologic extremes - an intercomparison of multiple gridded statistical downscaling methods
NASA Astrophysics Data System (ADS)
Werner, Arelia T.; Cannon, Alex J.
2016-04-01
Gridded statistical downscaling methods are the main means of preparing climate model data to drive distributed hydrological models. Past work on the validation of climate downscaling methods has focused on temperature and precipitation, with less attention paid to the ultimate outputs from hydrological models. Also, as attention shifts towards projections of extreme events, downscaling comparisons now commonly assess methods in terms of climate extremes, but hydrologic extremes are less well explored. Here, we test the ability of gridded downscaling models to replicate historical properties of climate and hydrologic extremes, as measured in terms of temporal sequencing (i.e. correlation tests) and distributional properties (i.e. tests for equality of probability distributions). Outputs from seven downscaling methods - bias correction constructed analogues (BCCA), double BCCA (DBCCA), BCCA with quantile mapping reordering (BCCAQ), bias correction spatial disaggregation (BCSD), BCSD using minimum/maximum temperature (BCSDX), the climate imprint delta method (CI), and bias corrected CI (BCCI) - are used to drive the Variable Infiltration Capacity (VIC) model over the snow-dominated Peace River basin, British Columbia. Outputs are tested using split-sample validation on 26 climate extremes indices (ClimDEX) and two hydrologic extremes indices (3-day peak flow and 7-day peak flow). To characterize observational uncertainty, four atmospheric reanalyses are used as climate model surrogates and two gridded observational data sets are used as downscaling target data. The skill of the downscaling methods generally depended on reanalysis and gridded observational data set. However, CI failed to reproduce the distribution and BCSD and BCSDX the timing of winter 7-day low-flow events, regardless of reanalysis or observational data set. Overall, DBCCA passed the greatest number of tests for the ClimDEX indices, while BCCAQ, which is designed to more accurately resolve event
Hydrologic extremes - an intercomparison of multiple gridded statistical downscaling methods
NASA Astrophysics Data System (ADS)
Werner, A. T.; Cannon, A. J.
2015-06-01
Gridded statistical downscaling methods are the main means of preparing climate model data to drive distributed hydrological models. Past work on the validation of climate downscaling methods has focused on temperature and precipitation, with less attention paid to the ultimate outputs from hydrological models. Also, as attention shifts towards projections of extreme events, downscaling comparisons now commonly assess methods in terms of climate extremes, but hydrologic extremes are less well explored. Here, we test the ability of gridded downscaling models to replicate historical properties of climate and hydrologic extremes, as measured in terms of temporal sequencing (i.e., correlation tests) and distributional properties (i.e., tests for equality of probability distributions). Outputs from seven downscaling methods - bias correction constructed analogues (BCCA), double BCCA (DBCCA), BCCA with quantile mapping reordering (BCCAQ), bias correction spatial disaggregation (BCSD), BCSD using minimum/maximum temperature (BCSDX), climate imprint delta method (CI), and bias corrected CI (BCCI) - are used to drive the Variable Infiltration Capacity (VIC) model over the snow-dominated Peace River basin, British Columbia. Outputs are tested using split-sample validation on 26 climate extremes indices (ClimDEX) and two hydrologic extremes indices (3 day peak flow and 7 day peak flow). To characterize observational uncertainty, four atmospheric reanalyses are used as climate model surrogates and two gridded observational datasets are used as downscaling target data. The skill of the downscaling methods generally depended on reanalysis and gridded observational dataset. However, CI failed to reproduce the distribution and BCSD and BCSDX the timing of winter 7 day low flow events, regardless of reanalysis or observational dataset. Overall, DBCCA passed the greatest number of tests for the ClimDEX indices, while BCCAQ, which is designed to more accurately resolve event
NASA Technical Reports Server (NTRS)
Mccormick, S.; Quinlan, D.
1989-01-01
The fast adaptive composite grid method (FAC) is an algorithm that uses various levels of uniform grids (global and local) to provide adaptive resolution and fast solution of PDEs. Like all such methods, it offers parallelism by using possibly many disconnected patches per level, but is hindered by the need to handle these levels sequentially. The finest levels must therefore wait for processing to be essentially completed on all the coarser ones. A recently developed asynchronous version of FAC, called AFAC, completely eliminates this bottleneck to parallelism. This paper describes timing results for AFAC, coupled with a simple load balancing scheme, applied to the solution of elliptic PDEs on an Intel iPSC hypercube. These tests include performance of certain processes necessary in adaptive methods, including moving grids and changing refinement. A companion paper reports on numerical and analytical results for estimating convergence factors of AFAC applied to very large scale examples.
Methods for Procuring Power System Flexibility, Greening the Grid
Katz, Jessica; Cochran, Jaquelin; Miller, Mackay
2015-05-01
Greening the Grid provides technical assistance to energy system planners, regulators, and grid operators to overcome challenges associated with integrating variable renewable energy into the grid. This document, part of a Greening the Grid toolkit, introduces administrative and incentive-based mechanisms for procuring a cost-effective mix of flexibility sources.
Numerical Modeling of Spray Combustion with an Unstructured-Grid Method
NASA Technical Reports Server (NTRS)
Shang, H. M.; Chen, Y. S.; Liaw, P.; Shih, M. H.; Wang, T. S.
1996-01-01
The present unstructured-grid method follows strictly the basic finite volume forms of the conservation laws of the governing equations for the entire flow domain. High-order spatially accurate formulation has been employed for the numerical solutions of the Navier-Stokes equations. A two-equation k-epsilon turbulence model is also incorporated in the unstructured-grid solver. The convergence of the resulted linear algebraic equation is accelerated with preconditioned Conjugate Gradient method. A statistical spray combustion model has been incorporated into the present unstructured-grid solver. In this model, spray is represented by discrete particles, rather than by continuous distributions. A finite number of computational particles are used to predict a sample of total population of particles. Particle trajectories are integrated using their momentum and motion equations and particles exchange mass, momentum and energy with the gas within the computational cell in which they are located. The interaction calculations are performed simultaneously and eliminate global iteration for the two-phase momentum exchange. A transient spray flame in a high pressure combustion chamber is predicted and then the solution of liquid-fuel combusting flow with a rotating cup atomizer is presented and compared with the experimental data. The major conclusion of this investigation is that the unstructured-grid method can be employed to study very complicated flow fields of turbulent spray combustion. Grid adaptation can be easily achieved in any flow domain such as droplet evaporation and combustion zone. Future applications of the present model can be found in the full three-dimensional study of flow fields of gas turbine and liquid propulsion engine combustion chambers with multi-injectors.
Improving merge methods for grid-based digital elevation models
NASA Astrophysics Data System (ADS)
Leitão, J. P.; Prodanović, D.; Maksimović, Č.
2016-03-01
Digital Elevation Models (DEMs) are used to represent the terrain in applications such as, for example, overland flow modelling or viewshed analysis. DEMs generated from digitising contour lines or obtained by LiDAR or satellite data are now widely available. However, in some cases, the area of study is covered by more than one of the available elevation data sets. In these cases the relevant DEMs may need to be merged. The merged DEM must retain the most accurate elevation information available while generating consistent slopes and aspects. In this paper we present a thorough analysis of three conventional grid-based DEM merging methods that are available in commercial GIS software. These methods are evaluated for their applicability in merging DEMs and, based on evaluation results, a method for improving the merging of grid-based DEMs is proposed. DEMs generated by the proposed method, called MBlend, showed significant improvements when compared to DEMs produced by the three conventional methods in terms of elevation, slope and aspect accuracy, ensuring also smooth elevation transitions between the original DEMs. The results produced by the improved method are highly relevant different applications in terrain analysis, e.g., visibility, or spotting irregularities in landforms and for modelling terrain phenomena, such as overland flow.
Fair Energy Scheduling for Vehicle-to-Grid Networks Using Adaptive Dynamic Programming.
Xie, Shengli; Zhong, Weifeng; Xie, Kan; Yu, Rong; Zhang, Yan
2016-08-01
Research on the smart grid is being given enormous supports worldwide due to its great significance in solving environmental and energy crises. Electric vehicles (EVs), which are powered by clean energy, are adopted increasingly year by year. It is predictable that the huge charge load caused by high EV penetration will have a considerable impact on the reliability of the smart grid. Therefore, fair energy scheduling for EV charge and discharge is proposed in this paper. By using the vehicle-to-grid technology, the scheduler controls the electricity loads of EVs considering fairness in the residential distribution network. We propose contribution-based fairness, in which EVs with high contributions have high priorities to obtain charge energy. The contribution value is defined by both the charge/discharge energy and the timing of the action. EVs can achieve higher contribution values when discharging during the load peak hours. However, charging during this time will decrease the contribution values seriously. We formulate the fair energy scheduling problem as an infinite-horizon Markov decision process. The methodology of adaptive dynamic programming is employed to maximize the long-term fairness by processing online network training. The numerical results illustrate that the proposed EV energy scheduling is able to mitigate and flatten the peak load in the distribution network. Furthermore, contribution-based fairness achieves a fast recovery of EV batteries that have deeply discharged and guarantee fairness in the full charge time of all EVs.
Fair Energy Scheduling for Vehicle-to-Grid Networks Using Adaptive Dynamic Programming.
Xie, Shengli; Zhong, Weifeng; Xie, Kan; Yu, Rong; Zhang, Yan
2016-08-01
Research on the smart grid is being given enormous supports worldwide due to its great significance in solving environmental and energy crises. Electric vehicles (EVs), which are powered by clean energy, are adopted increasingly year by year. It is predictable that the huge charge load caused by high EV penetration will have a considerable impact on the reliability of the smart grid. Therefore, fair energy scheduling for EV charge and discharge is proposed in this paper. By using the vehicle-to-grid technology, the scheduler controls the electricity loads of EVs considering fairness in the residential distribution network. We propose contribution-based fairness, in which EVs with high contributions have high priorities to obtain charge energy. The contribution value is defined by both the charge/discharge energy and the timing of the action. EVs can achieve higher contribution values when discharging during the load peak hours. However, charging during this time will decrease the contribution values seriously. We formulate the fair energy scheduling problem as an infinite-horizon Markov decision process. The methodology of adaptive dynamic programming is employed to maximize the long-term fairness by processing online network training. The numerical results illustrate that the proposed EV energy scheduling is able to mitigate and flatten the peak load in the distribution network. Furthermore, contribution-based fairness achieves a fast recovery of EV batteries that have deeply discharged and guarantee fairness in the full charge time of all EVs. PMID:26930694
Two methods for the study of vortex patch evolution on locally refined grids
Minion, M.L.
1994-05-01
Two numerical methods for the solution of the two-dimensional Euler equations for incompressible flow on locally refined grids are presented. The first is a second order projection method adapted from the method of Bell, Colella, and Glaz. The second method is based on the vorticity-stream function form of the Euler equations and is designed to be free-stream preserving and conservative. Second order accuracy of both methods in time and space is established, and they are shown to agree on problems with a localized vorticity distribution. The filamentation of a perturbed patch of circular vorticity and the merger of two smooth vortex patches are studied. It is speculated that for nearly stable patches of vorticity, an arbitrarily small amount of viscosity is sufficient to effectively eliminate vortex filaments from the evolving patch and that the filamentation process affects the evolution of such patches very little. Solutions of the vortex merger problem show that filamentation is responsible for the creation of large gradients in the vorticity which, in the presence of an arbitrarily small viscosity, will lead to vortex merger. It is speculated that a small viscosity in this problem does not substantially affect the transition of the flow to a statistical equilibrium solution. The main contributions of this thesis concern the formulation and implementation of a projection for refined grids. A careful analysis of the adjointness relation between gradient and divergence operators for a refined grid MAC projection is presented, and a uniformly accurate, approximately stable projection is developed. An efficient multigrid method which exactly solves the projection is developed, and a method for casting certain approximate projections as MAC projections on refined grids is presented.
A multilevel adaptive projection method for unsteady incompressible flow
NASA Technical Reports Server (NTRS)
Howell, Louis H.
1993-01-01
There are two main requirements for practical simulation of unsteady flow at high Reynolds number: the algorithm must accurately propagate discontinuous flow fields without excessive artificial viscosity, and it must have some adaptive capability to concentrate computational effort where it is most needed. We satisfy the first of these requirements with a second-order Godunov method similar to those used for high-speed flows with shocks, and the second with a grid-based refinement scheme which avoids some of the drawbacks associated with unstructured meshes. These two features of our algorithm place certain constraints on the projection method used to enforce incompressibility. Velocities are cell-based, leading to a Laplacian stencil for the projection which decouples adjacent grid points. We discuss features of the multigrid and multilevel iteration schemes required for solution of the resulting decoupled problem. Variable-density flows require use of a modified projection operator--we have found a multigrid method for this modified projection that successfully handles density jumps of thousands to one. Numerical results are shown for the 2D adaptive and 3D variable-density algorithms.
The block adaptive multigrid method applied to the solution of the Euler equations
NASA Technical Reports Server (NTRS)
Pantelelis, Nikos
1993-01-01
In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.
An overset grid method for global geomagnetic induction
NASA Astrophysics Data System (ADS)
Weiss, Chester J.
2014-07-01
A new finite difference solution to the global geomagnetic induction problem is developed and tested, based on a modified Lorenz gauge of the magnetic vector and electric scalar potentials and implementing a novel, overset `Yin-Yang' grid that avoids unnecessary mesh refinement at the geographic poles. Previously used in whole-earth mantle convection models, the overset grid is built from a pair of partially overlapping mid-latitude latitude-longitude (lat/lon) grids, one of which is rotated with respect to the other for complete coverage of the sphere. Because of this symmetry, only one set of finite difference templates is required for global discretization of the governing Maxwell equations, a redundancy that is exploited for computational efficiency and multithreaded parallelization. Comparisons between solutions obtained by the proposed method show excellent agreement with those obtained by independent integral equation methods for 1-D, 2-D and 3-D problem geometries. The computational footprint of the method is minimized through a (non-symmetric) matrix-free BiCG-STAB iterative solver which computes finite difference matrix coefficients `on the fly' as needed, rather than pulling stored values from memory. Scaling of the matrix-free BiCG-STAB algorithm with problem size shows behaviour similar to that seen with the (symmetric) QMR algorithm used in the Cartesian case from which the present algorithm is based. The proposed method may therefore provide a competitive addition to the existing body of global-scale geomagnetic induction modelling algorithms, allowing for resource-efficient forward modelling as the kernel for large-scale computing such as inversion of geomagnetic response functions, computational hypothesis testing and parametric studies of mantle geodynamics and physiochemical state.
NASA Astrophysics Data System (ADS)
Møyner, Olav; Lie, Knut-Andreas
2016-01-01
A wide variety of multiscale methods have been proposed in the literature to reduce runtime and provide better scaling for the solution of Poisson-type equations modeling flow in porous media. We present a new multiscale restricted-smoothed basis (MsRSB) method that is designed to be applicable to both rectilinear grids and unstructured grids. Like many other multiscale methods, MsRSB relies on a coarse partition of the underlying fine grid and a set of local prolongation operators (multiscale basis functions) that map unknowns associated with the fine grid cells to unknowns associated with blocks in the coarse partition. These mappings are constructed by restricted smoothing: Starting from a constant, a localized iterative scheme is applied directly to the fine-scale discretization to compute prolongation operators that are consistent with the local properties of the differential operators. The resulting method has three main advantages: First of all, both the coarse and the fine grid can have general polyhedral geometry and unstructured topology. This means that partitions and good prolongation operators can easily be constructed for complex models involving high media contrasts and unstructured cell connections introduced by faults, pinch-outs, erosion, local grid refinement, etc. In particular, the coarse partition can be adapted to geological or flow-field properties represented on cells or faces to improve accuracy. Secondly, the method is accurate and robust when compared to existing multiscale methods and does not need expensive recomputation of local basis functions to account for transient behavior: Dynamic mobility changes are incorporated by continuing to iterate a few extra steps on existing basis functions. This way, the cost of updating the prolongation operators becomes proportional to the amount of change in fluid mobility and one reduces the need for expensive, tolerance-based updates. Finally, since the MsRSB method is formulated on top of a cell
Method and system for managing power grid data
Yin, Jian; Akyol, Bora A.; Gorton, Ian
2015-11-10
A system and method of managing time-series data for smart grids is disclosed. Data is collected from a plurality of sensors. An index is modified for a newly created block. A one disk operation per read or write is performed. The one disk operation per read includes accessing and looking up the index to locate the data without movement of an arm of the disk, and obtaining the data. The one disk operation per write includes searching the disk for free space, calculating an offset, modifying the index, and writing the data contiguously into a block of the disk the index points to.
Adaptive computational methods for aerothermal heating analysis
NASA Technical Reports Server (NTRS)
Price, John M.; Oden, J. Tinsley
1988-01-01
The development of adaptive gridding techniques for finite-element analysis of fluid dynamics equations is described. The developmental work was done with the Euler equations with concentration on shock and inviscid flow field capturing. Ultimately this methodology is to be applied to a viscous analysis for the purpose of predicting accurate aerothermal loads on complex shapes subjected to high speed flow environments. The development of local error estimate strategies as a basis for refinement strategies is discussed, as well as the refinement strategies themselves. The application of the strategies to triangular elements and a finite-element flux-corrected-transport numerical scheme are presented. The implementation of these strategies in the GIM/PAGE code for 2-D and 3-D applications is documented and demonstrated.
Risky Group Decision-Making Method for Distribution Grid Planning
NASA Astrophysics Data System (ADS)
Li, Cunbin; Yuan, Jiahang; Qi, Zhiqiang
2015-12-01
With rapid speed on electricity using and increasing in renewable energy, more and more research pay attention on distribution grid planning. For the drawbacks of existing research, this paper proposes a new risky group decision-making method for distribution grid planning. Firstly, a mixing index system with qualitative and quantitative indices is built. On the basis of considering the fuzziness of language evaluation, choose cloud model to realize "quantitative to qualitative" transformation and construct interval numbers decision matrices according to the "3En" principle. An m-dimensional interval numbers decision vector is regarded as super cuboids in m-dimensional attributes space, using two-level orthogonal experiment to arrange points uniformly and dispersedly. The numbers of points are assured by testing numbers of two-level orthogonal arrays and these points compose of distribution points set to stand for decision-making project. In order to eliminate the influence of correlation among indices, Mahalanobis distance is used to calculate the distance from each solutions to others which means that dynamic solutions are viewed as the reference. Secondly, due to the decision-maker's attitude can affect the results, this paper defines the prospect value function based on SNR which is from Mahalanobis-Taguchi system and attains the comprehensive prospect value of each program as well as the order. At last, the validity and reliability of this method is illustrated by examples which prove the method is more valuable and superiority than the other.
Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics
NASA Astrophysics Data System (ADS)
Martí, José María; Müller, Ewald
2015-12-01
An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates.
A sparse grid based method for generative dimensionality reduction of high-dimensional data
NASA Astrophysics Data System (ADS)
Bohn, Bastian; Garcke, Jochen; Griebel, Michael
2016-03-01
Generative dimensionality reduction methods play an important role in machine learning applications because they construct an explicit mapping from a low-dimensional space to the high-dimensional data space. We discuss a general framework to describe generative dimensionality reduction methods, where the main focus lies on a regularized principal manifold learning variant. Since most generative dimensionality reduction algorithms exploit the representer theorem for reproducing kernel Hilbert spaces, their computational costs grow at least quadratically in the number n of data. Instead, we introduce a grid-based discretization approach which automatically scales just linearly in n. To circumvent the curse of dimensionality of full tensor product grids, we use the concept of sparse grids. Furthermore, in real-world applications, some embedding directions are usually more important than others and it is reasonable to refine the underlying discretization space only in these directions. To this end, we employ a dimension-adaptive algorithm which is based on the ANOVA (analysis of variance) decomposition of a function. In particular, the reconstruction error is used to measure the quality of an embedding. As an application, the study of large simulation data from an engineering application in the automotive industry (car crash simulation) is performed.
NASA Technical Reports Server (NTRS)
Shih, T. I.-P.; Bailey, R. T.; Nguyen, H. L.; Roelke, R. J.
1990-01-01
An efficient computer program, called GRID2D/3D was developed to generate single and composite grid systems within geometrically complex two- and three-dimensional (2- and 3-D) spatial domains that can deform with time. GRID2D/3D generates single grid systems by using algebraic grid generation methods based on transfinite interpolation in which the distribution of grid points within the spatial domain is controlled by stretching functions. All single grid systems generated by GRID2D/3D can have grid lines that are continuous and differentiable everywhere up to the second-order. Also, grid lines can intersect boundaries of the spatial domain orthogonally. GRID2D/3D generates composite grid systems by patching together two or more single grid systems. The patching can be discontinuous or continuous. For continuous composite grid systems, the grid lines are continuous and differentiable everywhere up to the second-order except at interfaces where different single grid systems meet. At interfaces where different single grid systems meet, the grid lines are only differentiable up to the first-order. For 2-D spatial domains, the boundary curves are described by using either cubic or tension spline interpolation. For 3-D spatial domains, the boundary surfaces are described by using either linear Coon's interpolation, bi-hyperbolic spline interpolation, or a new technique referred to as 3-D bi-directional Hermite interpolation. Since grid systems generated by algebraic methods can have grid lines that overlap one another, GRID2D/3D contains a graphics package for evaluating the grid systems generated. With the graphics package, the user can generate grid systems in an interactive manner with the grid generation part of GRID2D/3D. GRID2D/3D is written in FORTRAN 77 and can be run on any IBM PC, XT, or AT compatible computer. In order to use GRID2D/3D on workstations or mainframe computers, some minor modifications must be made in the graphics part of the program; no
A Spectral Adaptive Mesh Refinement Method for the Burgers equation
NASA Astrophysics Data System (ADS)
Nasr Azadani, Leila; Staples, Anne
2013-03-01
Adaptive mesh refinement (AMR) is a powerful technique in computational fluid dynamics (CFD). Many CFD problems have a wide range of scales which vary with time and space. In order to resolve all the scales numerically, high grid resolutions are required. The smaller the scales the higher the resolutions should be. However, small scales are usually formed in a small portion of the domain or in a special period of time. AMR is an efficient method to solve these types of problems, allowing high grid resolutions where and when they are needed and minimizing memory and CPU time. Here we formulate a spectral version of AMR in order to accelerate simulations of a 1D model for isotropic homogenous turbulence, the Burgers equation, as a first test of this method. Using pseudo spectral methods, we applied AMR in Fourier space. The spectral AMR (SAMR) method we present here is applied to the Burgers equation and the results are compared with the results obtained using standard solution methods performed using a fine mesh.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
The application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems is discussed. The methods consist of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line-, or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to that of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
Application of multi-grid methods for solving the Navier-Stokes equations
NASA Technical Reports Server (NTRS)
Demuren, A. O.
1989-01-01
This paper presents the application of a class of multi-grid methods to the solution of the Navier-Stokes equations for two-dimensional laminar flow problems. The methods consists of combining the full approximation scheme-full multi-grid technique (FAS-FMG) with point-, line- or plane-relaxation routines for solving the Navier-Stokes equations in primitive variables. The performance of the multi-grid methods is compared to those of several single-grid methods. The results show that much faster convergence can be procured through the use of the multi-grid approach than through the various suggestions for improving single-grid methods. The importance of the choice of relaxation scheme for the multi-grid method is illustrated.
NASA Technical Reports Server (NTRS)
Johnson, F. T.; Samant, S. S.; Bieterman, M. B.; Melvin, R. G.; Young, D. P.; Bussoletti, J. E.; Hilmes, C. L.
1992-01-01
A new computer program, called TranAir, for analyzing complex configurations in transonic flow (with subsonic or supersonic freestream) was developed. This program provides accurate and efficient simulations of nonlinear aerodynamic flows about arbitrary geometries with the ease and flexibility of a typical panel method program. The numerical method implemented in TranAir is described. The method solves the full potential equation subject to a set of general boundary conditions and can handle regions with differing total pressure and temperature. The boundary value problem is discretized using the finite element method on a locally refined rectangular grid. The grid is automatically constructed by the code and is superimposed on the boundary described by networks of panels; thus no surface fitted grid generation is required. The nonlinear discrete system arising from the finite element method is solved using a preconditioned Krylov subspace method embedded in an inexact Newton method. The solution is obtained on a sequence of successively refined grids which are either constructed adaptively based on estimated solution errors or are predetermined based on user inputs. Many results obtained by using TranAir to analyze aerodynamic configurations are presented.
Specialized CFD Grid Generation Methods for Near-Field Sonic Boom Prediction
NASA Technical Reports Server (NTRS)
Park, Michael A.; Campbell, Richard L.; Elmiligui, Alaa; Cliff, Susan E.; Nayani, Sudheer N.
2014-01-01
Ongoing interest in analysis and design of low sonic boom supersonic transports re- quires accurate and ecient Computational Fluid Dynamics (CFD) tools. Specialized grid generation techniques are employed to predict near- eld acoustic signatures of these con- gurations. A fundamental examination of grid properties is performed including grid alignment with ow characteristics and element type. The issues a ecting the robustness of cylindrical surface extrusion are illustrated. This study will compare three methods in the extrusion family of grid generation methods that produce grids aligned with the freestream Mach angle. These methods are applied to con gurations from the First AIAA Sonic Boom Prediction Workshop.
An efficient second-order accurate and continuous interpolation for block-adaptive grids
NASA Astrophysics Data System (ADS)
Borovikov, Dmitry; Sokolov, Igor V.; Tóth, Gábor
2015-09-01
In this paper we present a second-order and continuous interpolation algorithm for cell-centered adaptive-mesh-refinement (AMR) grids. Continuity requirement poses a non-trivial problem at resolution changes. We develop a classification of the resolution changes, which allows us to employ efficient and simple linear interpolation in the majority of the computational domain. The algorithm is well suited for massively parallel computations. Our interpolation algorithm allows extracting jump-free interpolated data distribution along lines and surfaces within the computational domain. This capability is important for various applications, including kinetic particles tracking in three dimensional vector fields, visualization (i.e. surface extraction) and extracting variables along one-dimensional curves such as field lines, streamlines and satellite trajectories, etc. Particular examples are models for acceleration of solar energetic particles (SEPs) along magnetic field-lines. As such models are sensitive to sharp gradients and discontinuities the capability to interpolate the data from the AMR grid to be passed to the SEP model without producing false gradients numerically becomes crucial. We provide a complete description of the algorithm and make the code publicly available as a Fortran 90 library.
An Adaptive Reputation-Based Algorithm for Grid Virtual Organization Formation
NASA Astrophysics Data System (ADS)
Cui, Yongrui; Li, Mingchu; Ren, Yizhi; Sakurai, Kouichi
A novel adaptive reputation-based virtual organization formation is proposed. It restrains the bad performers effectively based on the consideration of the global experience of the evaluator and evaluates the direct trust relation between two grid nodes accurately by consulting the previous trust value rationally. It also consults and improves the reputation evaluation process in PathTrust model by taking account of the inter-organizational trust relationship and combines it with direct and recommended trust in a weighted way, which makes the algorithm more robust against collusion attacks. Additionally, the proposed algorithm considers the perspective of the VO creator and takes required VO services as one of the most important fine-grained evaluation criterion, which makes the algorithm more suitable for constructing VOs in grid environments that include autonomous organizations. Simulation results show that our algorithm restrains the bad performers and resists against fake transaction attacks and badmouth attacks effectively. It provides a clear advantage in the design of a VO infrastructure.
Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel
2004-01-01
A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of
Investigation of advancing front method for generating unstructured grid
NASA Astrophysics Data System (ADS)
Thomas, A. M.; Tiwari, S. N.
1992-06-01
The advancing front technique is used to generate an unstructured grid about simple aerodynamic geometries. Unstructured grids are generated using VGRID2D and VGRID3D software. Specific problems considered are a NACA 0012 airfoil, a bi-plane consisting of two NACA 0012 airfoil, a four element airfoil in its landing configuration, and an ONERA M6 wing. Inviscid time dependent solutions are computed on these geometries using USM3D and the results are compared with standard test results obtained by other investigators. A grid convergence study is conducted for the NACA 0012 airfoil and compared with a structured grid. A structured grid is generated using GRIDGEN software and inviscid solutions computed using CFL3D flow solver. The results obtained by unstructured grid for NACA 0012 airfoil showed an asymmetric distribution of flow quantities, and a fine distribution of grid was required to remove this asymmetry. On the other hand, the structured grid predicted a very symmetric distribution, but when the total number of points were compared to obtain the same results it was seen that structured grid required more grid points.
Complex Volume Grid Generation Through the Use of Grid Reusability
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1997-01-01
This paper presents a set of surface and volume grid generation techniques which reuse existing surface and volume grids. These methods use combinations of data manipulations to reduce grid generation time, improve grid characteristics, and increase the capabilities of existing domain discretization software. The manipulation techniques utilize physical and computational domains to produce basis function on which to operate and modify grid character and smooth grids using Trans-Finite Interpolation, a vector interpolation method and parametric re-mapping technique. With these new techniques, inviscid grids can be converted to viscous grids, multiple zone grid adaption can be performed to improve CFD solver efficiency, and topological changes to improve modeling of flow fields can be done simply and quickly. Examples of these capabilities are illustrated as applied to various configurations.
Axisymmetric modeling of cometary mass loading on an adaptively refined grid: MHD results
NASA Technical Reports Server (NTRS)
Gombosi, Tamas I.; Powell, Kenneth G.; De Zeeuw, Darren L.
1994-01-01
The first results of an axisymmetric magnetohydrodynamic (MHD) model of the interaction of an expanding cometary atmosphere with the solar wind are presented. The model assumes that far upstream the plasma flow lines are parallel to the magnetic field vector. The effects of mass loading and ion-neutral friction are taken into account by the governing equations, whcih are solved on an adaptively refined unstructured grid using a Monotone Upstream Centered Schemes for Conservative Laws (MUSCL)-type numerical technique. The combination of the adaptive refinement with the MUSCL-scheme allows the entire cometary atmosphere to be modeled, while still resolving both the shock and the near nucleus of the comet. The main findingsare the following: (1) A shock is formed approximately = 0.45 Mkm upstream of the comet (its location is controlled by the sonic and Alfvenic Mach numbers of the ambient solar wind flow and by the cometary mass addition rate). (2) A contact surface is formed approximately = 5,600 km upstream of the nucleus separating an outward expanding cometary ionosphere from the nearly stagnating solar wind flow. The location of the contact surface is controlled by the upstream flow conditions, the mass loading rate and the ion-neutral drag. The contact surface is also the boundary of the diamagnetic cavity. (3) A closed inner shock terminates the supersonic expansion of the cometary ionosphere. This inner shock is closer to the nucleus on dayside than on the nightside.
Yu, Rong; Zhong, Weifeng; Xie, Shengli; Zhang, Yan; Zhang, Yun
2016-02-01
As the next-generation power grid, smart grid will be integrated with a variety of novel communication technologies to support the explosive data traffic and the diverse requirements of quality of service (QoS). Cognitive radio (CR), which has the favorable ability to improve the spectrum utilization, provides an efficient and reliable solution for smart grid communications networks. In this paper, we study the QoS differential scheduling problem in the CR-based smart grid communications networks. The scheduler is responsible for managing the spectrum resources and arranging the data transmissions of smart grid users (SGUs). To guarantee the differential QoS, the SGUs are assigned to have different priorities according to their roles and their current situations in the smart grid. Based on the QoS-aware priority policy, the scheduler adjusts the channels allocation to minimize the transmission delay of SGUs. The entire transmission scheduling problem is formulated as a semi-Markov decision process and solved by the methodology of adaptive dynamic programming. A heuristic dynamic programming (HDP) architecture is established for the scheduling problem. By the online network training, the HDP can learn from the activities of primary users and SGUs, and adjust the scheduling decision to achieve the purpose of transmission delay minimization. Simulation results illustrate that the proposed priority policy ensures the low transmission delay of high priority SGUs. In addition, the emergency data transmission delay is also reduced to a significantly low level, guaranteeing the differential QoS in smart grid.
Optimal grid-based methods for thin film micromagnetics simulations
NASA Astrophysics Data System (ADS)
Muratov, C. B.; Osipov, V. V.
2006-08-01
Thin film micromagnetics are a broad class of materials with many technological applications, primarily in magnetic memory. The dynamics of the magnetization distribution in these materials is traditionally modeled by the Landau-Lifshitz-Gilbert (LLG) equation. Numerical simulations of the LLG equation are complicated by the need to compute the stray field due to the inhomogeneities in the magnetization which presents the chief bottleneck for the simulation speed. Here, we introduce a new method for computing the stray field in a sample for a reduced model of ultra-thin film micromagnetics. The method uses a recently proposed idea of optimal finite difference grids for approximating Neumann-to-Dirichlet maps and has an advantage of being able to use non-uniform discretization in the film plane, as well as an efficient way of dealing with the boundary conditions at infinity for the stray field. We present several examples of the method's implementation and give a detailed comparison of its performance for studying domain wall structures compared to the conventional FFT-based methods.
Domain adaptive boosting method and its applications
NASA Astrophysics Data System (ADS)
Geng, Jie; Miao, Zhenjiang
2015-03-01
Differences of data distributions widely exist among datasets, i.e., domains. For many pattern recognition, nature language processing, and content-based analysis systems, a decrease in performance caused by the domain differences between the training and testing datasets is still a notable problem. We propose a domain adaptation method called domain adaptive boosting (DAB). It is based on the AdaBoost approach with extensions to cover the domain differences between the source and target domains. Two main stages are contained in this approach: source-domain clustering and source-domain sample selection. By iteratively adding the selected training samples from the source domain, the discrimination model is able to achieve better domain adaptation performance based on a small validation set. The DAB algorithm is suitable for the domains with large scale samples and easy to extend for multisource adaptation. We implement this method on three computer vision systems: the skin detection model in single images, the video concept detection model, and the object classification model. In the experiments, we compare the performances of several commonly used methods and the proposed DAB. Under most situations, the DAB is superior.
Machine Learning Methods for Attack Detection in the Smart Grid.
Ozay, Mete; Esnaola, Inaki; Yarman Vural, Fatos Tunay; Kulkarni, Sanjeev R; Poor, H Vincent
2016-08-01
Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings. In this approach, machine learning algorithms are used to classify measurements as being either secure or attacked. An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach. Well-known batch and online learning algorithms (supervised and semisupervised) are employed with decision- and feature-level fusion to model the attack detection problem. The relationships between statistical and geometric properties of attack vectors employed in the attack scenarios and learning algorithms are analyzed to detect unobservable attacks using statistical learning methods. The proposed algorithms are examined on various IEEE test systems. Experimental analyses show that machine learning algorithms can detect attacks with performances higher than attack detection algorithms that employ state vector estimation methods in the proposed attack detection framework.
Machine Learning Methods for Attack Detection in the Smart Grid.
Ozay, Mete; Esnaola, Inaki; Yarman Vural, Fatos Tunay; Kulkarni, Sanjeev R; Poor, H Vincent
2016-08-01
Attack detection problems in the smart grid are posed as statistical learning problems for different attack scenarios in which the measurements are observed in batch or online settings. In this approach, machine learning algorithms are used to classify measurements as being either secure or attacked. An attack detection framework is provided to exploit any available prior knowledge about the system and surmount constraints arising from the sparse structure of the problem in the proposed approach. Well-known batch and online learning algorithms (supervised and semisupervised) are employed with decision- and feature-level fusion to model the attack detection problem. The relationships between statistical and geometric properties of attack vectors employed in the attack scenarios and learning algorithms are analyzed to detect unobservable attacks using statistical learning methods. The proposed algorithms are examined on various IEEE test systems. Experimental analyses show that machine learning algorithms can detect attacks with performances higher than attack detection algorithms that employ state vector estimation methods in the proposed attack detection framework. PMID:25807571
NASA Astrophysics Data System (ADS)
Bennett, Beth Anne V.; Fielding, Joseph; Mauro, Richard J.; Long, Marshall B.; Smooke, Mitchell D.
1999-12-01
Axisymmetric laminar methane-air Bunsen flames are computed for two equivalence ratios: lean (icons/Journals/Common/Phi" ALT="Phi" ALIGN="TOP"/> = 0.776), in which the traditional Bunsen cone forms above the burner; and rich (icons/Journals/Common/Phi" ALT="Phi" ALIGN="TOP"/> = 1.243), in which the premixed Bunsen cone is accompanied by a diffusion flame halo located further downstream. Because the extremely large gradients at premixed flame fronts greatly exceed those in diffusion flames, their resolution requires a more sophisticated adaptive numerical method than those ordinarily applied to diffusion flames. The local rectangular refinement (LRR) solution-adaptive gridding method produces robust unstructured rectangular grids, utilizes multiple-scale finite-difference discretizations, and incorporates Newton's method to solve elliptic partial differential equation systems simultaneously. The LRR method is applied to the vorticity-velocity formulation of the fully elliptic governing equations, in conjunction with detailed chemistry, multicomponent transport and an optically-thin radiation model. The computed lean flame is lifted above the burner, and this liftoff is verified experimentally. For both lean and rich flames, grid spacing greatly influences the Bunsen cone's position, which only stabilizes with adequate refinement. In the rich configuration, the oxygen-free region above the Bunsen cone inhibits the complete decay of CH4, thus indirectly initiating the diffusion flame halo where CO oxidizes to CO2. In general, the results computed by the LRR method agree quite well with those obtained on equivalently refined conventional grids, yet the former require less than half the computational resources.
A High-Resolution Godunov Method for Compressible Multi-Material Flow on Overlapping Grids
Banks, J W; Schwendeman, D W; Kapila, A K; Henshaw, W D
2006-02-13
A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid resolution near shocks and material interfaces. The discretization of the governing equations is based on a high-resolution Godunov method, but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard, conservative shock-capturing schemes. The energy correction is constructed based on a uniform pressure-velocity flow and is significant only near the captured interface. A variety of two-material flows are presented to verify the accuracy of the numerical approach and to illustrate its use. These flows assume an equation of state for the mixture based on Jones-Wilkins-Lee (JWL) forms for the components. This equation of state includes a mixture of ideal gases as a special case. Flow problems considered include unsteady one-dimensional shock-interface collision, steady interaction of an planar interface and an oblique shock, planar shock interaction with a collection of gas-filled cylindrical inhomogeneities, and the impulsive motion of the two-component mixture in a rigid cylindrical vessel.
An adaptive selective frequency damping method
NASA Astrophysics Data System (ADS)
Jordi, Bastien; Cotter, Colin; Sherwin, Spencer
2015-03-01
The selective frequency damping (SFD) method is used to obtain unstable steady-state solutions of dynamical systems. The stability of this method is governed by two parameters that are the control coefficient and the filter width. Convergence is not guaranteed for arbitrary choice of these parameters. Even when the method does converge, the time necessary to reach a steady-state solution may be very long. We present an adaptive SFD method. We show that by modifying the control coefficient and the filter width all along the solver execution, we can reach an optimum convergence rate. This method is based on successive approximations of the dominant eigenvalue of the flow studied. We design a one-dimensional model to select SFD parameters that enable us to control the evolution of the least stable eigenvalue of the system. These parameters are then used for the application of the SFD method to the multi-dimensional flow problem. We apply this adaptive method to a set of classical test cases of computational fluid dynamics and show that the steady-state solutions obtained are similar to what can be found in the literature. Then we apply it to a specific vortex dominated flow (of interest for the automotive industry) whose stability had never been studied before. Seventh Framework Programme of the European Commission - ANADE project under Grant Contract PITN-GA-289428.
Method for the depth corrected detection of ionizing events from a co-planar grids sensor
De Geronimo, Gianluigi; Bolotnikov, Aleksey E.; Carini, Gabriella
2009-05-12
A method for the detection of ionizing events utilizing a co-planar grids sensor comprising a semiconductor substrate, cathode electrode, collecting grid and non-collecting grid. The semiconductor substrate is sensitive to ionizing radiation. A voltage less than 0 Volts is applied to the cathode electrode. A voltage greater than the voltage applied to the cathode is applied to the non-collecting grid. A voltage greater than the voltage applied to the non-collecting grid is applied to the collecting grid. The collecting grid and the non-collecting grid are summed and subtracted creating a sum and difference respectively. The difference and sum are divided creating a ratio. A gain coefficient factor for each depth (distance between the ionizing event and the collecting grid) is determined, whereby the difference between the collecting electrode and the non-collecting electrode multiplied by the corresponding gain coefficient is the depth corrected energy of an ionizing event. Therefore, the energy of each ionizing event is the difference between the collecting grid and the non-collecting grid multiplied by the corresponding gain coefficient. The depth of the ionizing event can also be determined from the ratio.
NASA Astrophysics Data System (ADS)
Langer, Stefan
2014-11-01
For unstructured finite volume methods an agglomeration multigrid with an implicit multistage Runge-Kutta method as a smoother is developed for solving the compressible Reynolds averaged Navier-Stokes (RANS) equations. The implicit Runge-Kutta method is interpreted as a preconditioned explicit Runge-Kutta method. The construction of the preconditioner is based on an approximate derivative. The linear systems are solved approximately with a symmetric Gauss-Seidel method. To significantly improve this solution method grid anisotropy is treated within the Gauss-Seidel iteration in such a way that the strong couplings in the linear system are resolved by tridiagonal systems constructed along these directions of strong coupling. The agglomeration strategy is adapted to this procedure by taking into account exactly these anisotropies in such a way that a directional coarsening is applied along these directions of strong coupling. Turbulence effects are included by a Spalart-Allmaras model, and the additional transport-type equation is approximately solved in a loosely coupled manner with the same method. For two-dimensional and three-dimensional numerical examples and a variety of differently generated meshes we show the wide range of applicability of the solution method. Finally, we exploit the GMRES method to determine approximate spectral information of the linearized RANS equations. This approximate spectral information is used to discuss and compare characteristics of multistage Runge-Kutta methods.
Solution of Reactive Compressible Flows Using an Adaptive Wavelet Method
NASA Astrophysics Data System (ADS)
Zikoski, Zachary; Paolucci, Samuel; Powers, Joseph
2008-11-01
This work presents numerical simulations of reactive compressible flow, including detailed multicomponent transport, using an adaptive wavelet algorithm. The algorithm allows for dynamic grid adaptation which enhances our ability to fully resolve all physically relevant scales. The thermodynamic properties, equation of state, and multicomponent transport properties are provided by CHEMKIN and TRANSPORT libraries. Results for viscous detonation in a H2:O2:Ar mixture, and other problems in multiple dimensions, are included.
A software package using a mesh-grid method for simulating HPGe detector efficiencies
Gritzo, Russell E; Jackman, Kevin R; Biegalski, Steven R
2009-01-01
Traditional ways of determining the absolute full-energy peak efficiencies of high-purity germanium (HPGe) detectors are often time consuming, cost prohibitive, or not feasible. A software package, KMESS (Kevin's Mesh Efficiency Simulator Software), was developed to assist in predicting these efficiencies. It uses a semiempirical mesh-grid method and works for arbitrary source shapes and counting geometries. The model assumes that any gamma-ray source shape can be treated as a large enough collection of point sources. The code is readily adaptable, has a web-based graphical front-end. and could easily be coupled to a 3D scanner. As will be shown. this software can estimate absolute full-energy peak efficiencies with good accuracy in reasonable computation times. It has applications to the field of gamma-ray spectroscopy because it is a quick and accurate way to assist in performing quantitative analyses using HPGe detectors.
NASA Technical Reports Server (NTRS)
Madsen, Niel K.
1992-01-01
Several new discrete surface integral (DSI) methods for solving Maxwell's equations in the time-domain are presented. These methods, which allow the use of general nonorthogonal mixed-polyhedral unstructured grids, are direct generalizations of the canonical staggered-grid finite difference method. These methods are conservative in that they locally preserve divergence or charge. Employing mixed polyhedral cells, (hexahedral, tetrahedral, etc.) these methods allow more accurate modeling of non-rectangular structures and objects because the traditional stair-stepped boundary approximations associated with the orthogonal grid based finite difference methods can be avoided. Numerical results demonstrating the accuracy of these new methods are presented.
Webster, Clayton G; Zhang, Guannan; Gunzburger, Max D
2012-10-01
Accurate predictive simulations of complex real world applications require numerical approximations to first, oppose the curse of dimensionality and second, converge quickly in the presence of steep gradients, sharp transitions, bifurcations or finite discontinuities in high-dimensional parameter spaces. In this paper we present a novel multi-dimensional multi-resolution adaptive (MdMrA) sparse grid stochastic collocation method, that utilizes hierarchical multiscale piecewise Riesz basis functions constructed from interpolating wavelets. The basis for our non-intrusive method forms a stable multiscale splitting and thus, optimal adaptation is achieved. Error estimates and numerical examples will used to compare the efficiency of the method with several other techniques.
Finite-difference modeling with variable grid-size and adaptive time-step in porous media
NASA Astrophysics Data System (ADS)
Liu, Xinxin; Yin, Xingyao; Wu, Guochen
2014-04-01
Forward modeling of elastic wave propagation in porous media has great importance for understanding and interpreting the influences of rock properties on characteristics of seismic wavefield. However, the finite-difference forward-modeling method is usually implemented with global spatial grid-size and time-step; it consumes large amounts of computational cost when small-scaled oil/gas-bearing structures or large velocity-contrast exist underground. To overcome this handicap, combined with variable grid-size and time-step, this paper developed a staggered-grid finite-difference scheme for elastic wave modeling in porous media. Variable finite-difference coefficients and wavefield interpolation were used to realize the transition of wave propagation between regions of different grid-size. The accuracy and efficiency of the algorithm were shown by numerical examples. The proposed method is advanced with low computational cost in elastic wave simulation for heterogeneous oil/gas reservoirs.
An overlapped grid method for multigrid, finite volume/difference flow solvers: MaGGiE
NASA Technical Reports Server (NTRS)
Baysal, Oktay; Lessard, Victor R.
1990-01-01
The objective is to develop a domain decomposition method via overlapping/embedding the component grids, which is to be used by upwind, multi-grid, finite volume solution algorithms. A computer code, given the name MaGGiE (Multi-Geometry Grid Embedder) is developed to meet this objective. MaGGiE takes independently generated component grids as input, and automatically constructs the composite mesh and interpolation data, which can be used by the finite volume solution methods with or without multigrid convergence acceleration. Six demonstrative examples showing various aspects of the overlap technique are presented and discussed. These cases are used for developing the procedure for overlapping grids of different topologies, and to evaluate the grid connection and interpolation data for finite volume calculations on a composite mesh. Time fluxes are transferred between mesh interfaces using a trilinear interpolation procedure. Conservation losses are minimal at the interfaces using this method. The multi-grid solution algorithm, using the coaser grid connections, improves the convergence time history as compared to the solution on composite mesh without multi-gridding.
Efficient Combustion Simulation via the Adaptive Wavelet Collocation Method
NASA Astrophysics Data System (ADS)
Lung, Kevin; Brown-Dymkoski, Eric; Guerrero, Victor; Doran, Eric; Museth, Ken; Balme, Jo; Urberger, Bob; Kessler, Andre; Jones, Stephen; Moses, Billy; Crognale, Anthony
Rocket engine development continues to be driven by the intuition and experience of designers, progressing through extensive trial-and-error test campaigns. Extreme temperatures and pressures frustrate direct observation, while high-fidelity simulation can be impractically expensive owing to the inherent muti-scale, multi-physics nature of the problem. To address this cost, an adaptive multi-resolution PDE solver has been designed which targets the high performance, many-core architecture of GPUs. The adaptive wavelet collocation method is used to maintain a sparse-data representation of the high resolution simulation, greatly reducing the memory footprint while tightly controlling physical fidelity. The tensorial, stencil topology of wavelet-based grids lends itself to highly vectorized algorithms which are necessary to exploit the performance of GPUs. This approach permits efficient implementation of direct finite-rate kinetics, and improved resolution of steep thermodynamic gradients and the smaller mixing scales that drive combustion dynamics. Resolving these scales is crucial for accurate chemical kinetics, which are typically degraded or lost in statistical modeling approaches.
Yu, Rong; Zhong, Weifeng; Xie, Shengli; Zhang, Yan; Zhang, Yun
2016-02-01
As the next-generation power grid, smart grid will be integrated with a variety of novel communication technologies to support the explosive data traffic and the diverse requirements of quality of service (QoS). Cognitive radio (CR), which has the favorable ability to improve the spectrum utilization, provides an efficient and reliable solution for smart grid communications networks. In this paper, we study the QoS differential scheduling problem in the CR-based smart grid communications networks. The scheduler is responsible for managing the spectrum resources and arranging the data transmissions of smart grid users (SGUs). To guarantee the differential QoS, the SGUs are assigned to have different priorities according to their roles and their current situations in the smart grid. Based on the QoS-aware priority policy, the scheduler adjusts the channels allocation to minimize the transmission delay of SGUs. The entire transmission scheduling problem is formulated as a semi-Markov decision process and solved by the methodology of adaptive dynamic programming. A heuristic dynamic programming (HDP) architecture is established for the scheduling problem. By the online network training, the HDP can learn from the activities of primary users and SGUs, and adjust the scheduling decision to achieve the purpose of transmission delay minimization. Simulation results illustrate that the proposed priority policy ensures the low transmission delay of high priority SGUs. In addition, the emergency data transmission delay is also reduced to a significantly low level, guaranteeing the differential QoS in smart grid. PMID:25910254
Domain Decomposition By the Advancing-Partition Method for Parallel Unstructured Grid Generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.; Zagaris, George
2009-01-01
A new method of domain decomposition has been developed for generating unstructured grids in subdomains either sequentially or using multiple computers in parallel. Domain decomposition is a crucial and challenging step for parallel grid generation. Prior methods are generally based on auxiliary, complex, and computationally intensive operations for defining partition interfaces and usually produce grids of lower quality than those generated in single domains. The new technique, referred to as "Advancing Partition," is based on the Advancing-Front method, which partitions a domain as part of the volume mesh generation in a consistent and "natural" way. The benefits of this approach are: 1) the process of domain decomposition is highly automated, 2) partitioning of domain does not compromise the quality of the generated grids, and 3) the computational overhead for domain decomposition is minimal. The new method has been implemented in NASA's unstructured grid generation code VGRID.
A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids
Bungartz, H.J.
1996-12-31
In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.
Mathews, K.A.; Brennan, C.R.
1997-07-01
The exponential characteristic (EC) method is one of a family of nonlinear spatial quadratures for discrete ordinates radiation transport that are positive and at least second-order accurate and provide accurate results for deep-penetration problems using coarse meshes. The authors use a split-cell methodology to adapt the method to unstructured grids of arbitrarily shaped and oriented triangular cells that provide efficient representation of curved surfaces. Exponential representations of the flux entering through a cell edge and of the scattering source within a cell are constructed to match average values and first moments passed from the adjacent cell (or from the boundary conditions) or obtained from the angular quadrature of the directional flux spatial moments in the previous iteration (or from an initial guess). The resulting one- and two-dimensional nonlinear rootsolving problems are efficiently solved using Newton`s method with an accurate starting approximation. Improved algorithms, presented here, have increased the efficiency of the method by a factor of 10 as compared to an initial report. The EC method now costs only twice as much per cell as does the linear characteristic method but can be accurate with many fewer cells. Numerical testing shows the EC method to be robust and effective.
Domain decomposition by the advancing-partition method for parallel unstructured grid generation
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z. (Inventor); Banihashemi, legal representative, Soheila (Inventor)
2012-01-01
In a method for domain decomposition for generating unstructured grids, a surface mesh is generated for a spatial domain. A location of a partition plane dividing the domain into two sections is determined. Triangular faces on the surface mesh that intersect the partition plane are identified. A partition grid of tetrahedral cells, dividing the domain into two sub-domains, is generated using a marching process in which a front comprises only faces of new cells which intersect the partition plane. The partition grid is generated until no active faces remain on the front. Triangular faces on each side of the partition plane are collected into two separate subsets. Each subset of triangular faces is renumbered locally and a local/global mapping is created for each sub-domain. A volume grid is generated for each sub-domain. The partition grid and volume grids are then merged using the local-global mapping.
Ensemble transform sensitivity method for adaptive observations
NASA Astrophysics Data System (ADS)
Zhang, Yu; Xie, Yuanfu; Wang, Hongli; Chen, Dehui; Toth, Zoltan
2016-01-01
The Ensemble Transform (ET) method has been shown to be useful in providing guidance for adaptive observation deployment. It predicts forecast error variance reduction for each possible deployment using its corresponding transformation matrix in an ensemble subspace. In this paper, a new ET-based sensitivity (ETS) method, which calculates the gradient of forecast error variance reduction in terms of analysis error variance reduction, is proposed to specify regions for possible adaptive observations. ETS is a first order approximation of the ET; it requires just one calculation of a transformation matrix, increasing computational efficiency (60%-80% reduction in computational cost). An explicit mathematical formulation of the ETS gradient is derived and described. Both the ET and ETS methods are applied to the Hurricane Irene (2011) case and a heavy rainfall case for comparison. The numerical results imply that the sensitive areas estimated by the ETS and ET are similar. However, ETS is much more efficient, particularly when the resolution is higher and the number of ensemble members is larger.
Makris, Evangelos; Neofytou, Panagiotis; Tsangaris, Sokrates; Housiadas, Christos
2012-10-01
In this study a description of a new approach, for the generation of multi-block structured computational grids on patient-specific bifurcation geometries is presented. The structured grid generation technique is applied to data obtained by medical imaging examination, resulting in a surface conforming, high quality, multi-block structured grid of the branching geometry. As a case study application a patient specific abdominal aorta bifurcation is selected. For the evaluation of the grid produced by the novel method, a grid convergence study and a comparison between the grid produced by the method and unstructured grids produced by commercial meshing software are carried out. PMID:22209311
NASA Astrophysics Data System (ADS)
Navaratne, Uditha Sudheera
The smart grid is the future of the power grid. Smart meters and the associated network play a major role in the distributed system of the smart grid. Advance Metering Infrastructure (AMI) can enhance the reliability of the grid, generate efficient energy management opportunities and many innovations around the future smart grid. These innovations involve intense research not only on the AMI network itself but as also on the influence an AMI network can have upon the rest of the power grid. This research describes a smart meter testbed with hardware in loop that can facilitate future research in an AMI network. The smart meters in the testbed were developed such that their functionality can be customized to simulate any given scenario such as integrating new hardware components into a smart meter or developing new encryption algorithms in firmware. These smart meters were integrated into the power system simulator to simulate the power flow variation in the power grid on different AMI activities. Each smart meter in the network also provides a communication interface to the home area network. This research delivers a testbed for emulating the AMI activities and monitoring their effect on the smart grid.
NASA Technical Reports Server (NTRS)
Finley, Dennis B.
1995-01-01
This report documents results from the Euler Technology Assessment program. The objective was to evaluate the efficacy of Euler computational fluid dynamics (CFD) codes for use in preliminary aircraft design. Both the accuracy of the predictions and the rapidity of calculations were to be assessed. This portion of the study was conducted by Lockheed Fort Worth Company, using a recently developed in-house Cartesian-grid code called SPLITFLOW. The Cartesian grid technique offers several advantages for this study, including ease of volume grid generation and reduced number of cells compared to other grid schemes. SPLITFLOW also includes grid adaptation of the volume grid during the solution convergence to resolve high-gradient flow regions. This proved beneficial in resolving the large vortical structures in the flow for several configurations examined in the present study. The SPLITFLOW code predictions of the configuration forces and moments are shown to be adequate for preliminary design analysis, including predictions of sideslip effects and the effects of geometry variations at low and high angles of attack. The time required to generate the results from initial surface definition is on the order of several hours, including grid generation, which is compatible with the needs of the design environment.
Adjoint-Based Algorithms for Adaptation and Design Optimizations on Unstructured Grids
NASA Technical Reports Server (NTRS)
Nielsen, Eric J.
2006-01-01
Schemes based on discrete adjoint algorithms present several exciting opportunities for significantly advancing the current state of the art in computational fluid dynamics. Such methods provide an extremely efficient means for obtaining discretely consistent sensitivity information for hundreds of design variables, opening the door to rigorous, automated design optimization of complex aerospace configuration using the Navier-Stokes equation. Moreover, the discrete adjoint formulation provides a mathematically rigorous foundation for mesh adaptation and systematic reduction of spatial discretization error. Error estimates are also an inherent by-product of an adjoint-based approach, valuable information that is virtually non-existent in today's large-scale CFD simulations. An overview of the adjoint-based algorithm work at NASA Langley Research Center is presented, with examples demonstrating the potential impact on complex computational problems related to design optimization as well as mesh adaptation.
NASA Astrophysics Data System (ADS)
Furzeland, R. M.; Verwer, J. G.; Zegeling, P. A.
1990-08-01
In recent years, several sophisticated packages based on the method of lines (MOL) have been developed for the automatic numerical integration of time-dependent problems in partial differential equations (PDEs), notably for problems in one space dimension. These packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers. However, from the PDE point of view, they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes, but use just a fixed space grid, chosen a priori, for the entire calculation. For solutions possessing sharp spatial transitions that move, e.g., travelling wave fronts or emerging boundary and interior layers, a grid held fixed for the entire calculation is computationally inefficient, since for a good solution this grid often must contain a very large number of nodes. In such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity. Methods and codes that operate this way belong to the realm of adaptive or moving-grid methods. Following the MOL approach, this paper is devoted to an evaluation and comparison, mainly based on extensive numerical tests, of three moving-grid methods for 1D problems, viz., the finite-element method of Miller and co-workers, the method published by Petzold, and a method based on ideas adopted from Dorfi and Drury. Our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability, robustness, and efficiency of the conventional MOL approach. Therefore, considerable attention is paid to the temporal performance of the methods.
Qualitative Life-Grids: A Proposed Method for Comparative European Educational Research
ERIC Educational Resources Information Center
Abbas, Andrea; Ashwin, Paul; McLean, Monica
2013-01-01
Drawing upon their large three-year mixed-method study comparing four English university sociology departments, the authors demonstrate the benefits to be gained from concisely recording biographical stories on life-grids. They argue that life-grids have key benefits which are important for comparative European educational research. Some of these…
Action Research to Improve Methods of Delivery and Feedback in an Access Grid Room Environment
ERIC Educational Resources Information Center
McArthur, Lynne C.; Klass, Lara; Eberhard, Andrew; Stacey, Andrew
2011-01-01
This article describes a qualitative study which was undertaken to improve the delivery methods and feedback opportunity in honours mathematics lectures which are delivered through Access Grid Rooms. Access Grid Rooms are facilities that provide two-way video and audio interactivity across multiple sites, with the inclusion of smart boards. The…
An adaptive mesh refinement algorithm for the discrete ordinates method
Jessee, J.P.; Fiveland, W.A.; Howell, L.H.; Colella, P.; Pember, R.B.
1996-03-01
The discrete ordinates form of the radiative transport equation (RTE) is spatially discretized and solved using an adaptive mesh refinement (AMR) algorithm. This technique permits the local grid refinement to minimize spatial discretization error of the RTE. An error estimator is applied to define regions for local grid refinement; overlapping refined grids are recursively placed in these regions; and the RTE is then solved over the entire domain. The procedure continues until the spatial discretization error has been reduced to a sufficient level. The following aspects of the algorithm are discussed: error estimation, grid generation, communication between refined levels, and solution sequencing. This initial formulation employs the step scheme, and is valid for absorbing and isotopically scattering media in two-dimensional enclosures. The utility of the algorithm is tested by comparing the convergence characteristics and accuracy to those of the standard single-grid algorithm for several benchmark cases. The AMR algorithm provides a reduction in memory requirements and maintains the convergence characteristics of the standard single-grid algorithm; however, the cases illustrate that efficiency gains of the AMR algorithm will not be fully realized until three-dimensional geometries are considered.
Adaptive Accommodation Control Method for Complex Assembly
NASA Astrophysics Data System (ADS)
Kang, Sungchul; Kim, Munsang; Park, Shinsuk
Robotic systems have been used to automate assembly tasks in manufacturing and in teleoperation. Conventional robotic systems, however, have been ineffective in controlling contact force in multiple contact states of complex assemblythat involves interactions between complex-shaped parts. Unlike robots, humans excel at complex assembly tasks by utilizing their intrinsic impedance, forces and torque sensation, and tactile contact clues. By examining the human behavior in assembling complex parts, this study proposes a novel geometry-independent control method for robotic assembly using adaptive accommodation (or damping) algorithm. Two important conditions for complex assembly, target approachability and bounded contact force, can be met by the proposed control scheme. It generates target approachable motion that leads the object to move closer to a desired target position, while contact force is kept under a predetermined value. Experimental results from complex assembly tests have confirmed the feasibility and applicability of the proposed method.
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods.
Li, Zhilin; Song, Peng
2012-01-01
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy.
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods
Li, Zhilin; Song, Peng
2012-01-01
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function φ(x,y). Our adaptive mesh refinement is done within a small tube of |φ(x,y)|≤ δ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy. PMID:22670155
NASA Technical Reports Server (NTRS)
Kim, Hyoungin; Liou, Meng-Sing
2011-01-01
In this paper, we demonstrate improved accuracy of the level set method for resolving deforming interfaces by proposing two key elements: (1) accurate level set solutions on adapted Cartesian grids by judiciously choosing interpolation polynomials in regions of different grid levels and (2) enhanced reinitialization by an interface sharpening procedure. The level set equation is solved using a fifth order WENO scheme or a second order central differencing scheme depending on availability of uniform stencils at each grid point. Grid adaptation criteria are determined so that the Hamiltonian functions at nodes adjacent to interfaces are always calculated by the fifth order WENO scheme. This selective usage between the fifth order WENO and second order central differencing schemes is confirmed to give more accurate results compared to those in literature for standard test problems. In order to further improve accuracy especially near thin filaments, we suggest an artificial sharpening method, which is in a similar form with the conventional re-initialization method but utilizes sign of curvature instead of sign of the level set function. Consequently, volume loss due to numerical dissipation on thin filaments is remarkably reduced for the test problems
Adaptive method with intercessory feedback control for an intelligent agent
Goldsmith, Steven Y.
2004-06-22
An adaptive architecture method with feedback control for an intelligent agent provides for adaptively integrating reflexive and deliberative responses to a stimulus according to a goal. An adaptive architecture method with feedback control for multiple intelligent agents provides for coordinating and adaptively integrating reflexive and deliberative responses to a stimulus according to a goal. Re-programming of the adaptive architecture is through a nexus which coordinates reflexive and deliberator components.
NASA Astrophysics Data System (ADS)
Egorova, Tatiana; Gatsonis, Nikolaos A.; Demetriou, Michael A.
2013-11-01
In this work the process of gas release into the atmosphere by a moving aerial source is simulated and estimated using a sensing aerial vehicle (SAV). The process is modeled with atmospheric advection diffusion equation, which is solved by the finite volume method (FVM). Advective fluxes are constrained using total variation diminishing (TVD) approach. The estimator provides on-line estimates of concentration field and proximity of the source. The guidance of the SAV is dictated by the performance of the estimator. To further improve the estimation algorithm from the computational prospective, the grid is adapted dynamically through local refinement and coarsening. The adaptation algorithm uses the current sensor position as a center of refinement, with the areas further away from the SAV being covered by a coarse grid. This leads to the time varying state matrix of the estimator and the variation depends on the SAV motion. Advantages of the adaptive FVM-TVD implementation are illustrated on the examples of estimator performance for different source trajectories.
NASA Astrophysics Data System (ADS)
Aula, Fadhil T.; Lee, Samuel C.
2013-04-01
This paper addresses the problems associated with power management of the grid containing renewable power systems and proposes a method for enhancing its operational power management. Since renewable energy provides uncertain and uncontrollable energy resources, the renewable power systems can only generate irregular power. This power irregularity creates problems affecting the grid power management process and influencing the parallel operations of conventional power plants on the grid. To demonstrate this power management method for this type of grid, weatherdependent wind and photovoltaic power systems are chosen an example. This study also deals with other uncertain quantities which are system loads. In this example, the management method is based on adapting short-term weather and load forecasting data. The new load demand curve (NLDC) can be produced by merging the loads with the power generated from the renewable power systems. The NLDC is used for setting the loads for the baseload power plants and knowing when other plants are needed to increase or decrease their supplies to the grid. This will decrease the irregularity behavior effects of the renewable power system and at the same time will enhance the smoothing of the power management for the grid. The aim of this paper is to show the use of the weather and load forecasting data to achieve the optimum operational power management of the grid contains renewable power systems. An illustrative example of such a power system is presented and verified by simulation.
Logically rectangular finite volume methods with adaptive refinement on the sphere.
Berger, Marsha J; Calhoun, Donna A; Helzel, Christiane; LeVeque, Randall J
2009-11-28
The logically rectangular finite volume grids for two-dimensional partial differential equations on a sphere and for three-dimensional problems in a spherical shell introduced recently have nearly uniform cell size, avoiding severe Courant number restrictions. We present recent results with adaptive mesh refinement using the GeoClaw software and demonstrate well-balanced methods that exactly maintain equilibrium solutions, such as shallow water equations for an ocean at rest over arbitrary bathymetry.
Smart electric vehicle (EV) charging and grid integration apparatus and methods
Gadh, Rajit; Mal, Siddhartha; Prabhu, Shivanand; Chu, Chi-Cheng; Sheikh, Omar; Chung, Ching-Yen; He, Lei; Xiao, Bingjun; Shi, Yiyu
2015-05-05
An expert system manages a power grid wherein charging stations are connected to the power grid, with electric vehicles connected to the charging stations, whereby the expert system selectively backfills power from connected electric vehicles to the power grid through a grid tie inverter (if present) within the charging stations. In more traditional usage, the expert system allows for electric vehicle charging, coupled with user preferences as to charge time, charge cost, and charging station capabilities, without exceeding the power grid capacity at any point. A robust yet accurate state of charge (SOC) calculation method is also presented, whereby initially an open circuit voltage (OCV) based on sampled battery voltages and currents is calculated, and then the SOC is obtained based on a mapping between a previously measured reference OCV (ROCV) and SOC. The OCV-SOC calculation method accommodates likely any battery type with any current profile.
Method for fabricating solar cells having integrated collector grids
NASA Technical Reports Server (NTRS)
Evans, J. C., Jr. (Inventor)
1979-01-01
A heterojunction or Schottky barrier photovoltaic device comprising a conductive base metal layer compatible with and coating predominately the exposed surface of the p-type substrate of the device such that a back surface field region is formed at the interface between the device and the base metal layer, a transparent, conductive mixed metal oxide layer in integral contact with the n-type layer of the heterojunction or Schottky barrier device having a metal alloy grid network of the same metal elements of the oxide constituents of the mixed metal oxide layer embedded in the mixed metal oxide layer, an insulating layer which prevents electrical contact between the conductive metal base layer and the transparent, conductive metal oxide layer, and a metal contact means covering the insulating layer and in intimate contact with the metal grid network embedded in the transparent, conductive oxide layer for conducting electrons generated by the photovoltaic process from the device.
Linearly-Constrained Adaptive Signal Processing Methods
NASA Astrophysics Data System (ADS)
Griffiths, Lloyd J.
1988-01-01
In adaptive least-squares estimation problems, a desired signal d(n) is estimated using a linear combination of L observation values samples xi (n), x2(n), . . . , xL-1(n) and denoted by the vector X(n). The estimate is formed as the inner product of this vector with a corresponding L-dimensional weight vector W. One particular weight vector of interest is Wopt which minimizes the mean-square between d(n) and the estimate. In this context, the term `mean-square difference' is a quadratic measure such as statistical expectation or time average. The specific value of W which achieves the minimum is given by the prod-uct of the inverse data covariance matrix and the cross-correlation between the data vector and the desired signal. The latter is often referred to as the P-vector. For those cases in which time samples of both the desired and data vector signals are available, a variety of adaptive methods have been proposed which will guarantee that an iterative weight vector Wa(n) converges (in some sense) to the op-timal solution. Two which have been extensively studied are the recursive least-squares (RLS) method and the LMS gradient approximation approach. There are several problems of interest in the communication and radar environment in which the optimal least-squares weight set is of interest and in which time samples of the desired signal are not available. Examples can be found in array processing in which only the direction of arrival of the desired signal is known and in single channel filtering where the spectrum of the desired response is known a priori. One approach to these problems which has been suggested is the P-vector algorithm which is an LMS-like approximate gradient method. Although it is easy to derive the mean and variance of the weights which result with this algorithm, there has never been an identification of the corresponding underlying error surface which the procedure searches. The purpose of this paper is to suggest an alternative
An adaptive multifluid interface-capturing method for compressible flow in complex geometries
Greenough, J.A.; Beckner, V.; Pember, R.B.; Crutchfield, W.Y.; Bell, J.B.; Colella, P.
1995-04-01
We present a numerical method for solving the multifluid equations of gas dynamics using an operator-split second-order Godunov method for flow in complex geometries in two and three dimensions. The multifluid system treats the fluid components as thermodynamically distinct entities and correctly models fluids with different compressibilities. This treatment allows a general equation-of-state (EOS) specification and the method is implemented so that the EOS references are minimized. The current method is complementary to volume-of-fluid (VOF) methods in the sense that a VOF representation is used, but no interface reconstruction is performed. The Godunov integrator captures the interface during the solution process. The basic multifluid integrator is coupled to a Cartesian grid algorithm that also uses a VOF representation of the fluid-body interface. This representation of the fluid-body interface allows the algorithm to easily accommodate arbitrarily complex geometries. The resulting single grid multifluid-Cartesian grid integration scheme is coupled to a local adaptive mesh refinement algorithm that dynamically refines selected regions of the computational grid to achieve a desired level of accuracy. The overall method is fully conservative with respect to the total mixture. The method will be used for a simple nozzle problem in two-dimensional axisymmetric coordinates.
Adaptive model training system and method
Bickford, Randall L; Palnitkar, Rahul M
2014-11-18
An adaptive model training system and method for filtering asset operating data values acquired from a monitored asset for selectively choosing asset operating data values that meet at least one predefined criterion of good data quality while rejecting asset operating data values that fail to meet at least the one predefined criterion of good data quality; and recalibrating a previously trained or calibrated model having a learned scope of normal operation of the asset by utilizing the asset operating data values that meet at least the one predefined criterion of good data quality for adjusting the learned scope of normal operation of the asset for defining a recalibrated model having the adjusted learned scope of normal operation of the asset.
Adaptive model training system and method
Bickford, Randall L; Palnitkar, Rahul M; Lee, Vo
2014-04-15
An adaptive model training system and method for filtering asset operating data values acquired from a monitored asset for selectively choosing asset operating data values that meet at least one predefined criterion of good data quality while rejecting asset operating data values that fail to meet at least the one predefined criterion of good data quality; and recalibrating a previously trained or calibrated model having a learned scope of normal operation of the asset by utilizing the asset operating data values that meet at least the one predefined criterion of good data quality for adjusting the learned scope of normal operation of the asset for defining a recalibrated model having the adjusted learned scope of normal operation of the asset.
Post, R.F.
1960-08-01
An electronic grid is designed employing magnetic forces for controlling the passage of charged particles. The grid is particularly applicable to use in gas-filled tubes such as ignitrons. thyratrons, etc., since the magnetic grid action is impartial to the polarity of the charged particles and, accordingly. the sheath effects encountered with electrostatic grids are not present. The grid comprises a conductor having sections spaced apart and extending in substantially opposite directions in the same plane, the ends of the conductor being adapted for connection to a current source.
NASA Astrophysics Data System (ADS)
Malgarinos, Ilias; Nikolopoulos, Nikolaos; Gavaises, Manolis
2015-11-01
This study presents the implementation of an interface sharpening scheme on the basis of the Volume of Fluid (VOF) method, as well as its application in a number of theoretical and real cases usually modelled in literature. More specifically, the solution of an additional sharpening equation along with the standard VOF model equations is proposed, offering the advantage of "restraining" interface numerical diffusion, while also keeping a quite smooth induced velocity field around the interface. This sharpening equation is solved right after volume fraction advection; however a novel method for its coupling with the momentum equation has been applied in order to save computational time. The advantages of the proposed sharpening scheme lie on the facts that a) it is mass conservative thus its application does not have a negative impact on one of the most important benefits of VOF method and b) it can be used in coarser grids as now the suppression of the numerical diffusion is grid independent. The coupling of the solved equation with an adaptive local grid refinement technique is used for further decrease of computational time, while keeping high levels of accuracy at the area of maximum interest (interface). The numerical algorithm is initially tested against two theoretical benchmark cases for interface tracking methodologies followed by its validation for the case of a free-falling water droplet accelerated by gravity, as well as the normal liquid droplet impingement onto a flat substrate. Results indicate that the coupling of the interface sharpening equation with the HRIC discretization scheme used for volume fraction flux term, not only decreases the interface numerical diffusion, but also allows the induced velocity field to be less perturbed owed to spurious velocities across the liquid-gas interface. With the use of the proposed algorithmic flow path, coarser grids can replace finer ones at the slight expense of accuracy.
NASA Technical Reports Server (NTRS)
Kamhawi, Hilmi N.
2012-01-01
This report documents the work performed from March 2010 to March 2012. The Integrated Design and Engineering Analysis (IDEA) environment is a collaborative environment based on an object-oriented, multidisciplinary, distributed framework using the Adaptive Modeling Language (AML) as a framework and supporting the configuration design and parametric CFD grid generation. This report will focus on describing the work in the area of parametric CFD grid generation using novel concepts for defining the interaction between the mesh topology and the geometry in such a way as to separate the mesh topology from the geometric topology while maintaining the link between the mesh topology and the actual geometry.
Online Adaptive Replanning Method for Prostate Radiotherapy
Ahunbay, Ergun E.; Peng Cheng; Holmes, Shannon; Godley, Andrew; Lawton, Colleen; Li, X. Allen
2010-08-01
Purpose: To report the application of an adaptive replanning technique for prostate cancer radiotherapy (RT), consisting of two steps: (1) segment aperture morphing (SAM), and (2) segment weight optimization (SWO), to account for interfraction variations. Methods and Materials: The new 'SAM+SWO' scheme was retroactively applied to the daily CT images acquired for 10 prostate cancer patients on a linear accelerator and CT-on-Rails combination during the course of RT. Doses generated by the SAM+SWO scheme based on the daily CT images were compared with doses generated after patient repositioning using the current planning target volume (PTV) margin (5 mm, 3 mm toward rectum) and a reduced margin (2 mm), along with full reoptimization scans based on the daily CT images to evaluate dosimetry benefits. Results: For all cases studied, the online replanning method provided significantly better target coverage when compared with repositioning with reduced PTV (13% increase in minimum prostate dose) and improved organ sparing when compared with repositioning with regular PTV (13% decrease in the generalized equivalent uniform dose of rectum). The time required to complete the online replanning process was 6 {+-} 2 minutes. Conclusion: The proposed online replanning method can be used to account for interfraction variations for prostate RT with a practically acceptable time frame (5-10 min) and with significant dosimetric benefits. On the basis of this study, the developed online replanning scheme is being implemented in the clinic for prostate RT.
A three-dimensional grid generation method for gas-turbine combustor flow computations
NASA Astrophysics Data System (ADS)
Shyy, Wei; Braaten, Mark E.; Sober, Janet S.
1987-02-01
A special-purpose code suitable for generating a curvilinear nonorthogonal grid system for gas-turbine combustor flow computations has been produced. The code is capable of handling an arbitrary number of dilution holes with any radii as well as film-cooling slots on the top and bottom surfaces. A zonal approach has been developed to handle the fast length scale variations imposed by the geometric constraints and to minimize the overall computational efforts needed to generate the grids. The code combines partial differential equation and algebraic interpolation methods to generate the grid system. The salient features of the grid characteristics are discussed. Also included are sample results of a 3-D turbulent combusting flow field calculated on the grid system produced by this methodology.
Determining displacement and strain maps immune from aliasing effect with the grid method
NASA Astrophysics Data System (ADS)
Sur, Frédéric; Blaysat, Benoît; Grédiac, Michel
2016-11-01
Spatial aliasing may affect methods based on grid image processing to retrieve displacement and strain maps in experimental mechanics. Such methods aim at estimating these maps on the surface of a specimen subjected to a loading test. Aliasing, which is often not noticeable to the naked eye in the grid images, may give spurious fringes in the strain maps. This paper presents an analysis of aliasing in this context and provides the reader with simple guidelines to minimize the effect of aliasing on strain maps extracted from grid images.
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.
Moving body overset grid methods for complete aircraft tiltrotor simulations
NASA Technical Reports Server (NTRS)
Meakin, Robert L.
1993-01-01
A hypothetical, but realistic, set of flight conditions for the V-22 aircraft is established to facilitate rigorous testing of a new domain connectivity algorithm, and to carry out an overset grid proof-of-concept tiltrotor simulation. Relative motion and interference effects between the V-22 airframe and rotor-blades are directly simulated within the context of an unsteady, thin-layer Navier-Stokes computation. The domain connectivity algorithm is verified to perform at rates equal to or greater than those realized previously for store-separation-like applications. The feasibility of carrying out unsteady Navier-Stokes analyses of rotorcraft problems is demonstrated.
Numerical simulation of dynamic processes in biomechanics using the grid-characteristic method
NASA Astrophysics Data System (ADS)
Beklemysheva, K. A.; Vasyukov, A. V.; Petrov, I. B.
2015-08-01
Results of the numerical simulation of mechanical processes occurring in biological tissues under dynamic actions are presented. The grid-characteristic method on unstructured grids is used to solve the system of equations of mechanics of deformable solids; this method takes into account the characteristic properties of the constitutive system of partial differential equations and produces adequate algorithms on interfaces between media and on the boundaries of integration domains.
On the Quality of Velocity Interpolation Schemes for Marker-In-Cell Methods on 3-D Staggered Grids
NASA Astrophysics Data System (ADS)
Kaus, B.; Pusok, A. E.; Popov, A.
2015-12-01
The marker-in-cell method is generally considered to be a flexible and robust method to model advection of heterogenous non-diffusive properties (i.e. rock type or composition) in geodynamic problems or incompressible Stokes problems. In this method, Lagrangian points carrying compositional information are advected with the ambient velocity field on an immobile, Eulerian grid. However, velocity interpolation from grid points to marker locations is often performed without preserving the zero divergence of the velocity field at the interpolated locations (i.e. non-conservative). Such interpolation schemes can induce non-physical clustering of markers when strong velocity gradients are present (Jenny et al., 2001) and this may, eventually, result in empty grid cells, a serious numerical violation of the marker-in-cell method. Solutions to this problem include: using larger mesh resolutions and/or marker densities, or repeatedly controlling the marker distribution (i.e. inject/delete), but which does not have an established physical background. To remedy this at low computational costs, Jenny et al. (2001) and Meyer and Jenny (2004) proposed a simple, conservative velocity interpolation (CVI) scheme for 2-D staggered grid, while Wang et al. (2015) extended the formulation to 3-D finite element methods. Here, we follow up with these studies and report on the quality of velocity interpolation methods for 2-D and 3-D staggered grids. We adapt the formulations from both Jenny et al. (2001) and Wang et al. (2015) for use on 3-D staggered grids, where the velocity components have different node locations as compared to finite element, where they share the same node location. We test the different interpolation schemes (CVI and non-CVI) in combination with different advection schemes (Euler, RK2 and RK4) and with/out marker control on Stokes problems with strong velocity gradients, which are discretized using a finite difference method. We show that a conservative formulation
Evaluation of Grid Modification Methods for On- and Off-Track Sonic Boom Analysis
NASA Technical Reports Server (NTRS)
Nayani, Sudheer N.; Campbell, Richard L.
2013-01-01
Grid modification methods have been under development at NASA to enable better predictions of low boom pressure signatures from supersonic aircraft. As part of this effort, two new codes, Stretched and Sheared Grid - Modified (SSG) and Boom Grid (BG), have been developed in the past year. The CFD results from these codes have been compared with ones from the earlier grid modification codes Stretched and Sheared Grid (SSGRID) and Mach Cone Aligned Prism (MCAP) and also with the available experimental results. NASA's unstructured grid suite of software TetrUSS and the automatic sourcing code AUTOSRC were used for base grid generation and flow solutions. The BG method has been evaluated on three wind tunnel models. Pressure signatures have been obtained up to two body lengths below a Gulfstream aircraft wind tunnel model. Good agreement with the wind tunnel results have been obtained for both on-track and off-track (up to 53 degrees) cases. On-track pressure signatures up to ten body lengths below a Straight Line Segmented Leading Edge (SLSLE) wind tunnel model have been extracted. Good agreement with the wind tunnel results have been obtained. Pressure signatures have been obtained at 1.5 body lengths below a Lockheed Martin aircraft wind tunnel model. Good agreement with the wind tunnel results have been obtained for both on-track and off-track (up to 40 degrees) cases. Grid sensitivity studies have been carried out to investigate any grid size related issues. Methods have been evaluated for fully turbulent, mixed laminar/turbulent and fully laminar flow conditions.
Method, memory media and apparatus for detection of grid disconnect
Ye, Zhihong; Du, Pengwei
2008-09-23
A phase shift procedure for detecting a disconnect of a power grid from a feeder that is connected to a load and a distributed generator. The phase shift procedure compares a current phase shift of the output voltage of the distributed generator with a predetermined threshold and if greater, a command is issued for a disconnect of the distributed generator from the feeder. To extend the range of detection, the phase shift procedure is used when a power mismatch between the distributed generator and the load exceeds a threshold and either or both of an under/over frequency procedure and an under/over voltage procedure is used when any power mismatch does not exceed the threshold.
New ghost-node method for linking different models with varied grid refinement
James, S.C.; Dickinson, J.E.; Mehl, S.W.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Eddebbarh, A.-A.
2006-01-01
A flexible, robust method for linking grids of locally refined ground-water flow models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined "child" model that is contained within a larger and coarser "parent" model that is based on the iterative method of Steffen W. Mehl and Mary C. Hill (2002, Advances in Water Res., 25, p. 497-511; 2004, Advances in Water Res., 27, p. 899-912). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has matching grids (parent cells border an integer number of child cells) or nonmatching grids. The coupled grids are simulated by using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child-cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models. When the grids are nonmatching, model accuracy is slightly increased compared to that for matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to couple distinct models because the overall head and flow errors relative to the analytical solution are less than if only the regional coarse-grid model was used to simulate flow in the child model's domain.
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.
NASA Astrophysics Data System (ADS)
Kacem, S.; Eichwald, O.; Ducasse, O.; Renon, N.; Yousfi, M.; Charrada, K.
2012-01-01
Streamers dynamics are characterized by the fast propagation of ionized shock waves at the nanosecond scale under very sharp space charge variations. The streamer dynamics modelling needs the solution of charged particle transport equations coupled to the elliptic Poisson's equation. The latter has to be solved at each time step of the streamers evolution in order to follow the propagation of the resulting space charge electric field. In the present paper, a full multi grid (FMG) and a multi grid (MG) methods have been adapted to solve Poisson's equation for streamer discharge simulations between asymmetric electrodes. The validity of the FMG method for the computation of the potential field is first shown by performing direct comparisons with analytic solution of the Laplacian potential in the case of a point-to-plane geometry. The efficiency of the method is also compared with the classical successive over relaxation method (SOR) and MUltifrontal massively parallel solver (MUMPS). MG method is then applied in the case of the simulation of positive streamer propagation and its efficiency is evaluated from comparisons to SOR and MUMPS methods in the chosen point-to-plane configuration. Very good agreements are obtained between the three methods for all electro-hydrodynamics characteristics of the streamer during its propagation in the inter-electrode gap. However in the case of MG method, the computational time to solve the Poisson's equation is at least 2 times faster in our simulation conditions.
Jyobira, Yasuhiro; Ito, Daisuke; Fukumasa, Osamu
2008-02-15
Volume production of hydrogen negative ion H{sup -} is studied in pure hydrogen plasmas using a grid bias method for plasma parameter control. The purposes of the present study are as follows. One is to investigate the possibility of controlling plasma parameters with a grid bias method in dc discharge plasmas; the other is to realize efficient negative ion production in H{sub 2} plasmas and to discuss the difference in plasma parameters control and H{sup -} production between the grid bias method and the usual magnetic filter method. The relationship between plasma parameters and extracted H{sup -} ion currents is discussed. It is confirmed that both high and low electron temperature T{sub e} plasmas are produced in the separated regions when the grid is negatively biased. The negative ion production depends strongly on the grid potential and related plasma conditions. Within certain plasma conditions, H{sup -} production with grid bias method is much higher than one with magnetic filter method.
Carson, James P.; Kuprat, Andrew P.; Jiao, Xiangmin; Dyedov, Volodymyr; del Pin, Facundo; Guccione, Julius M.; Ratcliffe, Mark B.; Einstein, Daniel R.
2010-04-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where, the fluid and solid phases must match geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to share the same surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh.
Carson, J.P.; Kuprat, A.P; Jiao, X.; Dyedov, V.; del Pin, F.; Johnson, G.A.; Guccione, J.M.; Ratcliffe, M.B.; Einstein, D.R.
2009-01-01
Spatial discretization of complex imaging-derived fluid-solid geometries, such as the cardiac environment, is a critical but often overlooked challenge in biomechanical computations. This is particularly true in problems with Lagrangian interfaces, where the fluid and solid phases share a common interface geometrically. For simplicity and better accuracy, it is also highly desirable for the two phases to have a matching surface mesh at the interface between them. We outline a method for solving this problem, and illustrate the approach with a 3D fluid-solid mesh of the mouse heart. An MRI perfusion-fixed dataset of a mouse heart with 50μm isotropic resolution was semi-automatically segmented using a customized multimaterial connected-threshold approach that divided the volume into non-overlapping regions of blood, tissue and background. Subsequently, a multimaterial marching cubes algorithm was applied to the segmented data to produce two detailed, compatible isosurfaces, one for blood and one for tissue. Both isosurfaces were simultaneously smoothed with a multimaterial smoothing algorithm that exactly conserves the volume for each phase. Using these two isosurfaces, we developed and applied novel automated meshing algorithms to generate anisotropic hybrid meshes on arbitrary biological geometries with the number of layers and the desired element anisotropy for each phase as the only input parameters. Since our meshes adapt to the local feature sizes and include boundary layer prisms, they are more efficient and accurate than non-adaptive, isotropic meshes, and the fluid-structure interaction computations will tend to have relative error equilibrated over the whole mesh. PMID:19727874
Jablonowski, Christiane
2015-07-14
The research investigates and advances strategies how to bridge the scale discrepancies between local, regional and global phenomena in climate models without the prohibitive computational costs of global cloud-resolving simulations. In particular, the research explores new frontiers in computational geoscience by introducing high-order Adaptive Mesh Refinement (AMR) techniques into climate research. AMR and statically-adapted variable-resolution approaches represent an emerging trend for atmospheric models and are likely to become the new norm in future-generation weather and climate models. The research advances the understanding of multi-scale interactions in the climate system and showcases a pathway how to model these interactions effectively with advanced computational tools, like the Chombo AMR library developed at the Lawrence Berkeley National Laboratory. The research is interdisciplinary and combines applied mathematics, scientific computing and the atmospheric sciences. In this research project, a hierarchy of high-order atmospheric models on cubed-sphere computational grids have been developed that serve as an algorithmic prototype for the finite-volume solution-adaptive Chombo-AMR approach. The foci of the investigations have lied on the characteristics of both static mesh adaptations and dynamically-adaptive grids that can capture flow fields of interest like tropical cyclones. Six research themes have been chosen. These are (1) the introduction of adaptive mesh refinement techniques into the climate sciences, (2) advanced algorithms for nonhydrostatic atmospheric dynamical cores, (3) an assessment of the interplay between resolved-scale dynamical motions and subgrid-scale physical parameterizations, (4) evaluation techniques for atmospheric model hierarchies, (5) the comparison of AMR refinement strategies and (6) tropical cyclone studies with a focus on multi-scale interactions and variable-resolution modeling. The results of this research project
A Dynamically Adaptive Arbitrary Lagrangian-Eulerian Method for Solution of the Euler Equations
Anderson, R W; Elliott, N S; Pember, R B
2003-02-14
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. The novel components of the methods are driven by the need to reconcile traditional AMR techniques with the staggered variables and moving, deforming meshes associated with Lagrange based ALE schemes. We develop interlevel solution transfer operators and interlevel boundary conditions first in the case of purely Lagrangian hydrodynamics, and then extend these ideas into an ALE method by developing adaptive extensions of elliptic mesh relaxation techniques. Conservation properties of the method are analyzed, and a series of test problem calculations are presented which demonstrate the utility and efficiency of the method.
Semi-implicit Integration Factor Methods on Sparse Grids for High-Dimensional Systems
Wang, Dongyong; Chen, Weitao; Nie, Qing
2015-01-01
Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method. PMID:25897178
Grid-based precision aim system and method for disrupting suspect objects
Gladwell, Thomas Scott; Garretson, Justin; Hobart, Clinton G.; Monda, Mark J.
2014-06-10
A system and method for disrupting at least one component of a suspect object is provided. The system has a source for passing radiation through the suspect object, a grid board positionable adjacent the suspect object (the grid board having a plurality of grid areas, the radiation from the source passing through the grid board), a screen for receiving the radiation passing through the suspect object and generating at least one image, a weapon for deploying a discharge, and a targeting unit for displaying the image of the suspect object and aiming the weapon according to a disruption point on the displayed image and deploying the discharge into the suspect object to disable the suspect object.
Prusa, Joseph
2012-05-08
This project had goals of advancing the performance capabilities of the numerical general circulation model EULAG and using it to produce a fully operational atmospheric global climate model (AGCM) that can employ either static or dynamic grid stretching for targeted phenomena. The resulting AGCM combined EULAG's advanced dynamics core with the physics of the NCAR Community Atmospheric Model (CAM). Effort discussed below shows how we improved model performance and tested both EULAG and the coupled CAM-EULAG in several ways to demonstrate the grid stretching and ability to simulate very well a wide range of scales, that is, multi-scale capability. We leveraged our effort through interaction with an international EULAG community that has collectively developed new features and applications of EULAG, which we exploited for our own work summarized here. Overall, the work contributed to over 40 peer- reviewed publications and over 70 conference/workshop/seminar presentations, many of them invited.
NEW GHOST-NODE METHOD FOR LINKING DIFFERENT MODELS WITH VARIED GRID REFINEMENT
S.C. James; J.E. Dickinson; S.W. Mehl; M.C. Hill; S.A. Leake; G.A. zyvoloski; A. Eddebbarh
2006-02-15
A flexible, robust method for linking grids of locally refined models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined ''child'' model that is contained within a larger and coarser ''parent'' model that is based on the iterative method of Mehl and Hill (2002, 2004). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has either matching grids (parent cells border an integer number of child cells; Figure 2a) or non-matching grids (parent cells border a non-integer number of child cells; Figure 2b). The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models (Mehl and Hill, 2002). When the grids are non-matching, model accuracy is slightly increased over matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models because the overall error is less than if only the regional model was used to simulate flow in the child model's domain.
New Ghost-node method for linking different models with varied grid refinement.
Mehl, Steffen W.; Hill, Mary Catherine.; James, Scott Carlton; Leake, Stanley A.; Zyvoloski, George A.; Dickinson, Jesse E.; Eddebbarh, Al A.
2006-01-01
A flexible, robust method for linking grids of locally refined models constructed with different numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method for a refined 'child' model that is contained within a larger and coarser 'parent' model that is based on the iterative method of Mehl and Hill (2002, 2004). The method is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that has either matching grids (parent cells border an integer number of child cells; Figure 2a) or non-matching grids (parent cells border a non-integer number of child cells; Figure 2b). The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM, respectively. The simulations require no alteration of the MODFLOW or FEHM models and are executed using a batch file on Windows operating systems. Results indicate that when the grids are matched spatially so that nodes and child cell boundaries are aligned, the new coupling technique has error nearly equal to that when coupling two MODFLOW models (Mehl and Hill, 2002). When the grids are non-matching, model accuracy is slightly increased over matching-grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models because the overall error is less than if only the regional model was used to simulate flow in the child model's domain.
NASA Astrophysics Data System (ADS)
Zanotti, O.; Dumbser, M.; Fambri, F.
2016-05-01
We describe a new method for the solution of the ideal MHD equations in special relativity which adopts the following strategy: (i) the main scheme is based on Discontinuous Galerkin (DG) methods, allowing for an arbitrary accuracy of order N+1, where N is the degree of the basis polynomials; (ii) in order to cope with oscillations at discontinuities, an ”a-posteriori” sub-cell limiter is activated, which scatters the DG polynomials of the previous time-step onto a set of 2N+1 sub-cells, over which the solution is recomputed by means of a robust finite volume scheme; (iii) a local spacetime Discontinuous-Galerkin predictor is applied both on the main grid of the DG scheme and on the sub-grid of the finite volume scheme; (iv) adaptive mesh refinement (AMR) with local time-stepping is used. We validate the new scheme and comment on its potential applications in high energy astrophysics.
Progress in Grid Generation: From Chimera to DRAGON Grids
NASA Technical Reports Server (NTRS)
Liou, Meng-Sing; Kao, Kai-Hsiung
1994-01-01
Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are
Rupture Dynamics Simulation for Non-Planar fault by a Curved Grid Finite Difference Method
NASA Astrophysics Data System (ADS)
Zhang, Z.; Zhu, G.; Chen, X.
2011-12-01
We first implement the non-staggered finite difference method to solve the dynamic rupture problem, with split-node, for non-planar fault. Split-node method for dynamic simulation has been used widely, because of that it's more precise to represent the fault plane than other methods, for example, thick fault, stress glut and so on. The finite difference method is also a popular numeric method to solve kinematic and dynamic problem in seismology. However, previous works focus most of theirs eyes on the staggered-grid method, because of its simplicity and computational efficiency. However this method has its own disadvantage comparing to non-staggered finite difference method at some fact for example describing the boundary condition, especially the irregular boundary, or non-planar fault. Zhang and Chen (2006) proposed the MacCormack high order non-staggered finite difference method based on curved grids to precisely solve irregular boundary problem. Based upon on this non-staggered grid method, we make success of simulating the spontaneous rupture problem. The fault plane is a kind of boundary condition, which could be irregular of course. So it's convinced that we could simulate rupture process in the case of any kind of bending fault plane. We will prove this method is valid in the case of Cartesian coordinate first. In the case of bending fault, the curvilinear grids will be used.
Simulating Multi-scale Fluid Flows Using Adaptive Mesh Refinement Methods
NASA Astrophysics Data System (ADS)
Rowe, Kristopher; Lamb, Kevin
2015-11-01
When modelling flows with disparate length scales one must use a computational mesh that is fine enough to capture the smallest phenomena of interest. Traditional computational fluid dynamics models apply a mesh of uniform resolution to the entire computational domain; however, if the smallest scales of interest are isolated much of the computational resources used in these simulations will be wasted in regions where they are not needed. Adaptive mesh refinement methods seek to only apply resolution where it is needed. Beginning with a single coarse grid, a nested hierarchy of block structured grids is built in regions of the fluid flow where more resolution is necessary. As the fluid flow varies in time this hierarchy of grids is dynamically rebuilt to follow the phenomena of interest. Through the modelling of the interaction of vortices with wall boundary layers, it will be demonstrated that adaptive mesh refinement methods will produce equivalent results to traditional single resolution codes while using less processors, memory, and wall-clock time. Additionally, it is possible to model such flows to higher Reynolds numbers than have been feasible previously. This work was supported by NSERC and SHARCNET.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov Maxwell system
NASA Astrophysics Data System (ADS)
Besse, Nicolas; Latu, Guillaume; Ghizzo, Alain; Sonnendrücker, Eric; Bertrand, Pierre
2008-08-01
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Self-adjusting grid methods for one-dimensional hyperbolic conservation laws
NASA Technical Reports Server (NTRS)
Harten, A.; Hyman, J. M.
1983-01-01
The automatic adjustment of a grid which follows the dynamics of the numerical solution of hyperbolic conservation laws is given. The grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals. The resulting algorithm is a simple extension of many currently popular Godunov-type methods. Computer codes using one of these methods can be easily modified to add the moving mesh as an option. Numerical examples are given that illustrate the improved accuracy of Godunov's and Roe's methods on a self-adjusting mesh. Previously announced in STAR as N83-15008
Principles and Methods of Adapted Physical Education.
ERIC Educational Resources Information Center
Arnheim, Daniel D.; And Others
Programs in adapted physical education are presented preceded by a background of services for the handicapped, by the psychosocial implications of disability, and by the growth and development of the handicapped. Elements of conducting programs discussed are organization and administration, class organization, facilities, exercise programs…
A NEW GHOST-NODE METHOD FOR LINKING DIFFERENT MODELS WITH VARIED GRID REFINEMENT
J. dickinson; S.C. James; S. Mehl; M.C. Hill; S. Leake; G.A. Zyvoloski
2005-10-18
A flexible, robust method for linking grids of locally refined models that may be constructed using different types of numerical methods is needed to address a variety of hydrologic problems. This work outlines and tests a new ghost-node model-linking method based on the iterative method of Mehl and Hill (2002, 2004). It is applicable to steady-state solutions for ground-water flow. Tests are presented for a homogeneous two-dimensional system that facilitates clear analysis of typical problems. The coupled grids are simulated using the finite-difference and finite-element models MODFLOW and FEHM. Results indicate that when the grids are matched spatially so that nodes and control volume boundaries are aligned, the new coupling technique has approximately twice the error as coupling using two MODFLOW models. When the grids are non-matching; model accuracy is slightly increased over matching grid cases. Overall, results indicate that the ghost-node technique is a viable means to accurately couple distinct models.
Feasibility of a simple method of hybrid collimation for megavoltage grid therapy
Almendral, Pedro; Mancha, Pedro J.; Roberto, Daniel
2013-05-15
Purpose: Megavoltage grid therapy is currently delivered with step-and-shoot multisegment techniques or using a high attenuation block with divergent holes. However, the commercial availability of grid blocks is limited, their construction is difficult, and step-and-shoot techniques require longer treatment times and are not practical with some multileaf collimators. This work studies the feasibility of a hybrid collimation system for grid therapy that does not require multiple segments and can be easily implemented with widely available technical means. Methods: The authors have developed a system to generate a grid of beamlets by the simultaneous use of two perpendicular sets of equally spaced leaves that project stripe patterns in orthogonal directions. One of them is generated with the multileaf collimator integrated in the accelerator and the other with an in-house made collimator constructed with a low melting point alloy commonly available at radiation oncology departments. The characteristics of the grid fields for 6 and 18 MV have been studied with a shielded diode, an unshielded diode, and radiochromic film. Results: The grid obtained with the hybrid collimation is similar to some of the grids used clinically with respect to the beamlet size (about 1 cm) and the percentage of open beam (1/4 of the total field). The grid fields are less penetrating than the open fields of the same energy. Depending on the depth and the direction of the profiles (diagonal or along the principal axes), the measured valley-to-peak dose ratios range from 5% to 16% for 6 MV and from 9% to 20% for 18 MV. All the detectors yield similar results in the measurement of profiles and percent depth dose, but the shielded diode seems to overestimate the output factors. Conclusions: The combination of two stripe pattern collimators in orthogonal directions is a feasible method to obtain two-dimensional arrays of beamlets and has potential usefulness as an efficient way to deliver grid
Newton-Krylov-Schwarz methods in unstructured grid Euler flow
Keyes, D.E.
1996-12-31
Newton-Krylov methods and Krylov-Schwarz (domain decomposition) methods have begun to become established in computational fluid dynamics (CFD) over the past decade. The former employ a Krylov method inside of Newton`s method in a Jacobian-free manner, through directional differencing. The latter employ an overlapping Schwarz domain decomposition to derive a preconditioner for the Krylov accelerator that relies primarily on local information, for data-parallel concurrency. They may be composed as Newton-Krylov-Schwarz (NKS) methods, which seem particularly well suited for solving nonlinear elliptic systems in high-latency, distributed-memory environments. We give a brief description of this family of algorithms, with an emphasis on domain decomposition iterative aspects. We then describe numerical simulations with Newton-Krylov-Schwarz methods on an aerodynamic application emphasizing comparisons with a standard defect-correction approach and subdomain preconditioner consistency.
Franck-Condon Factors for Diatomics: Insights and Analysis Using the Fourier Grid Hamiltonian Method
ERIC Educational Resources Information Center
Ghosh, Supriya; Dixit, Mayank Kumar; Bhattacharyya, S. P.; Tembe, B. L.
2013-01-01
Franck-Condon factors (FCFs) play a crucial role in determining the intensities of the vibrational bands in electronic transitions. In this article, a relatively simple method to calculate the FCFs is illustrated. An algorithm for the Fourier Grid Hamiltonian (FGH) method for computing the vibrational wave functions and the corresponding energy…
Online Optimization Method for Operation of Generators in a Micro Grid
NASA Astrophysics Data System (ADS)
Hayashi, Yasuhiro; Miyamoto, Hideki; Matsuki, Junya; Iizuka, Toshio; Azuma, Hitoshi
Recently a lot of studies and developments about distributed generator such as photovoltaic generation system, wind turbine generation system and fuel cell have been performed under the background of the global environment issues and deregulation of the electricity market, and the technique of these distributed generators have progressed. Especially, micro grid which consists of several distributed generators, loads and storage battery is expected as one of the new operation system of distributed generator. However, since precipitous load fluctuation occurs in micro grid for the reason of its smaller capacity compared with conventional power system, high-accuracy load forecasting and control scheme to balance of supply and demand are needed. Namely, it is necessary to improve the precision of operation in micro grid by observing load fluctuation and correcting start-stop schedule and output of generators online. But it is not easy to determine the operation schedule of each generator in short time, because the problem to determine start-up, shut-down and output of each generator in micro grid is a mixed integer programming problem. In this paper, the authors propose an online optimization method for the optimal operation schedule of generators in micro grid. The proposed method is based on enumeration method and particle swarm optimization (PSO). In the proposed method, after picking up all unit commitment patterns of each generators satisfied with minimum up time and minimum down time constraint by using enumeration method, optimal schedule and output of generators are determined under the other operational constraints by using PSO. Numerical simulation is carried out for a micro grid model with five generators and photovoltaic generation system in order to examine the validity of the proposed method.
Adaptive method for electron bunch profile prediction
Scheinker, Alexander; Gessner, Spencer
2015-10-01
We report on an experiment performed at the Facility for Advanced Accelerator Experimental Tests (FACET) at SLAC National Accelerator Laboratory, in which a new adaptive control algorithm, one with known, bounded update rates, despite operating on analytically unknown cost functions, was utilized in order to provide quasi-real-time bunch property estimates of the electron beam. Multiple parameters, such as arbitrary rf phase settings and other time-varying accelerator properties, were simultaneously tuned in order to match a simulated bunch energy spectrum with a measured energy spectrum. The simple adaptive scheme was digitally implemented using matlab and the experimental physics and industrial control system. The main result is a nonintrusive, nondestructive, real-time diagnostic scheme for prediction of bunch profiles, as well as other beam parameters, the precise control of which are important for the plasma wakefield acceleration experiments being explored at FACET. © 2015 authors. Published by the American Physical Society.
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)
Sanmiguel-Rojas, Enrique; Ortega-Casanova, Joaquin; del Pino, Carlos; Fernandez-Feria, Ramon
2004-11-01
A method for generating a non-uniform cartesian grid for irregular two-dimensional (2D) geometries such that all the boundary points are regular mesh points is given. The resulting non-uniform grid is used to discretize the Navier-Stokes equations for 2D incompressible viscous flows using finite difference approximations. To that end, finite-difference approximations of the derivatives on a non-uniform mesh are given. We test the method with two different examples: the shallow water flow on a lake with irregular contour, and the pressure driven flow through an irregular array of circular cylinders.
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Simon, Horst D.; Sohn, Andrew
1996-01-01
The computational requirements for an adaptive solution of unsteady problems change as the simulation progresses. This causes workload imbalance among processors on a parallel machine which, in turn, requires significant data movement at runtime. We present a new dynamic load-balancing framework, called JOVE, that balances the workload across all processors with a global view. Whenever the computational mesh is adapted, JOVE is activated to eliminate the load imbalance. JOVE has been implemented on an IBM SP2 distributed-memory machine in MPI for portability. Experimental results for two model meshes demonstrate that mesh adaption with load balancing gives more than a sixfold improvement over one without load balancing. We also show that JOVE gives a 24-fold speedup on 64 processors compared to sequential execution.
Outlier Measures and Norming Methods for Computerized Adaptive Tests.
ERIC Educational Resources Information Center
Bradlow, Eric T.; Weiss, Robert E.
2001-01-01
Compares four methods that map outlier statistics to a familiarity probability scale (a "P" value). Explored these methods in the context of computerized adaptive test data from a 1995 nationally administered computerized examination for professionals in the medical industry. (SLD)
An Adaptive and Implicit Immersed Boundary Method for Cardiovascular Device Modeling
NASA Astrophysics Data System (ADS)
Bhalla, Amneet Pal S.; Griffith, Boyce E.
2015-11-01
Computer models and numerical simulations are playing an increasingly important role in understanding the mechanics of fluid-structure interactions (FSI) in cardiovascular devices. To model cardiac devices realistically, there is a need to solve the classical fluid-structure interaction equations efficiently. Peskin's explicit immersed boundary method is one such approach to model FSI equations for elastic structures efficiently. However, in the presence of rigid structures the IB method faces a severe timestep restriction. To overcome this limitation, we are developing an implicit version of immersed boundary method on adaptive Cartesian grids. Higher grid resolution is employed in spatial regions occupying the structure while relatively coarser discretization is used elsewhere. The resulting discrete system is solved using geometric multigrid solver for the combined Stokes and elasticity operators. We use a rediscretization approach for standard finite difference approximations to the divergence, gradient, and viscous stress. In contrast, coarse grid versions of the Eulerian elasticity operator are constructed via a Galerkin approach. The implicit IB method is tested for a pulse duplicator cardiac device system that consists of both rigid mountings and elastic membrane.
ADAPTIVE-GRID SIMULATION OF GROUNDWATER FLOW IN HETEROGENEOUS AQUIFERS. (R825689C068)
The prediction of contaminant transport in porous media requires the computation of the flow velocity. This work presents a methodology for high-accuracy computation of flow in a heterogeneous isotropic formation, employing a dual-flow formulation and adaptive...
High resolution finite volume methods on arbitrary grids via wave propagation
NASA Technical Reports Server (NTRS)
Leveque, Randall J.
1987-01-01
A generalization of Godunov's method for systems of conservation laws has been developed and analyzed that can be applied with arbitrary time steps on arbitrary grids in one space dimension. Stability for arbitrary time steps is achieved by allowing waves to propagate through more than one mesh cell in a time step. The method is extended here to second order accuracy and to a finite volume method in two space dimensions. This latter method is based on solving one dimensional normal and tangential Riemann problems at cell interfaces and again propagating waves through one or more mesh cells. By avoiding the usual time step restriction of explicit methods, it is possible to use reasonable time steps on irregular grids where the minimum cell area is much smaller than the average cell. Boundary conditions for the Euler equations are discussed and special attention is given to the case of a Cartesian grid cut by an irregular boundary. In this case small grid cells arise only near the boundary, and it is desirable to use a time step appropriate for the regular interior cells. Numerical results in two dimensions show that this can be achieved.
Assessing Adaptive Instructional Design Tools and Methods in ADAPT[IT].
ERIC Educational Resources Information Center
Eseryel, Deniz; Spector, J. Michael
ADAPT[IT] (Advanced Design Approach for Personalized Training - Interactive Tools) is a European project within the Information Society Technologies program that is providing design methods and tools to guide a training designer according to the latest cognitive science and standardization principles. ADAPT[IT] addresses users in two significantly…
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.
Advanced adaptive computational methods for Navier-Stokes simulations in rotorcraft aerodynamics
NASA Technical Reports Server (NTRS)
Stowers, S. T.; Bass, J. M.; Oden, J. T.
1993-01-01
A phase 2 research and development effort was conducted in area transonic, compressible, inviscid flows with an ultimate goal of numerically modeling complex flows inherent in advanced helicopter blade designs. The algorithms and methodologies therefore are classified as adaptive methods, which are error estimation techniques for approximating the local numerical error, and automatically refine or unrefine the mesh so as to deliver a given level of accuracy. The result is a scheme which attempts to produce the best possible results with the least number of grid points, degrees of freedom, and operations. These types of schemes automatically locate and resolve shocks, shear layers, and other flow details to an accuracy level specified by the user of the code. The phase 1 work involved a feasibility study of h-adaptive methods for steady viscous flows, with emphasis on accurate simulation of vortex initiation, migration, and interaction. Phase 2 effort focused on extending these algorithms and methodologies to a three-dimensional topology.
A New Adaptive Image Denoising Method Based on Neighboring Coefficients
NASA Astrophysics Data System (ADS)
Biswas, Mantosh; Om, Hari
2016-03-01
Many good techniques have been discussed for image denoising that include NeighShrink, improved adaptive wavelet denoising method based on neighboring coefficients (IAWDMBNC), improved wavelet shrinkage technique for image denoising (IWST), local adaptive wiener filter (LAWF), wavelet packet thresholding using median and wiener filters (WPTMWF), adaptive image denoising method based on thresholding (AIDMT). These techniques are based on local statistical description of the neighboring coefficients in a window. These methods however do not give good quality of the images since they cannot modify and remove too many small wavelet coefficients simultaneously due to the threshold. In this paper, a new image denoising method is proposed that shrinks the noisy coefficients using an adaptive threshold. Our method overcomes these drawbacks and it has better performance than the NeighShrink, IAWDMBNC, IWST, LAWF, WPTMWF, and AIDMT denoising methods.
High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids
McCorquodale, P. W.; Colella, P.; Dorr, M. R.; Hittinger, J. A. F.
2015-01-13
We present an approach to solving hyperbolic conservation laws by finite-volume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) [10] for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a block, we reduce the inter-block communication problem to finding an accurate, robust interpolation into these ghost cells from neighboring blocks. Lastly, we demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.
An adaptive pseudospectral method for discontinuous problems
NASA Technical Reports Server (NTRS)
Augenbaum, Jeffrey M.
1988-01-01
The accuracy of adaptively chosen, mapped polynomial approximations is studied for functions with steep gradients or discontinuities. It is shown that, for steep gradient functions, one can obtain spectral accuracy in the original coordinate system by using polynomial approximations in a transformed coordinate system with substantially fewer collocation points than are necessary using polynomial expansion directly in the original, physical, coordinate system. It is also shown that one can avoid the usual Gibbs oscillation associated with steep gradient solutions of hyperbolic pde's by approximation in suitably chosen coordinate systems. Continuous, high gradient solutions are computed with spectral accuracy (as measured in the physical coordinate system). Discontinuous solutions associated with nonlinear hyperbolic equations can be accurately computed by using an artificial viscosity chosen to smooth out the solution in the mapped, computational domain. Thus, shocks can be effectively resolved on a scale that is subgrid to the resolution available with collocation only in the physical domain. Examples with Fourier and Chebyshev collocation are given.
Adaptable radiation monitoring system and method
Archer, Daniel E.; Beauchamp, Brock R.; Mauger, G. Joseph; Nelson, Karl E.; Mercer, Michael B.; Pletcher, David C.; Riot, Vincent J.; Schek, James L.; Knapp, David A.
2006-06-20
A portable radioactive-material detection system capable of detecting radioactive sources moving at high speeds. The system has at least one radiation detector capable of detecting gamma-radiation and coupled to an MCA capable of collecting spectral data in very small time bins of less than about 150 msec. A computer processor is connected to the MCA for determining from the spectral data if a triggering event has occurred. Spectral data is stored on a data storage device, and a power source supplies power to the detection system. Various configurations of the detection system may be adaptably arranged for various radiation detection scenarios. In a preferred embodiment, the computer processor operates as a server which receives spectral data from other networked detection systems, and communicates the collected data to a central data reporting system.
NASA Astrophysics Data System (ADS)
Chiappini, D.; Donno, A.
2016-06-01
In this paper we present a comparison of three different grids generated with a fractal method and used for fluid dynamic simulations through a kinetic approach. We start from the theoretical element definition and we introduce some optimizations in order to fulfil requirements. The study is performed with analysing results both in terms of friction factor at different Reynolds regimes and streamlines paths.
The sequential method for the black-oil reservoir simulation on unstructured grids
NASA Astrophysics Data System (ADS)
Li, Baoyan; Chen, Zhangxin; Huan, Guanren
2003-11-01
This paper presents new results for applying the sequential solution method to the black-oil reservoir simulation with unstructured grids. The fully implicit solution method has been successfully applied to reservoir simulation with unstructured grids. However, the complexity of the fully implicit method and the irregularity of the grids result in a very complicated structure of linear equation systems (LESs) and in high computational cost to solve them. To tackle this problem, the sequential method is applied to reduce the size of the LESs. To deal with instable problems caused by the low implicit degree of this method, some practical techniques are introduced to control convergence of Newton-Raphson's iterations which are exploited in the linearization of the governing equations of the black-oil model. These techniques are tested with the benchmark problem of the ninth comparative solution project (CSP) organized by the society of petroleum engineers (SPE) and applied to field-scale models of both saturated and undersaturated reservoirs. The simulation results show that the sequential method uses as little as 20.01% of the memory for solving the LESs and 23.89% of the total computational time of the fully implicit method to reach the same precision for the undersaturated reservoirs, when the same iteration control parameters are used for both solution methods. However, for the saturated reservoirs, the sequential method must use stricter iteration control parameters to reach the same precision as the fully implicit method.
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.
Hong Luo; Yidong Xia; Robert Nourgaliev; Chunpei Cai
2011-06-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on unstructured tetrahedral grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on unstructured grids. The preliminary results indicate that this RDG method is stable on unstructured tetrahedral grids, and provides a viable and attractive alternative for the discretization of the viscous and heat fluxes in the Navier-Stokes equations.
NASA Astrophysics Data System (ADS)
Alfieri, Luisa
2015-12-01
Power quality (PQ) disturbances are becoming an important issue in smart grids (SGs) due to the significant economic consequences that they can generate on sensible loads. However, SGs include several distributed energy resources (DERs) that can be interconnected to the grid with static converters, which lead to a reduction of the PQ levels. Among DERs, wind turbines and photovoltaic systems are expected to be used extensively due to the forecasted reduction in investment costs and other economic incentives. These systems can introduce significant time-varying voltage and current waveform distortions that require advanced spectral analysis methods to be used. This paper provides an application of advanced parametric methods for assessing waveform distortions in SGs with dispersed generation. In particular, the Standard International Electrotechnical Committee (IEC) method, some parametric methods (such as Prony and Estimation of Signal Parameters by Rotational Invariance Technique (ESPRIT)), and some hybrid methods are critically compared on the basis of their accuracy and the computational effort required.
Grid-based methods for biochemical ab initio quantum chemical applications
Colvin, M.E.; Nelson, J.S.; Mori, E.
1997-01-01
A initio quantum chemical methods are seeing increased application in a large variety of real-world problems including biomedical applications ranging from drug design to the understanding of environmental mutagens. The vast majority of these quantum chemical methods are {open_quotes}spectral{close_quotes}, that is they describe the charge distribution around the nuclear framework in terms of a fixed analytic basis set. Despite the additional complexity they bring, methods involving grid representations of the electron or solvent charge can provide more efficient schemes for evaluating spectral operators, inexpensive methods for calculating electron correlation, and methods for treating the electrostatic energy of salvation in polar solvents. The advantage of mixed or {open_quotes}pseudospectral{close_quotes} methods is that they allow individual non-linear operators in the partial differential equations, such as coulomb operators, to be calculated in the most appropriate regime. Moreover, these molecular grids can be used to integrate empirical functionals of the electron density. These so-called density functional methods (DFT) are an extremely promising alternative to conventional post-Hartree Fock quantum chemical methods. The introduction of a grid at the molecular solvent-accessible surface allows a very sophisticated treatment of a polarizable continuum solvent model (PCM). Where most PCM approaches use a truncated expansion of the solute`s electric multipole expansion, e.g. net charge (Born model) or dipole moment (Onsager model), such a grid-based boundary-element method (BEM) yields a nearly exact treatment of the solute`s electric field. This report describes the use of both DFT and BEM methods in several biomedical chemical applications.
Adaptive sequential methods for detecting network intrusions
NASA Astrophysics Data System (ADS)
Chen, Xinjia; Walker, Ernest
2013-06-01
In this paper, we propose new sequential methods for detecting port-scan attackers which routinely perform random "portscans" of IP addresses to find vulnerable servers to compromise. In addition to rigorously control the probability of falsely implicating benign remote hosts as malicious, our method performs significantly faster than other current solutions. Moreover, our method guarantees that the maximum amount of observational time is bounded. In contrast to the previous most effective method, Threshold Random Walk Algorithm, which is explicit and analytical in nature, our proposed algorithm involve parameters to be determined by numerical methods. We have introduced computational techniques such as iterative minimax optimization for quick determination of the parameters of the new detection algorithm. A framework of multi-valued decision for detecting portscanners and DoS attacks is also proposed.
LDRD Final Report: Adaptive Methods for Laser Plasma Simulation
Dorr, M R; Garaizar, F X; Hittinger, J A
2003-01-29
The goal of this project was to investigate the utility of parallel adaptive mesh refinement (AMR) in the simulation of laser plasma interaction (LPI). The scope of work included the development of new numerical methods and parallel implementation strategies. The primary deliverables were (1) parallel adaptive algorithms to solve a system of equations combining plasma fluid and light propagation models, (2) a research code implementing these algorithms, and (3) an analysis of the performance of parallel AMR on LPI problems. The project accomplished these objectives. New algorithms were developed for the solution of a system of equations describing LPI. These algorithms were implemented in a new research code named ALPS (Adaptive Laser Plasma Simulator) that was used to test the effectiveness of the AMR algorithms on the Laboratory's large-scale computer platforms. The details of the algorithm and the results of the numerical tests were documented in an article published in the Journal of Computational Physics [2]. A principal conclusion of this investigation is that AMR is most effective for LPI systems that are ''hydrodynamically large'', i.e., problems requiring the simulation of a large plasma volume relative to the volume occupied by the laser light. Since the plasma-only regions require less resolution than the laser light, AMR enables the use of efficient meshes for such problems. In contrast, AMR is less effective for, say, a single highly filamented beam propagating through a phase plate, since the resulting speckle pattern may be too dense to adequately separate scales with a locally refined mesh. Ultimately, the gain to be expected from the use of AMR is highly problem-dependent. One class of problems investigated in this project involved a pair of laser beams crossing in a plasma flow. Under certain conditions, energy can be transferred from one beam to the other via a resonant interaction with an ion acoustic wave in the crossing region. AMR provides an
Identification of nonlinear optical systems using adaptive kernel methods
NASA Astrophysics Data System (ADS)
Wang, Xiaodong; Zhang, Changjiang; Zhang, Haoran; Feng, Genliang; Xu, Xiuling
2005-12-01
An identification approach of nonlinear optical dynamic systems, based on adaptive kernel methods which are modified version of least squares support vector machine (LS-SVM), is presented in order to obtain the reference dynamic model for solving real time applications such as adaptive signal processing of the optical systems. The feasibility of this approach is demonstrated with the computer simulation through identifying a Bragg acoustic-optical bistable system. Unlike artificial neural networks, the adaptive kernel methods possess prominent advantages: over fitting is unlikely to occur by employing structural risk minimization criterion, the global optimal solution can be uniquely obtained owing to that its training is performed through the solution of a set of linear equations. Also, the adaptive kernel methods are still effective for the nonlinear optical systems with a variation of the system parameter. This method is robust with respect to noise, and it constitutes another powerful tool for the identification of nonlinear optical systems.
A METHOD OF TREATING UNSTRUCTURED CONCAVE CELLS IN STAGGERED-GRID LAGRANGIAN HYDRODYNAMICS
C. ROUSCULP; D. BURTON
2000-12-01
A method is proposed for the treatment of concave cells in staggered-grid Lagrangian hydrodynamics. The method is general enough to be applied to two- and three-dimensional unstructured cells. Instead of defining a cell-point as the geometric average of its nodes (a cell-center), the cell-point is that which equalizes the triangular/tetrahedral area/volume in two/three dimensions. Examples are given.
Huang, Zhenyu; Zhou, Ning; Tuffner, Francis K.; Chen, Yousu; Trudnowski, Daniel J.; Diao, Ruisheng; Fuller, Jason C.; Mittelstadt, William A.; Hauer, John F.; Dagle, Jeffery E.
2010-10-18
Small signal stability problems are one of the major threats to grid stability and reliability in the U.S. power grid. An undamped mode can cause large-amplitude oscillations and may result in system breakups and large-scale blackouts. There have been several incidents of system-wide oscillations. Of those incidents, the most notable is the August 10, 1996 western system breakup, a result of undamped system-wide oscillations. Significant efforts have been devoted to monitoring system oscillatory behaviors from measurements in the past 20 years. The deployment of phasor measurement units (PMU) provides high-precision, time-synchronized data needed for detecting oscillation modes. Measurement-based modal analysis, also known as ModeMeter, uses real-time phasor measurements to identify system oscillation modes and their damping. Low damping indicates potential system stability issues. Modal analysis has been demonstrated with phasor measurements to have the capability of estimating system modes from both oscillation signals and ambient data. With more and more phasor measurements available and ModeMeter techniques maturing, there is yet a need for methods to bring modal analysis from monitoring to actions. The methods should be able to associate low damping with grid operating conditions, so operators or automated operation schemes can respond when low damping is observed. The work presented in this report aims to develop such a method and establish a Modal Analysis for Grid Operation (MANGO) procedure to aid grid operation decision making to increase inter-area modal damping. The procedure can provide operation suggestions (such as increasing generation or decreasing load) for mitigating inter-area oscillations.
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 simulation of multiphase flows using octree adaptivity and the volume-of-fluid method
NASA Astrophysics Data System (ADS)
Agbaglah, Gilou; Delaux, Sébastien; Fuster, Daniel; Hoepffner, Jérôme; Josserand, Christophe; Popinet, Stéphane; Ray, Pascal; Scardovelli, Ruben; Zaleski, Stéphane
2011-02-01
We describe computations performed using the Gerris code, an open-source software implementing finite volume solvers on an octree adaptive grid together with a piecewise linear volume of fluid interface tracking method. The parallelisation of Gerris is achieved by domain decomposition. We show examples of the capabilities of Gerris on several types of problems. The impact of a droplet on a layer of the same liquid results in the formation of a thin air layer trapped between the droplet and the liquid layer that the adaptive refinement allows to capture. It is followed by the jetting of a thin corolla emerging from below the impacting droplet. The jet atomisation problem is another extremely challenging computational problem, in which a large number of small scales are generated. Finally we show an example of a turbulent jet computation in an equivalent resolution of 6×1024 cells. The jet simulation is based on the configuration of the Deepwater Horizon oil leak.
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.
Improved halftoning method for autostereoscopic display based on float grid-division multiplexing.
Chen, Duo; Sang, Xinzhu; Yu, Xunbo; Chen, Zhidong; Wang, Peng; Gao, Xin; Guo, Nan; Xie, Songlin
2016-08-01
Autostereoscopic printing is one of the most common ways for three-dimensional display, because it can present finer results by printing higher dots per inches (DPI). However, there are some problems for current methods. First, errors caused by dislocation between integer grids and non-customized lenticular lens result in severe vision quality. Second, the view-number and gray-level cannot be set arbitrarily. In this paper, an improved halftoning method for autostereoscopic printing based on float grid-division multiplexing (fGDM) is proposed. FGDM effectively addresses above two problems. GPU based program of fGDM is enabled to achieve the result very fast. Films with lenticular lens array are implemented in experiments to verify the effectiveness of proposed method which provides an improved three-dimensional performance, compared with the AM screening and random screening. PMID:27505777
NASA Technical Reports Server (NTRS)
Lee-Rausch, E. M.; Park, M. A.; Jones, W. T.; Hammond, D. P.; Nielsen, E. J.
2005-01-01
This paper demonstrates the extension of error estimation and adaptation methods to parallel computations enabling larger, more realistic aerospace applications and the quantification of discretization errors for complex 3-D solutions. Results were shown for an inviscid sonic-boom prediction about a double-cone configuration and a wing/body segmented leading edge (SLE) configuration where the output function of the adjoint was pressure integrated over a part of the cylinder in the near field. After multiple cycles of error estimation and surface/field adaptation, a significant improvement in the inviscid solution for the sonic boom signature of the double cone was observed. Although the double-cone adaptation was initiated from a very coarse mesh, the near-field pressure signature from the final adapted mesh compared very well with the wind-tunnel data which illustrates that the adjoint-based error estimation and adaptation process requires no a priori refinement of the mesh. Similarly, the near-field pressure signature for the SLE wing/body sonic boom configuration showed a significant improvement from the initial coarse mesh to the final adapted mesh in comparison with the wind tunnel results. Error estimation and field adaptation results were also presented for the viscous transonic drag prediction of the DLR-F6 wing/body configuration, and results were compared to a series of globally refined meshes. Two of these globally refined meshes were used as a starting point for the error estimation and field-adaptation process where the output function for the adjoint was the total drag. The field-adapted results showed an improvement in the prediction of the drag in comparison with the finest globally refined mesh and a reduction in the estimate of the remaining drag error. The adjoint-based adaptation parameter showed a need for increased resolution in the surface of the wing/body as well as a need for wake resolution downstream of the fuselage and wing trailing edge
A Cartesian Adaptive Level Set Method for Two-Phase Flows
NASA Technical Reports Server (NTRS)
Ham, F.; Young, Y.-N.
2003-01-01
In the present contribution we develop a level set method based on local anisotropic Cartesian adaptation as described in Ham et al. (2002). Such an approach should allow for the smallest possible Cartesian grid capable of resolving a given flow. The remainder of the paper is organized as follows. In section 2 the level set formulation for free surface calculations is presented and its strengths and weaknesses relative to the other free surface methods reviewed. In section 3 the collocated numerical method is described. In section 4 the method is validated by solving the 2D and 3D drop oscilation problem. In section 5 we present some results from more complex cases including the 3D drop breakup in an impulsively accelerated free stream, and the 3D immiscible Rayleigh-Taylor instability. Conclusions are given in section 6.
Accuracy enhancements for overset grids using a defect correction approach
NASA Technical Reports Server (NTRS)
Rogers, Stuart E.; Pulliam, Thomas H.
1994-01-01
A defect-correction approach is investigated as a means of enhancing the accuracy of flow computations on overset grids. Typically, overset-grid techniques process and pass information only at grid boundaries. In the current approach, error corrections at all overlapped interior points are injected between grids by using a defect-correction scheme. In some cases this is found to enhance the overall accuracy of the overset-grid method. Locally refined overset grids can be used to provide an efficient solution-adaptation method. The defect correction can also be ultilized as an error-correction technique for a coarse grid by evaluating the residual using a fine base grid, but solving the implicit equations only on the coarse grid. Numerical examples include an accuracy and dissipation study of an unsteady decaying vortex flow, the flow over a NACA 0012 airfoil, and the flow over a mulit-element high-lift airfoil.
Chertkov, Michael
2012-07-24
The goal of the DTRA project is to develop a mathematical framework that will provide the fundamental understanding of network survivability, algorithms for detecting/inferring pre-cursors of abnormal network behaviors, and methods for network adaptability and self-healing from cascading failures.
Adaptive Transmission Control Method for Communication-Broadcasting Integrated Services
NASA Astrophysics Data System (ADS)
Koto, Hideyuki; Furuya, Hiroki; Nakamura, Hajime
This paper proposes an adaptive transmission control method for massive and intensive telecommunication traffic generated by communication-broadcasting integrated services. The proposed method adaptively controls data transmissions from viewers depending on the congestion states, so that severe congestion can be effectively avoided. Furthermore, it utilizes the broadcasting channel which is not only scalable, but also reliable for controlling the responses from vast numbers of viewers. The performance of the proposed method is evaluated through experiments on a test bed where approximately one million viewers are emulated. The obtained results quantitatively demonstrate the performance of the proposed method and its effectiveness under massive and intensive traffic conditions.
The direct simulation Monte Carlo method using unstructured adaptive mesh and its application
NASA Astrophysics Data System (ADS)
Wu, J.-S.; Tseng, K.-C.; Kuo, C.-H.
2002-02-01
The implementation of an adaptive mesh-embedding (h-refinement) scheme using unstructured grid in two-dimensional direct simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new mesh where the local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging node, by introducing the an-isotropic refinement in the interfacial cells between refined and non-refined cells. Not only does this remedy increase a negligible amount of work, but it also removes all the difficulties presented in the originals scheme. We have tested the proposed scheme for argon gas in a high-speed driven cavity flow. The results show an improved flow resolution as compared with that of un-adaptive mesh. Finally, we have used triangular adaptive mesh to compute a near-continuum gas flow, a hypersonic flow over a cylinder. The results show fairly good agreement with previous studies. In summary, the proposed simple mesh adaptation is very useful in computing rarefied gas flows, which involve both complicated geometry and highly non-uniform density variations throughout the flow field. Copyright
An auto-adaptive background subtraction method for Raman spectra
NASA Astrophysics Data System (ADS)
Xie, Yi; Yang, Lidong; Sun, Xilong; Wu, Dewen; Chen, Qizhen; Zeng, Yongming; Liu, Guokun
2016-05-01
Background subtraction is a crucial step in the preprocessing of Raman spectrum. Usually, parameter manipulating of the background subtraction method is necessary for the efficient removal of the background, which makes the quality of the spectrum empirically dependent. In order to avoid artificial bias, we proposed an auto-adaptive background subtraction method without parameter adjustment. The main procedure is: (1) select the local minima of spectrum while preserving major peaks, (2) apply an interpolation scheme to estimate background, (3) and design an iteration scheme to improve the adaptability of background subtraction. Both simulated data and Raman spectra have been used to evaluate the proposed method. By comparing the backgrounds obtained from three widely applied methods: the polynomial, the Baek's and the airPLS, the auto-adaptive method meets the demand of practical applications in terms of efficiency and accuracy.
Parallel-wire grid assembly with method and apparatus for construction thereof
Lewandowski, E.F.; Vrabec, J.
1981-10-26
Disclosed is a parallel wire grid and an apparatus and method for making the same. The grid consists of a generally coplanar array of parallel spaced-apart wires secured between metallic frame members by an electrically conductive epoxy. The method consists of continuously winding a wire about a novel winding apparatus comprising a plurality of spaced-apart generally parallel spindles. Each spindle is threaded with a number of predeterminedly spaced-apart grooves which receive and accurately position the wire at predetermined positions along the spindle. Overlying frame members coated with electrically conductive epoxy are then placed on either side of the wire array and are drawn together. After the epoxy hardens, portions of the wire array lying outside the frame members are trimmed away.
Parallel-wire grid assembly with method and apparatus for construction thereof
Lewandowski, Edward F.; Vrabec, John
1984-01-01
Disclosed is a parallel wire grid and an apparatus and method for making the same. The grid consists of a generally coplanar array of parallel spaced-apart wires secured between metallic frame members by an electrically conductive epoxy. The method consists of continuously winding a wire about a novel winding apparatus comprising a plurality of spaced-apart generally parallel spindles. Each spindle is threaded with a number of predeterminedly spaced-apart grooves which receive and accurately position the wire at predetermined positions along the spindle. Overlying frame members coated with electrically conductive epoxy are then placed on either side of the wire array and are drawn together. After the epoxy hardens, portions of the wire array lying outside the frame members are trimmed away.
Implicit method for the computation of unsteady flows on unstructured grids
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.; Mavriplis, D. J.
1995-01-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.
Implicit method for the computation of unsteady flows on unstructured grids
Venkatakrishnan, V.; Mavriplis, D.J.
1996-09-01
An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed. 48 refs., 24 figs.
Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau
2010-01-01
A reconstruction-based discontinuous Galerkin (RDG) method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. The RDG method, originally developed for the compressible Euler equations, is extended to discretize viscous and heat fluxes in the Navier-Stokes equations using a so-called inter-cell reconstruction, where a smooth solution is locally reconstructed using a least-squares method from the underlying discontinuous DG solution. Similar to the recovery-based DG (rDG) methods, this reconstructed DG method eliminates the introduction of ad hoc penalty or coupling terms commonly found in traditional DG methods. Unlike rDG methods, this RDG method does not need to judiciously choose a proper form of a recovered polynomial, thus is simple, flexible, and robust, and can be used on arbitrary grids. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG method is able to deliver the same accuracy as the well-known Bassi-Rebay II scheme, at a half of its computing costs for the discretization of the viscous fluxes in the Navier-Stokes equations, clearly demonstrating its superior performance over the existing DG methods for solving the compressible Navier-Stokes equations.
Action research to improve methods of delivery and feedback in an Access Grid Room environment
NASA Astrophysics Data System (ADS)
McArthur, Lynne C.; Klass, Lara; Eberhard, Andrew; Stacey, Andrew
2011-12-01
This article describes a qualitative study which was undertaken to improve the delivery methods and feedback opportunity in honours mathematics lectures which are delivered through Access Grid Rooms. Access Grid Rooms are facilities that provide two-way video and audio interactivity across multiple sites, with the inclusion of smart boards. The principal aim was to improve the student learning experience, given the new environment. The specific aspects of the course delivery that the study focused on included presentation of materials and provision of opportunities for interaction between the students and between students and lecturers. The practical considerations in the delivery of distance learning are well documented in the literature, and similar problems arise in the Access Grid Room environment; in particular, those of limited access to face-to-face interaction and the reduction in peer support. The nature of the Access Grid Room classes implies that students studying the same course can be physically situated in different cities, and possibly in different countries. When studying, it is important that students have opportunity to discuss new concepts with others; particularly their peers and their lecturer. The Access Grid Room environment also presents new challenges for the lecturer, who must learn new skills in the delivery of materials. The unique nature of Access Grid Room technology offers unprecedented opportunity for effective course delivery and positive outcomes for students, and was developed in response to a need to be able to interact with complex data, other students and the instructor, in real-time, at a distance and from multiple sites. This is a relatively new technology and as yet there has been little or no studies specifically addressing the use and misuse of the technology. The study found that the correct placement of cameras and the use of printed material and smart boards were all crucial to the student experience. In addition, the
Precision grid survey apparatus and method for the mapping of hidden ferromagnetic structures
von Wimmerspeg, Udo
2004-11-16
The present invention is for a precision grid surveyor having a stationary unit and a roving unit. The stationary unit has a light source unit that emits a light beam and a rotator to project the light beam toward detectors on a roving unit. The roving unit moves over an area to be surveyed. Further the invention is for a method of mapping details of hidden underground iron pipelines, and more particularly the location of bell joints.
NASA Astrophysics Data System (ADS)
Shi, Lei; Wang, Z. J.
2015-08-01
Adjoint-based mesh adaptive methods are capable of distributing computational resources to areas which are important for predicting an engineering output. In this paper, we develop an adjoint-based h-adaptation approach based on the high-order correction procedure via reconstruction formulation (CPR) to minimize the output or functional error. A dual-consistent CPR formulation of hyperbolic conservation laws is developed and its dual consistency is analyzed. Super-convergent functional and error estimate for the output with the CPR method are obtained. Factors affecting the dual consistency, such as the solution point distribution, correction functions, boundary conditions and the discretization approach for the non-linear flux divergence term, are studied. The presented method is then used to perform simulations for the 2D Euler and Navier-Stokes equations with mesh adaptation driven by the adjoint-based error estimate. Several numerical examples demonstrate the ability of the presented method to dramatically reduce the computational cost comparing with uniform grid refinement.
A two-dimensional adaptive spectral element method for the direct simulation of incompressible flow
NASA Astrophysics Data System (ADS)
Hsu, Li-Chieh
The spectral element method is a high order discretization scheme for the solution of nonlinear partial differential equations. The method draws its strengths from the finite element method for geometrical flexibility and spectral methods for high accuracy. Although the method is, in theory, very powerful for complex phenomena such as transitional flows, its practical implementation is limited by the arbitrary choice of domain discretization. For instance, it is hard to estimate the appropriate number of elements for a specific case. Selection of regions to be refined or coarsened is difficult especially as the flow becomes more complex and memory limits of the computer are stressed. We present an adaptive spectral element method in which the grid is automatically refined or coarsened in order to capture underresolved regions of the domain and to follow regions requiring high resolution as they develop in time. The objective is to provide the best and most efficient solution to a time-dependent nonlinear problem by continually optimizing resource allocation. The adaptivity is based on an error estimator which determines which regions need more resolution. The solution strategy is as follows: compute an initial solution with a suitable initial mesh, estimate errors in the solution locally in each element, modify the mesh according to the error estimators, interpolate old mesh solutions onto the new elements, and resume the numerical solution process. A two-dimensional adaptive spectral element method for the direct simulation of incompressible flows has been developed. The adaptive algorithm effectively diagnoses and refines regions of the flow where complexity of the solution requires increased resolution. The method has been demonstrated on two-dimensional examples in heat conduction, Stokes and Navier-Stokes flows.
A cross-domain communication resource scheduling method for grid-enabled communication networks
NASA Astrophysics Data System (ADS)
Zheng, Xiangquan; Wen, Xiang; Zhang, Yongding
2011-10-01
To support a wide range of different grid applications in environments where various heterogeneous communication networks coexist, it is important to enable advanced capabilities in on-demand and dynamical integration and efficient co-share with cross-domain heterogeneous communication resource, thus providing communication services which are impossible for single communication resource to afford. Based on plug-and-play co-share and soft integration with communication resource, Grid-enabled communication network is flexibly built up to provide on-demand communication services for gird applications with various requirements on quality of service. Based on the analysis of joint job and communication resource scheduling in grid-enabled communication networks (GECN), this paper presents a cross multi-domain communication resource cooperatively scheduling method and describes the main processes such as traffic requirement resolution for communication services, cross multi-domain negotiation on communication resource, on-demand communication resource scheduling, and so on. The presented method is to afford communication service capability to cross-domain traffic delivery in GECNs. Further research work towards validation and implement of the presented method is pointed out at last.
NASA Astrophysics Data System (ADS)
Sharan, Nek; Pantano, Carlos; Bodony, Daniel
2015-11-01
Overset grids provide an efficient and flexible framework to implement high-order finite difference methods for simulations of compressible viscous flows over complex geometries. However, prior overset methods were not provably stable and were applied with artificial dissipation in the interface regions. We will discuss new, provably time-stable methods for solving hyperbolic problems on overlapping grids. The proposed methods use the summation-by-parts (SBP) derivative approximations coupled with the simultaneous-approximation-term (SAT) methodology for applying boundary conditions and interface treatments. The performance of the methods will be assessed against the commonly-used approach of injecting the interpolated data onto each grid. Numerical results will be presented to confirm the stability and the accuracy of the methods for solving the Euler equations. The extension of these methods to solve the Navier-Stokes equations on overset grids in a time-stable manner will be briefly discussed.
NASA Astrophysics Data System (ADS)
Tian, Shuling; Wu, Yizhao; Xia, Jian
A parallel Navier-Stokes solver based on dynamic overset unstructured grids method is presented to simulate the unsteady turbulent flow field around helicopter in forward flight. The grid method has the advantages of unstructured grid and Chimera grid and is suitable to deal with multiple bodies in relatively moving. Unsteady Navier-Stokes equations are solved on overset unstructured grids by an explicit dual time-stepping, finite volume method. Preconditioning method applied to inner iteration of the dual-time stepping is used to speed up the convergence of numerical simulation. The Spalart-Allmaras one-equation turbulence model is used to evaluate the turbulent viscosity. Parallel computation is based on the dynamic domain decomposition method in overset unstructured grids system at each physical time step. A generic helicopter Robin with a four-blade rotor in forward flight is considered to validate the method presented in this paper. Numerical simulation results show that the parallel dynamic overset unstructured grids method is very efficient for the simulation of helicopter flow field and the results are reliable.
Arbitrarily High Order Transport Method of the Characteristic Type for Tetrahedral Grids
Azmy, YY
2001-06-27
A formalism is derived for the Arbitrarily High Order Transport (AHOT) method of the Characteristic type (AHOT-C) in three-dimensional geometry for unstructured grids (UG). The resulting equations are implemented in a computer code, AHOT-C-UG, in the C language. The transport solution on the unstructured grid is stored as two inter-linked lists of cell and face flux moments. This arrangement allows the transport sweep to select the order of evaluation dynamically so that the typical recursive ordering of the discrete ordinate's mesh sweep is maintained without the need to store a precomputed order for each ordinate. The dynamic cell sweep order thus reduces the memory demand without excessively increasing execution time. Comparison of AHOT-C-UG's solutions to fine mesh TORT solutions illustrate high accuracy of the new method. In particular, large half a million cell numerical tests illustrate a convergence rate for the error as O(h), where h is a measure of the longest edge in the tetrahedral grid. Execution time on a 700 MHz Intel Pentium III running Linux 2.4.0 is less than 0.2 ms per cell-angle sweep operation. Also the total memory requirement is of the order of 240 bytes per tetrahedral cell, where 64-bit arithmetic precision is employed throughout.
NASA Astrophysics Data System (ADS)
Egami, Yoshiyuki; Iwase, Shigeru; Tsukamoto, Shigeru; Ono, Tomoya; Hirose, Kikuji
2015-09-01
We develop a first-principles electron-transport simulator based on the Lippmann-Schwinger (LS) equation within the framework of the real-space finite-difference scheme. In our fully real-space-based LS (grid LS) method, the ratio expression technique for the scattering wave functions and the Green's function elements of the reference system is employed to avoid numerical collapse. Furthermore, we present analytical expressions and/or prominent calculation procedures for the retarded Green's function, which are utilized in the grid LS approach. In order to demonstrate the performance of the grid LS method, we simulate the electron-transport properties of the semiconductor-oxide interfaces sandwiched between semi-infinite jellium electrodes. The results confirm that the leakage current through the (001 )Si -SiO2 model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001 )Ge -GeO2 model is insensitive to the dangling bond state.
CFD simulation of automotive I.C. engines with advanced moving grid and multi-domain methods
NASA Astrophysics Data System (ADS)
Lai, Y. G.; Przekwas, A. J.; Sun, R. L. T.
1993-07-01
An efficient numerical method is presented with multi-domain and moving grid capabilities to best suit internal combustion engine applications. Multi-domain capability allows a user to arbitrarily cut the solution domain into many topologically simpler domains. Consequently, simultaneous coupling among components becomes natural and the task of grid generation becomes easier. The moving grid capability allows the computational grid to move and conform to the piston motion. As a result, the grid always fits the flow boundaries and no special remapping or interpolation is needed. The method has been implemented to solve 2D and 3D flows in a body-fitted coordinate system. Air ingestion and scavenging flow problems in a generic four-stroke engine and a two-stroke engine are simulated to demonstrate the proposed approach.
NASA Technical Reports Server (NTRS)
Atkins, Harold L.; Lockard, David P.
1999-01-01
A method for the prediction of acoustic scatter from complex geometries is presented. The discontinuous Galerkin method provides a framework for the development of a high-order method using unstructured grids. The method's compact form contributes to its accuracy and efficiency, and makes the method well suited for distributed memory parallel computing platforms. Mesh refinement studies are presented to validate the expected convergence properties of the method, and to establish the absolute levels of a error one can expect at a given level of resolution. For a two-dimensional shear layer instability wave and for three-dimensional wave propagation, the method is demonstrated to be insensitive to mesh smoothness. Simulations of scatter from a two-dimensional slat configuration and a three-dimensional blended-wing-body demonstrate the capability of the method to efficiently treat realistic geometries.
Zuzovski, Michael; Boag, Amir; Natan, Amir
2015-12-21
In this work we show the implementation of a linear scaling algorithm for the calculation of the Poisson integral. We use domain decomposition and non-uniform auxiliary grids (NGs) to calculate the electrostatic interaction. We demonstrate the approach within the PARSEC density functional theory code and perform calculations of long 1D carbon chains and other long molecules. Finally, we discuss possible applications to additional problems and geometries. PMID:26123448
On the Analysis of Multistep-Out-of-Grid Method for Celestial Mechanics Tasks
NASA Astrophysics Data System (ADS)
Olifer, L.; Choliy, V.
2016-09-01
Occasionally, there is a necessity in high-accurate prediction of celestial body trajectory. The most common way to do that is to solve Kepler's equation analytically or to use Runge-Kutta or Adams integrators to solve equation of motion numerically. For low-orbit satellites, there is a critical need in accounting geopotential and another forces which influence motion. As the result, the right side of equation of motion becomes much bigger, and classical integrators will not be quite effective. On the other hand, there is a multistep-out-of-grid (MOG) method which combines Runge-Kutta and Adams methods. The MOG method is based on using m on-grid values of the solution and n × m off-grid derivative estimations. Such method could provide stable integrators of maximum possible order, O (hm+mn+n-1). The main subject of this research was to implement and analyze the MOG method for solving satellite equation of motion with taking into account Earth geopotential model (ex. EGM2008 (Pavlis at al., 2008)) and with possibility to add other perturbations such as atmospheric drag or solar radiation pressure. Simulations were made for satellites on low orbit and with various eccentricities (from 0.1 to 0.9). Results of the MOG integrator were compared with results of Runge-Kutta and Adams integrators. It was shown that the MOG method has better accuracy than classical ones of the same order and less right-hand value estimations when is working on high orders. That gives it some advantage over "classical" methods.
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
Three-Dimensional High-Order Spectral Finite Volume Method for Unstructured Grids
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel; Wang, Z. J.; Kwak, Dochan (Technical Monitor)
2002-01-01
Many areas require a very high-order accurate numerical solution of conservation laws for complex shapes. This paper deals with the extension to three dimensions of the Spectral Finite Volume (SV) method for unstructured grids, which was developed to solve such problems. We first summarize the limitations of traditional methods such as finite-difference, and finite-volume for both structured and unstructured grids. We then describe the basic formulation of the spectral finite volume method. What distinguishes the SV method from conventional high-order finite-volume methods for unstructured triangular or tetrahedral grids is the data reconstruction. Instead of using a large stencil of neighboring cells to perform a high-order reconstruction, the stencil is constructed by partitioning each grid cell, called a spectral volume (SV), into 'structured' sub-cells, called control volumes (CVs). One can show that if all the SV cells are partitioned into polygonal or polyhedral CV sub-cells in a geometrically similar manner, the reconstructions for all the SVs become universal, irrespective of their shapes, sizes, orientations, or locations. It follows that the reconstruction is reduced to a weighted sum of unknowns involving just a few simple adds and multiplies, and those weights are universal and can be pre-determined once for all. The method is thus very efficient, accurate, and yet geometrically flexible. The most critical part of the SV method is the partitioning of the SV into CVs. In this paper we present the partitioning of a tetrahedral SV into polyhedral CVs with one free parameter for polynomial reconstructions up to degree of precision five. (Note that the order of accuracy of the method is one order higher than the reconstruction degree of precision.) The free parameter will be determined by minimizing the Lebesgue constant of the reconstruction matrix or similar criteria to obtain optimized partitions. The details of an efficient, parallelizable code to solve
Dynamic grid refinement for partial differential equations on parallel computers
NASA Technical Reports Server (NTRS)
Mccormick, S.; Quinlan, D.
1989-01-01
The fast adaptive composite grid method (FAC) is an algorithm that uses various levels of uniform grids to provide adaptive resolution and fast solution of PDEs. An asynchronous version of FAC, called AFAC, that completely eliminates the bottleneck to parallelism is presented. This paper describes the advantage that this algorithm has in adaptive refinement for moving singularities on multiprocessor computers. This work is applicable to the parallel solution of two- and three-dimensional shock tracking problems.
Grid Generation Techniques Utilizing the Volume Grid Manipulator
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
1998-01-01
This paper presents grid generation techniques available in the Volume Grid Manipulation (VGM) code. The VGM code is designed to manipulate existing line, surface and volume grids to improve the quality of the data. It embodies an easy to read rich language of commands that enables such alterations as topology changes, grid adaption and smoothing. Additionally, the VGM code can be used to construct simplified straight lines, splines, and conic sections which are common curves used in the generation and manipulation of points, lines, surfaces and volumes (i.e., grid data). These simple geometric curves are essential in the construction of domain discretizations for computational fluid dynamic simulations. By comparison to previously established methods of generating these curves interactively, the VGM code provides control of slope continuity and grid point-to-point stretchings as well as quick changes in the controlling parameters. The VGM code offers the capability to couple the generation of these geometries with an extensive manipulation methodology in a scripting language. The scripting language allows parametric studies of a vehicle geometry to be efficiently performed to evaluate favorable trends in the design process. As examples of the powerful capabilities of the VGM code, a wake flow field domain will be appended to an existing X33 Venturestar volume grid; negative volumes resulting from grid expansions to enable flow field capture on a simple geometry, will be corrected; and geometrical changes to a vehicle component of the X33 Venturestar will be shown.
R. M. Ferrer; Y. Y. Azmy
2009-05-01
We present a robust arbitrarily high order transport method of the characteristic type for unstructured tetrahedral grids. Previously encountered difficulties have been addressed through the reformulation of the method based on coordinate transformations, evaluation of the moments balance relation as a linear system of equations involving the expansion coefficients of the projected basis, and the asymptotic expansion of the integral kernels in the thin cell limit. The proper choice of basis functions for the high-order spatial expansion of the solution is discussed and its effect on problems involving scattering discussed. Numerical tests are presented to illustrate the beneficial effect of these improvements, and the improved robustness they yield.
A fourth order accurate adaptive mesh refinement method forpoisson's equation
Barad, Michael; Colella, Phillip
2004-08-20
We present a block-structured adaptive mesh refinement (AMR) method for computing solutions to Poisson's equation in two and three dimensions. It is based on a conservative, finite-volume formulation of the classical Mehrstellen methods. This is combined with finite volume AMR discretizations to obtain a method that is fourth-order accurate in solution error, and with easily verifiable solvability conditions for Neumann and periodic boundary conditions.
Wavelet methods in multi-conjugate adaptive optics
NASA Astrophysics Data System (ADS)
Helin, T.; Yudytskiy, M.
2013-08-01
The next generation ground-based telescopes rely heavily on adaptive optics for overcoming the limitation of atmospheric turbulence. In the future adaptive optics modalities, like multi-conjugate adaptive optics (MCAO), atmospheric tomography is the major mathematical and computational challenge. In this severely ill-posed problem, a fast and stable reconstruction algorithm is needed that can take into account many real-life phenomena of telescope imaging. We introduce a novel reconstruction method for the atmospheric tomography problem and demonstrate its performance and flexibility in the context of MCAO. Our method is based on using locality properties of compactly supported wavelets, both in the spatial and frequency domains. The reconstruction in the atmospheric tomography problem is obtained by solving the Bayesian MAP estimator with a conjugate-gradient-based algorithm. An accelerated algorithm with preconditioning is also introduced. Numerical performance is demonstrated on the official end-to-end simulation tool OCTOPUS of European Southern Observatory.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar Z.
2008-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed and implemented in the NASA unstructured grid generation code VGRID. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
Adaptive windowed range-constrained Otsu method using local information
NASA Astrophysics Data System (ADS)
Zheng, Jia; Zhang, Dinghua; Huang, Kuidong; Sun, Yuanxi; Tang, Shaojie
2016-01-01
An adaptive windowed range-constrained Otsu method using local information is proposed for improving the performance of image segmentation. First, the reason why traditional thresholding methods do not perform well in the segmentation of complicated images is analyzed. Therein, the influences of global and local thresholdings on the image segmentation are compared. Second, two methods that can adaptively change the size of the local window according to local information are proposed by us. The characteristics of the proposed methods are analyzed. Thereby, the information on the number of edge pixels in the local window of the binarized variance image is employed to adaptively change the local window size. Finally, the superiority of the proposed method over other methods such as the range-constrained Otsu, the active contour model, the double Otsu, the Bradley's, and the distance-regularized level set evolution is demonstrated. It is validated by the experiments that the proposed method can keep more details and acquire much more satisfying area overlap measure as compared with the other conventional methods.
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.
A Conditional Exposure Control Method for Multidimensional Adaptive Testing
ERIC Educational Resources Information Center
Finkelman, Matthew; Nering, Michael L.; Roussos, Louis A.
2009-01-01
In computerized adaptive testing (CAT), ensuring the security of test items is a crucial practical consideration. A common approach to reducing item theft is to define maximum item exposure rates, i.e., to limit the proportion of examinees to whom a given item can be administered. Numerous methods for controlling exposure rates have been proposed…
Likelihood Methods for Adaptive Filtering and Smoothing. Technical Report #455.
ERIC Educational Resources Information Center
Butler, Ronald W.
The dynamic linear model or Kalman filtering model provides a useful methodology for predicting the past, present, and future states of a dynamic system, such as an object in motion or an economic or social indicator that is changing systematically with time. Recursive likelihood methods for adaptive Kalman filtering and smoothing are developed.…
Visualization of grids conforming to geological structures: a topological approach
NASA Astrophysics Data System (ADS)
Caumon, Guillaume; Lévy, Bruno; Castanié, Laurent; Paul, Jean-Claude
2005-07-01
Flexible grids are used in many Geoscience applications because they can accurately adapt to the great diversity of shapes encountered in nature. These grids raise a number difficult challenges, in particular for fast volume visualization. We propose a generic incremental slicing algorithm for versatile visualization of unstructured grids, these being constituted of arbitrary convex cells. The tradeoff between the complexity of the grid and the efficiency of the method is addressed by special-purpose data structures and customizations. A general structure based on oriented edges is defined to address the general case. When only a limited number of polyhedron types is present in the grid (zoo grids), memory usage and rendering time are reduced by using a catalog of cell types generated automatically. This data structure is further optimized to deal with stratigraphic grids made of hexahedral cells. The visualization method is applied to several gridded subsurface models conforming to geological structures.
NASA Astrophysics Data System (ADS)
Jin, N.; Yang, F.; Shang, S. Y.; Tao, T.; Liu, J. S.
2016-08-01
According to the limitations of the LVRT technology of traditional photovoltaic inverter existed, this paper proposes a low voltage ride through (LVRT) control method based on model current predictive control (MCPC). This method can effectively improve the photovoltaic inverter output characteristics and response speed. The MCPC method of photovoltaic grid-connected inverter designed, the sum of the absolute value of the predictive current and the given current error is adopted as the cost function with the model predictive control method. According to the MCPC, the optimal space voltage vector is selected. Photovoltaic inverter has achieved automatically switches of priority active or reactive power control of two control modes according to the different operating states, which effectively improve the inverter capability of LVRT. The simulation and experimental results proves that the proposed method is correct and effective.
GridMan: A grid manipulation system
NASA Technical Reports Server (NTRS)
Eiseman, Peter R.; Wang, Zhu
1992-01-01
GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.
NASA Astrophysics Data System (ADS)
Zhalnin, R. V.; Ladonkina, M. E.; Masyagin, V. F.; Tishkin, V. F.
2016-06-01
A numerical algorithm is proposed for solving the problem of non-stationary filtration of substance in anisotropic media by the Galerkin method with discontinuous basis functions on unstructured triangular grids. A characteristic feature of this method is that the flux variables are considered on the dual grid. The dual grid comprises median control volumes around the nodes of the original triangular grid. The flux values of the quantities on the boundary of an element are calculated with the help of stabilizing additions. For averaging the permeability tensor over the cells of the dual grid, the method of support operators is applied. The method is studied on the example of a two-dimensional boundary value problem. The convergence and approximation of the numerical method are analyzed, and results of mathematical modeling are presented. The numerical results demonstrate the applicability of this approach for solving problems of non-stationary filtration of substance in anisotropic media by the discontinuous Galerkin method on unstructured triangular grids.
Solving Chemical Master Equations by an Adaptive Wavelet Method
Jahnke, Tobias; Galan, Steffen
2008-09-01
Solving chemical master equations is notoriously difficult due to the tremendous number of degrees of freedom. We present a new numerical method which efficiently reduces the size of the problem in an adaptive way. The method is based on a sparse wavelet representation and an algorithm which, in each time step, detects the essential degrees of freedom required to approximate the solution up to the desired accuracy.
Method and system for environmentally adaptive fault tolerant computing
NASA Technical Reports Server (NTRS)
Copenhaver, Jason L. (Inventor); Jeremy, Ramos (Inventor); Wolfe, Jeffrey M. (Inventor); Brenner, Dean (Inventor)
2010-01-01
A method and system for adapting fault tolerant computing. The method includes the steps of measuring an environmental condition representative of an environment. An on-board processing system's sensitivity to the measured environmental condition is measured. It is determined whether to reconfigure a fault tolerance of the on-board processing system based in part on the measured environmental condition. The fault tolerance of the on-board processing system may be reconfigured based in part on the measured environmental condition.
Chen, Zhihuan; Yuan, Yanbin; Yuan, Xiaohui; Huang, Yuehua; Li, Xianshan; Li, Wenwu
2015-05-01
A hydraulic turbine regulating system (HTRS) is one of the most important components of hydropower plant, which plays a key role in maintaining safety, stability and economical operation of hydro-electrical installations. At present, the conventional PID controller is widely applied in the HTRS system for its practicability and robustness, and the primary problem with respect to this control law is how to optimally tune the parameters, i.e. the determination of PID controller gains for satisfactory performance. In this paper, a kind of multi-objective evolutionary algorithms, named adaptive grid particle swarm optimization (AGPSO) is applied to solve the PID gains tuning problem of the HTRS system. This newly AGPSO optimized method, which differs from a traditional one-single objective optimization method, is designed to take care of settling time and overshoot level simultaneously, in which a set of non-inferior alternatives solutions (i.e. Pareto solution) is generated. Furthermore, a fuzzy-based membership value assignment method is employed to choose the best compromise solution from the obtained Pareto set. An illustrative example associated with the best compromise solution for parameter tuning of the nonlinear HTRS system is introduced to verify the feasibility and the effectiveness of the proposed AGPSO-based optimization approach, as compared with two another prominent multi-objective algorithms, i.e. Non-dominated Sorting Genetic Algorithm II (NSGAII) and Strength Pareto Evolutionary Algorithm II (SPEAII), for the quality and diversity of obtained Pareto solutions set. Consequently, simulation results show that this AGPSO optimized approach outperforms than compared methods with higher efficiency and better quality no matter whether the HTRS system works under unload or load conditions.
Fabrication of infrared wire-grid polarizer by sol–gel method and soft imprint lithography
NASA Astrophysics Data System (ADS)
Yamada, Itsunari; Ishihara, Yoshiro
2016-05-01
An infrared wire-grid polarizer was fabricated by forming a subwavelength grating of zirconia by imprinting techniques, a sol–gel method, and Al shadow thermal evaporation. After imprinting on a dropped zirconia nanoparticle dispersion using a silicone mold, 100-nm-thick Al was deposited on the fabricated zirconia grating with 400 nm period by evaporation. The extinction ratio of the fabricated element was 27.5 dB at 5.4 µm wavelength. The TM polarization transmittance was higher than that of the Si plate in the 4.2–5.3 µm wavelength range because the zirconia film acted as an antireflection film.
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.
Numerical Simulation of Parachute Inflation Process Using AN Overset Deforming Grids Method
NASA Astrophysics Data System (ADS)
Xia, Jian; Tian, Shuling; Wu, Yizhao
A numerical method for the simulation of parachute inflation process is presented in this paper. The unsteady compressible N-S equations are fully coupled with MSD (Mass Spring Damper) structure model and integrated forward in time. The CFD solver is based on an unstructured finite volume algorithm and the preconditioning technique is applied to alleviate the stiffness caused by low Mach number. The Spalart-Allmaras one-equation turbulence model is implemented to evaluate the turbulent viscosity. The whole system (fluid equations and structural model equations) is marched implicitly in time using a dual time stepping method. An overset deforming grids method is adopted in this paper to deal with the very large domain deformation during the parachute inflation process. Finally numerical test is performed to validate the robustness of this method.
An Adaptive Cross-Architecture Combination Method for Graph Traversal
You, Yang; Song, Shuaiwen; Kerbyson, Darren J.
2014-06-18
Breadth-First Search (BFS) is widely used in many real-world applications including computational biology, social networks, and electronic design automation. The combination method, using both top-down and bottom-up techniques, is the most effective BFS approach. However, current combination methods rely on trial-and-error and exhaustive search to locate the optimal switching point, which may cause significant runtime overhead. To solve this problem, we design an adaptive method based on regression analysis to predict an optimal switching point for the combination method at runtime within less than 0.1% of the BFS execution time.
An Adaptive Derivative-based Method for Function Approximation
Tong, C
2008-10-22
To alleviate the high computational cost of large-scale multi-physics simulations to study the relationships between the model parameters and the outputs of interest, response surfaces are often used in place of the exact functional relationships. This report explores a method for response surface construction using adaptive sampling guided by derivative information at each selected sample point. This method is especially suitable for applications that can readily provide added information such as gradients and Hessian with respect to the input parameters under study. When higher order terms (third and above) in the Taylor series are negligible, the approximation error for this method can be controlled. We present details of the adaptive algorithm and numerical results on a few test problems.
Adaptive IMEX schemes for high-order unstructured methods
NASA Astrophysics Data System (ADS)
Vermeire, Brian C.; Nadarajah, Siva
2015-01-01
We present an adaptive implicit-explicit (IMEX) method for use with high-order unstructured schemes. The proposed method makes use of the Gerschgorin theorem to conservatively estimate the influence of each individual degree of freedom on the spectral radius of the discretization. This information is used to split the system into implicit and explicit regions, adapting to unsteady features in the flow. We dynamically repartition the domain to balance the number of implicit and explicit elements per core. As a consequence, we are able to achieve an even load balance for each implicit/explicit stage of the IMEX scheme. We investigate linear advection-diffusion, isentropic vortex advection, unsteady laminar flow over an SD7003 airfoil, and turbulent flow over a circular cylinder. Results show that the proposed method consistently yields a stable discretization, and maintains the theoretical order of accuracy of the high-order spatial schemes.
A wavelet-MRA-based adaptive semi-Lagrangian method for the relativistic Vlasov-Maxwell system
Besse, Nicolas Latu, Guillaume Ghizzo, Alain Sonnendruecker, Eric Bertrand, Pierre
2008-08-10
In this paper we present a new method for the numerical solution of the relativistic Vlasov-Maxwell system on a phase-space grid using an adaptive semi-Lagrangian method. The adaptivity is performed through a wavelet multiresolution analysis, which gives a powerful and natural refinement criterion based on the local measurement of the approximation error and regularity of the distribution function. Therefore, the multiscale expansion of the distribution function allows to get a sparse representation of the data and thus save memory space and CPU time. We apply this numerical scheme to reduced Vlasov-Maxwell systems arising in laser-plasma physics. Interaction of relativistically strong laser pulses with overdense plasma slabs is investigated. These Vlasov simulations revealed a rich variety of phenomena associated with the fast particle dynamics induced by electromagnetic waves as electron trapping, particle acceleration, and electron plasma wavebreaking. However, the wavelet based adaptive method that we developed here, does not yield significant improvements compared to Vlasov solvers on a uniform mesh due to the substantial overhead that the method introduces. Nonetheless they might be a first step towards more efficient adaptive solvers based on different ideas for the grid refinement or on a more efficient implementation. Here the Vlasov simulations are performed in a two-dimensional phase-space where the development of thin filaments, strongly amplified by relativistic effects requires an important increase of the total number of points of the phase-space grid as they get finer as time goes on. The adaptive method could be more useful in cases where these thin filaments that need to be resolved are a very small fraction of the hyper-volume, which arises in higher dimensions because of the surface-to-volume scaling and the essentially one-dimensional structure of the filaments. Moreover, the main way to improve the efficiency of the adaptive method is to
Hong Luo; Luquing Luo; Robert Nourgaliev; Vincent Mousseau
2009-06-01
A reconstruction-based discontinuous Galerkin (DG) method is presented for the solution of the compressible Euler equations on arbitrary grids. By taking advantage of handily available and yet invaluable information, namely the derivatives, in the context of the discontinuous Galerkin methods, a solution polynomial of one degree higher is reconstructed using a least-squares method. The stencils used in the reconstruction involve only the van Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The resulting DG method can be regarded as an improvement of a recovery-based DG method in the sense that it shares the same nice features as the recovery-based DG method, such as high accuracy and efficiency, and yet overcomes some of its shortcomings such as a lack of flexibility, compactness, and robustness. The developed DG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate the accuracy and efficiency of the method. The numerical results indicate that this reconstructed DG method is able to obtain a third-order accurate solution at a slightly higher cost than its second-order DG method and provide an increase in performance over the third order DG method in terms of computing time and storage requirement.
NASA Astrophysics Data System (ADS)
Fakhari, Abbas; Geier, Martin; Lee, Taehun
2016-06-01
A mass-conserving lattice Boltzmann method (LBM) for multiphase flows is presented in this paper. The proposed LBM improves a previous model (Lee and Liu, 2010 [21]) in terms of mass conservation, speed-up, and efficiency, and also extends its capabilities for implementation on non-uniform grids. The presented model consists of a phase-field lattice Boltzmann equation (LBE) for tracking the interface between different fluids and a pressure-evolution LBM for recovering the hydrodynamic properties. In addition to the mass conservation property and the simplicity of the algorithm, the advantages of the current phase-field LBE are that it is an order of magnitude faster than the previous interface tracking LBE proposed by Lee and Liu (2010) [21] and it requires less memory resources for data storage. Meanwhile, the pressure-evolution LBM is equipped with a multi-relaxation-time (MRT) collision operator to facilitate attainability of small relaxation rates thereby allowing simulation of multiphase flows at higher Reynolds numbers. Additionally, we reformulate the presented MRT-LBM on nonuniform grids within an adaptive mesh refinement (AMR) framework. Various benchmark studies such as a rising bubble and a falling drop under buoyancy, droplet splashing on a wet surface, and droplet coalescence onto a fluid interface are conducted to examine the accuracy and versatility of the proposed AMR-LBM. The proposed model is further validated by comparing the results with other LB models on uniform grids. A factor of about 20 in savings of computational resources is achieved by using the proposed AMR-LBM. As a more demanding application, the Kelvin-Helmholtz instability (KHI) of a shear-layer flow is investigated for both density-matched and density-stratified binary fluids. The KHI results of the density-matched fluids are shown to be in good agreement with the benchmark AMR results based on the sharp-interface approach. When a density contrast between the two fluids exists, a
Advanced numerical methods in mesh generation and mesh adaptation
Lipnikov, Konstantine; Danilov, A; Vassilevski, Y; Agonzal, A
2010-01-01
Numerical solution of partial differential equations requires appropriate meshes, efficient solvers and robust and reliable error estimates. Generation of high-quality meshes for complex engineering models is a non-trivial task. This task is made more difficult when the mesh has to be adapted to a problem solution. This article is focused on a synergistic approach to the mesh generation and mesh adaptation, where best properties of various mesh generation methods are combined to build efficiently simplicial meshes. First, the advancing front technique (AFT) is combined with the incremental Delaunay triangulation (DT) to build an initial mesh. Second, the metric-based mesh adaptation (MBA) method is employed to improve quality of the generated mesh and/or to adapt it to a problem solution. We demonstrate with numerical experiments that combination of all three methods is required for robust meshing of complex engineering models. The key to successful mesh generation is the high-quality of the triangles in the initial front. We use a black-box technique to improve surface meshes exported from an unattainable CAD system. The initial surface mesh is refined into a shape-regular triangulation which approximates the boundary with the same accuracy as the CAD mesh. The DT method adds robustness to the AFT. The resulting mesh is topologically correct but may contain a few slivers. The MBA uses seven local operations to modify the mesh topology. It improves significantly the mesh quality. The MBA method is also used to adapt the mesh to a problem solution to minimize computational resources required for solving the problem. The MBA has a solid theoretical background. In the first two experiments, we consider the convection-diffusion and elasticity problems. We demonstrate the optimal reduction rate of the discretization error on a sequence of adaptive strongly anisotropic meshes. The key element of the MBA method is construction of a tensor metric from hierarchical edge
Adaptive explicit and implicit finite element methods for transient thermal analysis
NASA Technical Reports Server (NTRS)
Probert, E. J.; Hassan, O.; Morgan, K.; Peraire, J.
1992-01-01
The application of adaptive finite element methods to the solution of transient heat conduction problems in two dimensions is investigated. The computational domain is represented by an unstructured assembly of linear triangular elements and the mesh adaptation is achieved by local regeneration of the grid, using an error estimation procedure coupled to an automatic triangular mesh generator. Two alternative solution procedures are considered. In the first procedure, the solution is advanced by explicit timestepping, with domain decomposition being used to improve the computational efficiency of the method. In the second procedure, an algorithm for constructing continuous lines which pass only once through each node of the mesh is employed. The lines are used as the basis of a fully implicit method, in which the equation system is solved by line relaxation using a block tridiagonal equation solver. The numerical performance of the two procedures is compared for the analysis of a problem involving a moving heat source applied to a convectively cooled cylindrical leading edge.
Progress in unstructured-grid methods development for unsteady aerodynamic applications
NASA Technical Reports Server (NTRS)
Batina, John T.
1992-01-01
The development of unstructured-grid methods for the solution of the equations of fluid flow and what was learned over the course of the research are summarized. The focus of the discussion is on the solution of the time-dependent Euler equations including spatial discretizations, temporal discretizations, and boundary conditions. An example calculation with an implicit upwind method using a CFL number of infinity is presented for the Boeing 747 aircraft. The results were obtained in less than one hour CPU time on a Cray-2 computer, thus, demonstrating the speed and robustness of the capability. Additional calculations for the ONERA M6 wing demonstrate the accuracy of the method through the good agreement between calculated results and experimental data for a standard transonic flow case.
Space-time adaptive numerical methods for geophysical applications.
Castro, C E; Käser, M; Toro, E F
2009-11-28
In this paper we present high-order formulations of the finite volume and discontinuous Galerkin finite-element methods for wave propagation problems with a space-time adaptation technique using unstructured meshes in order to reduce computational cost without reducing accuracy. Both methods can be derived in a similar mathematical framework and are identical in their first-order version. In their extension to higher order accuracy in space and time, both methods use spatial polynomials of higher degree inside each element, a high-order solution of the generalized Riemann problem and a high-order time integration method based on the Taylor series expansion. The static adaptation strategy uses locally refined high-resolution meshes in areas with low wave speeds to improve the approximation quality. Furthermore, the time step length is chosen locally adaptive such that the solution is evolved explicitly in time by an optimal time step determined by a local stability criterion. After validating the numerical approach, both schemes are applied to geophysical wave propagation problems such as tsunami waves and seismic waves comparing the new approach with the classical global time-stepping technique. The problem of mesh partitioning for large-scale applications on multi-processor architectures is discussed and a new mesh partition approach is proposed and tested to further reduce computational cost. PMID:19840984
NASA Technical Reports Server (NTRS)
Evans, K. F.
1993-01-01
A new two-dimensional monochromatic method that computes the transfer of solar or thermal radiation through atmospheres with arbitrary optical properties is described. The model discretizes the radiative transfer equation by expanding the angular part of the radiance field in a spherical harmonic series and representing the spatial part with a discrete grid. The resulting sparse coupled system of equations is solved iteratively with the conjugate gradient method. A Monte Carlo model is used for extensive verification of outgoing flux and radiance values from both smooth and highly variable (multifractal) media. The spherical harmonic expansion naturally allows for different levels of approximation, but tests show that the 2D equivalent of the two-stream approximation is poor at approximating variations in the outgoing flux. The model developed here is shown to be highly efficient so that media with tens of thousands of grid points can be computed in minutes. The large improvement in efficiency will permit quick, accurate radiative transfer calculations of realistic cloud fields and improve our understanding of the effect of inhomogeneity on radiative transfer in cloudy atmospheres.
NASA Astrophysics Data System (ADS)
Chen, Hanming; Zhou, Hui; Sheng, Shanbo
2016-10-01
We develop the general rectangular grid discretization based time-space domain high-order staggered-grid finite-difference (SGFD) methods for modeling three-dimension (3D) scalar wave propagation. The proposed two high-order SGFD schemes can achieve the arbitrary even-order accuracy in space, and the fourth- and sixth-order accuracies in time, respectively. We derive the analytical expression of the high-order FD coefficients based on a general rectangular grid discretization with different grid spacing in all axial directions. The general rectangular grid discretization makes our time-space domain SGFD schemes more flexible than the existing ones developed on the cubic grid with the same grid spacing in the axial directions. Theoretical analysis indicates that our time-space domain SGFD schemes have a better stability and a higher accuracy than the traditional temporal second-order SGFD scheme. Our time-space domain SGFD schemes allow larger time steps than the traditional SGFD scheme for attaining a similar accuracy, and thus are more efficient. Numerical example further confirms the superior accuracy, stability and efficiency of our time-space domain SGFD schemes.
Modeling dam-break flows using finite volume method on unstructured grid
Technology Transfer Automated Retrieval System (TEKTRAN)
Two-dimensional shallow water models based on unstructured finite volume method and approximate Riemann solvers for computing the intercell fluxes have drawn growing attention because of their robustness, high adaptivity to complicated geometry and ability to simulate flows with mixed regimes and di...
Robust flicker evaluation method for low power adaptive dimming LCDs
NASA Astrophysics Data System (ADS)
Kim, Seul-Ki; Song, Seok-Jeong; Nam, Hyoungsik
2015-05-01
This paper describes a robust dimming flicker evaluation method of adaptive dimming algorithms for low power liquid crystal displays (LCDs). While the previous methods use sum of square difference (SSD) values without excluding the image sequence information, the proposed modified SSD (mSSD) values are obtained only with the dimming flicker effects by making use of differential images. The proposed scheme is verified for eight dimming configurations of two dimming level selection methods and four temporal filters over three test videos. Furthermore, a new figure of merit is introduced to cover the dimming flicker as well as image qualities and power consumption.
[An adaptive threshloding segmentation method for urinary sediment image].
Li, Yongming; Zeng, Xiaoping; Qin, Jian; Han, Liang
2009-02-01
In this paper is proposed a new method to solve the segmentation of the complicated defocusing urinary sediment image. The main points of the method are: (1) using wavelet transforms and morphology to erase the effect of defocusing and realize the first segmentation, (2) using adaptive threshold processing in accordance to the subimages after wavelet processing, and (3) using 'peel off' algorithm to deal with the overlapped cells' segmentations. The experimental results showed that this method was not affected by the defocusing, and it made good use of many kinds of characteristics of the images. So this new mehtod can get very precise segmentation; it is effective for defocusing urinary sediment image segmentation.
Advanced Unstructured Grid Generation for Complex Aerodynamic Applications
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
2010-01-01
A new approach for distribution of grid points on the surface and in the volume has been developed. In addition to the point and line sources of prior work, the new approach utilizes surface and volume sources for automatic curvature-based grid sizing and convenient point distribution in the volume. A new exponential growth function produces smoother and more efficient grids and provides superior control over distribution of grid points in the field. All types of sources support anisotropic grid stretching which not only improves the grid economy but also provides more accurate solutions for certain aerodynamic applications. The new approach does not require a three-dimensional background grid as in the previous methods. Instead, it makes use of an efficient bounding-box auxiliary medium for storing grid parameters defined by surface sources. The new approach is less memory-intensive and more efficient computationally. The grids generated with the new method either eliminate the need for adaptive grid refinement for certain class of problems or provide high quality initial grids that would enhance the performance of many adaptation methods.
Hong Luo; Hanping Xiao; Robert Nourgaliev; Chunpei Cai
2011-06-01
A comparative study of different reconstruction schemes for a reconstruction-based discontinuous Galerkin, termed RDG(P1P2) method is performed for compressible flow problems on arbitrary grids. The RDG method is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution via a reconstruction scheme commonly used in the finite volume method. Both Green-Gauss and least-squares reconstruction methods and a least-squares recovery method are implemented to obtain a quadratic polynomial representation of the underlying discontinuous Galerkin linear polynomial solution on each cell. These three reconstruction/recovery methods are compared for a variety of compressible flow problems on arbitrary meshes to access their accuracy and robustness. The numerical results demonstrate that all three reconstruction methods can significantly improve the accuracy of the underlying second-order DG method, although the least-squares reconstruction method provides the best performance in terms of both accuracy and robustness.
An adaptive locally optimal method detecting weak deterministic signals
NASA Astrophysics Data System (ADS)
Wang, C. H.
1983-10-01
A new method for detecting weak signals in interference and clutter in radar systems is presented. The detector which uses this method is adaptive for an environment varying with time and locally optimal for detecting targets and constant false-alarm ratio (CFAR) for the statistics of interference and clutter varying with time. The loss of CFAR is small, and the detector is also simple in structure. The statistical equivalent transfer characteristic of a rank quantizer which can be used as part of an adaptive locally most powerful detector (ALMP) is obtained. It is shown that the distribution-free Doppler processor of Dillard (1974) is not only a nonparameter detector, but also an ALMP detector under certain conditions.
Optimal and adaptive methods of processing hydroacoustic signals (review)
NASA Astrophysics Data System (ADS)
Malyshkin, G. S.; Sidel'nikov, G. B.
2014-09-01
Different methods of optimal and adaptive processing of hydroacoustic signals for multipath propagation and scattering are considered. Advantages and drawbacks of the classical adaptive (Capon, MUSIC, and Johnson) algorithms and "fast" projection algorithms are analyzed for the case of multipath propagation and scattering of strong signals. The classical optimal approaches to detecting multipath signals are presented. A mechanism of controlled normalization of strong signals is proposed to automatically detect weak signals. The results of simulating the operation of different detection algorithms for a linear equidistant array under multipath propagation and scattering are presented. An automatic detector is analyzed, which is based on classical or fast projection algorithms, which estimates the background proceeding from median filtering or the method of bilateral spatial contrast.
Method and apparatus for telemetry adaptive bandwidth compression
NASA Astrophysics Data System (ADS)
Graham, Olin L.
1987-07-01
Methods and apparatus are provided for automatic and/or manual adaptive bandwidth compression of telemetry. An adaptive sampler samples a video signal from a scanning sensor and generates a sequence of sampled fields. Each field and range rate information from the sensor are hence sequentially transmitted to and stored in a multiple and adaptive field storage means. The field storage means then, in response to an automatic or manual control signal, transfers the stored sampled field signals to a video monitor in a form for sequential or simultaneous display of a desired number of stored signal fields. The sampling ratio of the adaptive sample, the relative proportion of available communication bandwidth allocated respectively to transmitted data and video information, and the number of fields simultaneously displayed are manually or automatically selectively adjustable in functional relationship to each other and detected range rate. In one embodiment, when relatively little or no scene motion is detected, the control signal maximizes sampling ratio and causes simultaneous display of all stored fields, thus maximizing resolution and bandwidth available for data transmission. When increased scene motion is detected, the control signal is adjusted accordingly to cause display of fewer fields. If greater resolution is desired, the control signal is adjusted to increase the sampling ratio.
A Diffusion Synthetic Acceleration Method for Block Adaptive Mesh Refinement.
Ward, R. C.; Baker, R. S.; Morel, J. E.
2005-01-01
A prototype two-dimensional Diffusion Synthetic Acceleration (DSA) method on a Block-based Adaptive Mesh Refinement (BAMR) transport mesh has been developed. The Block-Adaptive Mesh Refinement Diffusion Synthetic Acceleration (BAMR-DSA) method was tested in the PARallel TIme-Dependent SN (PARTISN) deterministic transport code. The BAMR-DSA equations are derived by differencing the DSA equation using a vertex-centered diffusion discretization that is diamond-like and may be characterized as 'partially' consistent. The derivation of a diffusion discretization that is fully consistent with diamond transport differencing on BAMR mesh does not appear to be possible. However, despite being partially consistent, the BAMR-DSA method is effective for many applications. The BAMR-DSA solver was implemented and tested in two dimensions for rectangular (XY) and cylindrical (RZ) geometries. Testing results confirm that a partially consistent BAMR-DSA method will introduce instabilities for extreme cases, e.g., scattering ratios approaching 1.0 with optically thick cells, but for most realistic problems the BAMR-DSA method provides effective acceleration. The initial use of a full matrix to store and LU-Decomposition to solve the BAMR-DSA equations has been extended to include Compressed Sparse Row (CSR) storage and a Conjugate Gradient (CG) solver. The CSR and CG methods provide significantly more efficient and faster storage and solution methods.
An adaptive unsupervised hyperspectral classification method based on Gaussian distribution
NASA Astrophysics Data System (ADS)
Yue, Jiang; Wu, Jing-wei; Zhang, Yi; Bai, Lian-fa
2014-11-01
In order to achieve adaptive unsupervised clustering in the high precision, a method using Gaussian distribution to fit the similarity of the inter-class and the noise distribution is proposed in this paper, and then the automatic segmentation threshold is determined by the fitting result. First, according with the similarity measure of the spectral curve, this method assumes that the target and the background both in Gaussian distribution, the distribution characteristics is obtained through fitting the similarity measure of minimum related windows and center pixels with Gaussian function, and then the adaptive threshold is achieved. Second, make use of the pixel minimum related windows to merge adjacent similar pixels into a picture-block, then the dimensionality reduction is completed and the non-supervised classification is realized. AVIRIS data and a set of hyperspectral data we caught are used to evaluate the performance of the proposed method. Experimental results show that the proposed algorithm not only realizes the adaptive but also outperforms K-MEANS and ISODATA on the classification accuracy, edge recognition and robustness.
A Reconstructed Discontinuous Galerkin Method for the Euler Equations on Arbitrary Grids
Hong Luo; Luqing Luo; Robert Nourgaliev
2012-11-01
A reconstruction-based discontinuous Galerkin (RDG(P1P2)) method, a variant of P1P2 method, is presented for the solution of the compressible Euler equations on arbitrary grids. In this method, an in-cell reconstruction, designed to enhance the accuracy of the discontinuous Galerkin method, is used to obtain a quadratic polynomial solution (P2) from the underlying linear polynomial (P1) discontinuous Galerkin solution using a least-squares method. The stencils used in the reconstruction involve only the von Neumann neighborhood (face-neighboring cells) and are compact and consistent with the underlying DG method. The developed RDG method is used to compute a variety of flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results indicate that this RDG(P1P2) method is third-order accurate, and outperforms the third-order DG method (DG(P2)) in terms of both computing costs and storage requirements.
A New Online Calibration Method for Multidimensional Computerized Adaptive Testing.
Chen, Ping; Wang, Chun
2016-09-01
Multidimensional-Method A (M-Method A) has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing (MCAT) (Chen & Xin, Paper presented at the 78th Meeting of the Psychometric Society, Arnhem, The Netherlands, 2013). However, a key assumption of M-Method A is that it treats person parameter estimates as their true values, thus this method might yield erroneous item calibration when person parameter estimates contain non-ignorable measurement errors. To improve the performance of M-Method A, this paper proposes a new MCAT online calibration method, namely, the full functional MLE-M-Method A (FFMLE-M-Method A). This new method combines the full functional MLE (Jones & Jin in Psychometrika 59:59-75, 1994; Stefanski & Carroll in Annals of Statistics 13:1335-1351, 1985) with the original M-Method A in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration. Two correction schemes are also proposed when implementing the new method. A simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original M-Method A in almost all conditions. PMID:26608960
Rayleigh-Bénard convection via Lattice Boltzmann method: code validation and grid resolution effects
NASA Astrophysics Data System (ADS)
Lavezzo, V.; Clercx, H. J. H.; Toschi, F.
2011-12-01
Thermal plumes, formed at the wall of turbulent natural convection cells, play an important role in the re-suspension and dispersion process of inertial particles. For this reason, a good resolution of the region close to the wall is necessary to correctly describe the plumes and, consequently, the particle dynamics. In this work, a Lattice Boltzmann Method (LBM) coupled with Lagrangian particle tracking is used to understand the effects of the filtering action exerted by the grid resolution on particle trajectories. A validation of the numerical method against the work of Kunnen (2009) and Schumacher (2009) is presented and, in this framework, mean and RMS statistics on fluid temperature are considered and analyzed in detail.
Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows
NASA Technical Reports Server (NTRS)
Frink, Neal T.
1996-01-01
A method Is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization Is accomplished by a cell-centered finite-volume formulation using an accurate lin- ear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward- Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy In predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.
Assessment of an Unstructured-Grid Method for Predicting 3-D Turbulent Viscous Flows
NASA Technical Reports Server (NTRS)
Frink, Neal T.
1996-01-01
A method is presented for solving turbulent flow problems on three-dimensional unstructured grids. Spatial discretization is accomplished by a cell-centered finite-volume formulation using an accurate linear reconstruction scheme and upwind flux differencing. Time is advanced by an implicit backward-Euler time-stepping scheme. Flow turbulence effects are modeled by the Spalart-Allmaras one-equation model, which is coupled with a wall function to reduce the number of cells in the sublayer region of the boundary layer. A systematic assessment of the method is presented to devise guidelines for more strategic application of the technology to complex problems. The assessment includes the accuracy in predictions of skin-friction coefficient, law-of-the-wall behavior, and surface pressure for a flat-plate turbulent boundary layer, and for the ONERA M6 wing under a high Reynolds number, transonic, separated flow condition.
Dmitriy Y. Anistratov; Adrian Constantinescu; Loren Roberts; William Wieselquist
2007-04-30
This is a project in the field of fundamental research on numerical methods for solving the particle transport equation. Numerous practical problems require to use unstructured meshes, for example, detailed nuclear reactor assembly-level calculations, large-scale reactor core calculations, radiative hydrodynamics problems, where the mesh is determined by hydrodynamic processes, and well-logging problems in which the media structure has very complicated geometry. Currently this is an area of very active research in numerical transport theory. main issues in developing numerical methods for solving the transport equation are the accuracy of the numerical solution and effectiveness of iteration procedure. The problem in case of unstructured grids is that it is very difficult to derive an iteration algorithm that will be unconditionally stable.
Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids
Scheichl, Robert; Vassilevski, Panayot S.; Zikatanov, Ludmil T.
2012-06-21
We generalize the analysis of classical multigrid and two-level overlapping Schwarz methods for 2nd order elliptic boundary value problems to problems with large discontinuities in the coefficients that are not resolved by the coarse grids or the subdomain partition. The theoretical results provide a recipe for designing hierarchies of standard piecewise linear coarse spaces such that the multigrid convergence rate and the condition number of the Schwarz preconditioned system do not depend on the coefficient variation or on any mesh parameters. One assumption we have to make is that the coarse grids are sufficiently fine in the vicinity of cross points or where regions with large diffusion coefficients are separated by a narrow region where the coefficient is small. We do not need to align them with possible discontinuities in the coefficients. The proofs make use of novel stable splittings based on weighted quasi-interpolants and weighted Poincaré-type inequalities. Finally, numerical experiments are included that illustrate the sharpness of the theoretical bounds and the necessity of the technical assumptions.
Cost-effective accurate coarse-grid method for highly convective multidimensional unsteady flows
NASA Technical Reports Server (NTRS)
Leonard, B. P.; Niknafs, H. S.
1991-01-01
A fundamentally multidimensional convection scheme is described based on vector transient interpolation modeling rewritten in conservative control-volume form. Vector third-order upwinding is used as the basis of the algorithm; this automatically introduces important cross-difference terms that are absent from schemes using component-wise one-dimensional formulas. Third-order phase accuracy is good; this is important for coarse-grid large-eddy or full simulation. Potential overshoots or undershoots are avoided by using a recently developed universal limiter. Higher order accuracy is obtained locally, where needed, by the cost-effective strategy of adaptive stencil expansion in a direction normal to each control-volume face; this is controlled by monitoring the absolute normal gradient and curvature across the face. Higher (than third) order cross-terms do not appear to be needed. Since the wider stencil is used only in isolated narrow regions (near discontinuities), extremely high (in this case, seventh) order accuracy can be achieved for little more than the cost of a globally third-order scheme.
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 High-Order Finite Spectral Volume Method for Conservation Laws on Unstructured Grids
NASA Technical Reports Server (NTRS)
Wang, Z. J.; Liu, Yen; Kwak, Dochan (Technical Monitor)
2001-01-01
A time accurate, high-order, conservative, yet efficient method named Finite Spectral Volume (FSV) is developed for conservation laws on unstructured grids. The concept of a 'spectral volume' is introduced to achieve high-order accuracy in an efficient manner similar to spectral element and multi-domain spectral methods. In addition, each spectral volume is further sub-divided into control volumes (CVs), and cell-averaged data from these control volumes is used to reconstruct a high-order approximation in the spectral volume. Riemann solvers are used to compute the fluxes at spectral volume boundaries. Then cell-averaged state variables in the control volumes are updated independently. Furthermore, TVD (Total Variation Diminishing) and TVB (Total Variation Bounded) limiters are introduced in the FSV method to remove/reduce spurious oscillations near discontinuities. A very desirable feature of the FSV method is that the reconstruction is carried out only once, and analytically, and is the same for all cells of the same type, and that the reconstruction stencil is always non-singular, in contrast to the memory and CPU-intensive reconstruction in a high-order finite volume (FV) method. Discussions are made concerning why the FSV method is significantly more efficient than high-order finite volume and the Discontinuous Galerkin (DG) methods. Fundamental properties of the FSV method are studied and high-order accuracy is demonstrated for several model problems with and without discontinuities.
A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids
Hong Luo; Amjad Ali; Robert Nourgaliev; Vincent A. Mousseau
2010-01-01
A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a better performance than the third order DG method, in terms of both computing costs and storage requirements.
Adaptive density partitioning technique in the auxiliary plane wave method
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2006-01-01
We have developed the adaptive density partitioning technique (ADPT) in the auxiliary plane wave method, in which a part of the density is expanded to plane waves, for the fast evaluation of Coulomb matrix. Our partitioning is based on the error estimations and allows us to control the accuracy and efficiency. Moreover, we can drastically reduce the core Gaussian products that are left in Gaussian representation (its analytical integrals is the bottleneck in this method). For the taxol molecule with 6-31G** basis, the core Gaussian products accounted only for 5% in submicrohartree error.
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.
Investigation of the Multiple Method Adaptive Control (MMAC) method for flight control systems
NASA Technical Reports Server (NTRS)
Athans, M.; Baram, Y.; Castanon, D.; Dunn, K. P.; Green, C. S.; Lee, W. H.; Sandell, N. R., Jr.; Willsky, A. S.
1979-01-01
The stochastic adaptive control of the NASA F-8C digital-fly-by-wire aircraft using the multiple model adaptive control (MMAC) method is presented. The selection of the performance criteria for the lateral and the longitudinal dynamics, the design of the Kalman filters for different operating conditions, the identification algorithm associated with the MMAC method, the control system design, and simulation results obtained using the real time simulator of the F-8 aircraft at the NASA Langley Research Center are discussed.
An adaptive Tikhonov regularization method for fluorescence molecular tomography.
Cao, Xu; Zhang, Bin; Wang, Xin; Liu, Fei; Liu, Ke; Luo, Jianwen; Bai, Jing
2013-08-01
The high degree of absorption and scattering of photons propagating through biological tissues makes fluorescence molecular tomography (FMT) reconstruction a severe ill-posed problem and the reconstructed result is susceptible to noise in the measurements. To obtain a reasonable solution, Tikhonov regularization (TR) is generally employed to solve the inverse problem of FMT. However, with a fixed regularization parameter, the Tikhonov solutions suffer from low resolution. In this work, an adaptive Tikhonov regularization (ATR) method is presented. Considering that large regularization parameters can smoothen the solution with low spatial resolution, while small regularization parameters can sharpen the solution with high level of noise, the ATR method adaptively updates the spatially varying regularization parameters during the iteration process and uses them to penalize the solutions. The ATR method can adequately sharpen the feasible region with fluorescent probes and smoothen the region without fluorescent probes resorting to no complementary priori information. Phantom experiments are performed to verify the feasibility of the proposed method. The results demonstrate that the proposed method can improve the spatial resolution and reduce the noise of FMT reconstruction at the same time.
A perspective on unstructured grid flow solvers
NASA Technical Reports Server (NTRS)
Venkatakrishnan, V.
1995-01-01
This survey paper assesses the status of compressible Euler and Navier-Stokes solvers on unstructured grids. Different spatial and temporal discretization options for steady and unsteady flows are discussed. The integration of these components into an overall framework to solve practical problems is addressed. Issues such as grid adaptation, higher order methods, hybrid discretizations and parallel computing are briefly discussed. Finally, some outstanding issues and future research directions are presented.
Dickinson, J.E.; James, S.C.; Mehl, S.; Hill, M.C.; Leake, S.A.; Zyvoloski, G.A.; Faunt, C.C.; Eddebbarh, A.-A.
2007-01-01
A flexible, robust method for linking parent (regional-scale) and child (local-scale) grids of locally refined models that use different numerical methods is developed based on a new, iterative ghost-node method. Tests are presented for two-dimensional and three-dimensional pumped systems that are homogeneous or that have simple heterogeneity. The parent and child grids are simulated using the block-centered finite-difference MODFLOW and control-volume finite-element FEHM models, respectively. The models are solved iteratively through head-dependent (child model) and specified-flow (parent model) boundary conditions. Boundary conditions for models with nonmatching grids or zones of different hydraulic conductivity are derived and tested against heads and flows from analytical or globally-refined models. Results indicate that for homogeneous two- and three-dimensional models with matched grids (integer number of child cells per parent cell), the new method is nearly as accurate as the coupling of two MODFLOW models using the shared-node method and, surprisingly, errors are slightly lower for nonmatching grids (noninteger number of child cells per parent cell). For heterogeneous three-dimensional systems, this paper compares two methods for each of the two sets of boundary conditions: external heads at head-dependent boundary conditions for the child model are calculated using bilinear interpolation or a Darcy-weighted interpolation; specified-flow boundary conditions for the parent model are calculated using model-grid or hydrogeologic-unit hydraulic conductivities. Results suggest that significantly more accurate heads and flows are produced when both Darcy-weighted interpolation and hydrogeologic-unit hydraulic conductivities are used, while the other methods produce larger errors at the boundary between the regional and local models. The tests suggest that, if posed correctly, the ghost-node method performs well. Additional testing is needed for highly
Xiaodong Liu; Lijun Xuan; Hong Luo; Yidong Xia
2001-01-01
A reconstructed discontinuous Galerkin (rDG(P1P2)) method, originally introduced for the compressible Euler equations, is developed for the solution of the compressible Navier- Stokes equations on 3D hybrid grids. In this method, a piecewise quadratic polynomial solution is obtained from the underlying piecewise linear DG solution using a hierarchical Weighted Essentially Non-Oscillatory (WENO) reconstruction. The reconstructed quadratic polynomial solution is then used for the computation of the inviscid fluxes and the viscous fluxes using the second formulation of Bassi and Reay (Bassi-Rebay II). The developed rDG(P1P2) method is used to compute a variety of flow problems to assess its accuracy, efficiency, and robustness. The numerical results demonstrate that the rDG(P1P2) method is able to achieve the designed third-order of accuracy at a cost slightly higher than its underlying second-order DG method, outperform the third order DG method in terms of both computing costs and storage requirements, and obtain reliable and accurate solutions to the large eddy simulation (LES) and direct numerical simulation (DNS) of compressible turbulent flows.
A new volume conservation enforcement method for PLIC reconstruction in general convex grids
NASA Astrophysics Data System (ADS)
López, J.; Hernández, J.; Gómez, P.; Faura, F.
2016-07-01
A comprehensive study is made of methods for resolving the volume conservation enforcement problem in the PLIC reconstruction of an interface in general 3D convex grids. Different procedures to bracket the solution when solving the problem using previous standard methods are analyzed in detail. A new interpolation bracketing procedure and an improved analytical method to find the interface plane constant are proposed. These techniques are combined in a new method to enforce volume conservation, which does not require the sequential polyhedra truncation operations typically used in standard methods. The new methods have been implemented into existing geometrical routines described in López and Hernández [15], which are further improved by using more efficient formulae to compute areas and volumes of general convex 2 and 3D polytopes. Different tests using regular and irregular cell geometries are carried out to demonstrate the robustness and substantial improvement in computational efficiency of the proposed techniques, which increase the computation speed of the mentioned routines by up to 3 times for the 3D problems considered in this work.
A grid of MARCS model atmospheres for late-type stars. I. Methods and general properties
NASA Astrophysics Data System (ADS)
Gustafsson, B.; Edvardsson, B.; Eriksson, K.; Jørgensen, U. G.; Nordlund, Å.; Plez, B.
2008-08-01
Context: In analyses of stellar spectra and colours, and for the analysis of integrated light from galaxies, a homogeneous grid of model atmospheres of late-type stars and corresponding flux spectra is needed. Aims: We construct an extensive grid of spherically-symmetric models (supplemented with plane-parallel ones for the highest surface gravities), built on up-to-date atomic and molecular data, and make it available for public use. Methods: The most recent version of the MARCS program is used. Results: We present a grid of about 104 model atmospheres for stars with 2500 K ≤ T_eff ≤ 8000 K, -1 ≤ log g = log (GM/R^2) ≤ 5 (cgs) with various masses and radii, -5 ≤ [Me/H] ≤ +1, with [ α/Fe] = 0.0 and 0.4 and different choices of C and N abundances. This includes “CN-cycled” models with C/N = 4.07 (solar), 1.5 and 0.5, C/O ranging from 0.09 to (normally) 5.0 to also represent stars of spectral types R, S and N, and with 1.0 ≤ ξt ≤ 5 km s-1. We also list thermodynamic quantities (T, P_g, P_e, ρ, partial pressures of molecules, etc.) and provide them on the World Wide Web, as well as calculated fluxes in approximately 108 000 wavelength points. Underlying assumptions in addition to 1D stratification (spherical or plane-parallel) include hydrostatic equilibrium, mixing-length convection and local thermodynamic equilibrium. We discuss a number of general properties of the models, in particular in relation to the effects of changing abundances, of blanketing, and of sphericity. We illustrate positive and negative feedbacks between sphericity and molecular blanketing. We compare the models with those of other available grids and find excellent agreement with plane-parallel models of Castelli & Kurucz (if convection is treated consistently) within the overlapping parameter range. Although there are considerable departures from the spherically-symmetric NextGen models, the agreement with more recent PHOENIX models is gratifying. Conclusions: The models
Maliassov, S.Y.
1996-12-31
An approach to the construction of an iterative method for solving systems of linear algebraic equations arising from nonconforming finite element discretizations with nonmatching grids for second order elliptic boundary value problems with anisotropic coefficients is considered. The technique suggested is based on decomposition of the original domain into nonoverlapping subdomains. The elliptic problem is presented in the macro-hybrid form with Lagrange multipliers at the interfaces between subdomains. A block diagonal preconditioner is proposed which is spectrally equivalent to the original saddle point matrix and has the optimal order of arithmetical complexity. The preconditioner includes blocks for preconditioning subdomain and interface problems. It is shown that constants of spectral equivalence axe independent of values of coefficients and mesh step size.
Planetary gearbox fault diagnosis using an adaptive stochastic resonance method
NASA Astrophysics Data System (ADS)
Lei, Yaguo; Han, Dong; Lin, Jing; He, Zhengjia
2013-07-01
Planetary gearboxes are widely used in aerospace, automotive and heavy industry applications due to their large transmission ratio, strong load-bearing capacity and high transmission efficiency. The tough operation conditions of heavy duty and intensive impact load may cause gear tooth damage such as fatigue crack and teeth missed etc. The challenging issues in fault diagnosis of planetary gearboxes include selection of sensitive measurement locations, investigation of vibration transmission paths and weak feature extraction. One of them is how to effectively discover the weak characteristics from noisy signals of faulty components in planetary gearboxes. To address the issue in fault diagnosis of planetary gearboxes, an adaptive stochastic resonance (ASR) method is proposed in this paper. The ASR method utilizes the optimization ability of ant colony algorithms and adaptively realizes the optimal stochastic resonance system matching input signals. Using the ASR method, the noise may be weakened and weak characteristics highlighted, and therefore the faults can be diagnosed accurately. A planetary gearbox test rig is established and experiments with sun gear faults including a chipped tooth and a missing tooth are conducted. And the vibration signals are collected under the loaded condition and various motor speeds. The proposed method is used to process the collected signals and the results of feature extraction and fault diagnosis demonstrate its effectiveness.
Robust time and frequency domain estimation methods in adaptive control
NASA Technical Reports Server (NTRS)
Lamaire, Richard Orville
1987-01-01
A robust identification method was developed for use in an adaptive control system. The type of estimator is called the robust estimator, since it is robust to the effects of both unmodeled dynamics and an unmeasurable disturbance. The development of the robust estimator was motivated by a need to provide guarantees in the identification part of an adaptive controller. To enable the design of a robust control system, a nominal model as well as a frequency-domain bounding function on the modeling uncertainty associated with this nominal model must be provided. Two estimation methods are presented for finding parameter estimates, and, hence, a nominal model. One of these methods is based on the well developed field of time-domain parameter estimation. In a second method of finding parameter estimates, a type of weighted least-squares fitting to a frequency-domain estimated model is used. The frequency-domain estimator is shown to perform better, in general, than the time-domain parameter estimator. In addition, a methodology for finding a frequency-domain bounding function on the disturbance is used to compute a frequency-domain bounding function on the additive modeling error due to the effects of the disturbance and the use of finite-length data. The performance of the robust estimator in both open-loop and closed-loop situations is examined through the use of simulations.
An adaptive cut-cell method for animal-locomotion fluid mechanics
NASA Astrophysics Data System (ADS)
Pederzani, Jean-Noel; Haj-Hariri, H.
2011-11-01
In this work we present a numerical method for solving the incompressible Navier-Stokes equation for biomimetic fluid-structure interaction problems. The method is designed to study the flow generated by interaction with arbitrarily complex motion of a self-propelling animal. We consider the specific case of a manta ray. The method combines the embedded-boundary (or cut-cell) method for complex geometry with moving boundaries, and block-structured adaptive mesh refinement (AMR). The control volumes are formed by the intersection of the irregular boundary with Cartesian grid cells. These control volumes fit naturally within parallelizable, disjoint-block data structures, and permit dynamic AMR coarsening and refinement as the simulation progresses. We present two- and three-dimensional results to illustrate the accuracy of the method. Results are compared with experimental results for a flapping elliptical fin that mimics the natural motion of a manta ray. In particular the hydrodynamic signature of the vortex structure behind the fin is studied for its effect on swimming performance.
Parallel Anisotropic Tetrahedral Adaptation
NASA Technical Reports Server (NTRS)
Park, Michael A.; Darmofal, David L.
2008-01-01
An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The elemental operators and higher-level logic is described with their respective domain-decomposed parallelizations. An anisotropic tetrahedral grid adaptation scheme is demonstrated for 1000-1 stretching for a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for 1D and 3D domains.
The SMART CLUSTER METHOD - adaptive earthquake cluster analysis and declustering
NASA Astrophysics Data System (ADS)
Schaefer, Andreas; Daniell, James; Wenzel, Friedemann
2016-04-01
Earthquake declustering is an essential part of almost any statistical analysis of spatial and temporal properties of seismic activity with usual applications comprising of probabilistic seismic hazard assessments (PSHAs) and earthquake prediction methods. The nature of earthquake clusters and subsequent declustering of earthquake catalogues plays a crucial role in determining the magnitude-dependent earthquake return period and its respective spatial variation. Various methods have been developed to address this issue from other researchers. These have differing ranges of complexity ranging from rather simple statistical window methods to complex epidemic models. This study introduces the smart cluster method (SCM), a new methodology to identify earthquake clusters, which uses an adaptive point process for spatio-temporal identification. Hereby, an adaptive search algorithm for data point clusters is adopted. It uses the earthquake density in the spatio-temporal neighbourhood of each event to adjust the search properties. The identified clusters are subsequently analysed to determine directional anisotropy, focussing on a strong correlation along the rupture plane and adjusts its search space with respect to directional properties. In the case of rapid subsequent ruptures like the 1992 Landers sequence or the 2010/2011 Darfield-Christchurch events, an adaptive classification procedure is applied to disassemble subsequent ruptures which may have been grouped into an individual cluster using near-field searches, support vector machines and temporal splitting. The steering parameters of the search behaviour are linked to local earthquake properties like magnitude of completeness, earthquake density and Gutenberg-Richter parameters. The method is capable of identifying and classifying earthquake clusters in space and time. It is tested and validated using earthquake data from California and New Zealand. As a result of the cluster identification process, each event in
NASA Astrophysics Data System (ADS)
Wu, Xianming; He, Yigang
A systematic design method for 3-D grid multiscroll chaotic attractors by using staircase nonlinear functions (SNFs) is proposed in this paper. Equations of parameters for 3-D grid multiscroll chaotic attractors are derived in the consideration of the dynamic range for the active device and the number of multiscroll chaotic attractors. 5 × 4 and 4 × 3 of 3-D grid multiscroll chaotic attractors are generated by this method. A chaotic circuit is designed only using current feedback operational amplifiers (CFOAs). The circuit consists of three integrators and two nonlinear circuits. The parameters of the circuit are calculated by the parameters of 3-D grid multiscroll chaotic attractors. The circuit can generate 3-D grid multiscroll chaotic attractors. The central frequency of the circuit is higher with fewer active devices and simpler circuit construction for the good frequency characteristic and port characteristic of the CFOA. Numerical simulation results and the circuit simulation results show that the method is feasible and the designed circuit is correct.
An adaptive pseudo-spectral method for reaction diffusion problems
NASA Technical Reports Server (NTRS)
Bayliss, A.; Matkowsky, B. J.; Gottlieb, D.; Minkoff, M.
1989-01-01
The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.
An adaptive pseudo-spectral method for reaction diffusion problems
NASA Technical Reports Server (NTRS)
Bayliss, A.; Gottlieb, D.; Matkowsky, B. J.; Minkoff, M.
1987-01-01
The spectral interpolation error was considered for both the Chebyshev pseudo-spectral and Galerkin approximations. A family of functionals I sub r (u), with the property that the maximum norm of the error is bounded by I sub r (u)/J sub r, where r is an integer and J is the degree of the polynomial approximation, was developed. These functionals are used in the adaptive procedure whereby the problem is dynamically transformed to minimize I sub r (u). The number of collocation points is then chosen to maintain a prescribed error bound. The method is illustrated by various examples from combustion problems in one and two dimensions.
NASA Technical Reports Server (NTRS)
Liu, Yen; Vinokur, Marcel; Wang, Z. J.
2004-01-01
A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of
Wald, Ingo; Ize, Santiago
2015-07-28
Parallel population of a grid with a plurality of objects using a plurality of processors. One example embodiment is a method for parallel population of a grid with a plurality of objects using a plurality of processors. The method includes a first act of dividing a grid into n distinct grid portions, where n is the number of processors available for populating the grid. The method also includes acts of dividing a plurality of objects into n distinct sets of objects, assigning a distinct set of objects to each processor such that each processor determines by which distinct grid portion(s) each object in its distinct set of objects is at least partially bounded, and assigning a distinct grid portion to each processor such that each processor populates its distinct grid portion with any objects that were previously determined to be at least partially bounded by its distinct grid portion.
A Method for Flow Simulation About Complex Geometries Using Both Structured and Unstructured Grids
NASA Technical Reports Server (NTRS)
Debonis, James R.
1994-01-01
A computational fluid dynamics code which utilizes both structured and unstructured grids was developed. The objective of this study was to develop and demonstrate the ability of such a code to achieve solutions about complex geometries in two dimensions. An unstructured grid generator and flow solver were incorporated into the PARC2D structured flow solver. This new unstructured grid generator capability allows for easier generation and manipulation of complex grids. Several examples of the grid generation capabilities are provided. The coupling of different grid topologies and the manipulation of individual grids is shown. Also, grids for realistic geometries, a NACA 0012 airfoil and a wing/nacelle installation, were created. The flow over a NACA 0012 airfoil was used as a test case for the flow solver. Eight separate cases were run. They were both the inviscid and viscous solutions for two freestream Mach numbers and airfoil angle of attacks of 0 to 3.86 degrees. The Mach numbers chosen were for a subsonic case, Mach 0.6, and a case where supersonic regions and a shock wave exists, Mach 0.8. These test case conditions were selected to match experimentally obtained data for code comparison. The results show that the code accurately predicts the flow field for all cases.
An adaptive stepsize method for the chemical Langevin equation.
Ilie, Silvana; Teslya, Alexandra
2012-05-14
Mathematical and computational modeling are key tools in analyzing important biological processes in cells and living organisms. In particular, stochastic models are essential to accurately describe the cellular dynamics, when the assumption of the thermodynamic limit can no longer be applied. However, stochastic models are computationally much more challenging than the traditional deterministic models. Moreover, many biochemical systems arising in applications have multiple time-scales, which lead to mathematical stiffness. In this paper we investigate the numerical solution of a stochastic continuous model of well-stirred biochemical systems, the chemical Langevin equation. The chemical Langevin equation is a stochastic differential equation with multiplicative, non-commutative noise. We propose an adaptive stepsize algorithm for approximating the solution of models of biochemical systems in the Langevin regime, with small noise, based on estimates of the local error. The underlying numerical method is the Milstein scheme. The proposed adaptive method is tested on several examples arising in applications and it is shown to have improved efficiency and accuracy compared to the existing fixed stepsize schemes.
An adaptive-mesh finite-difference solution method for the Navier-Stokes equations
NASA Astrophysics Data System (ADS)
Luchini, Paolo
1987-02-01
An adjustable variable-spacing grid is presented which permits the addition or deletion of single points during iterative solutions of the Navier-Stokes equations by finite difference methods. The grid is designed for application to two-dimensional steady-flow problems which can be described by partial differential equations whose second derivatives are constrained to the Laplacian operator. An explicit Navier-Stokes equations solution technique defined for use with the grid incorporates a hybrid form of the convective terms. Three methods are developed for automatic modifications of the mesh during calculations.
William J. Gutowski; Joseph M. Prusa, Piotr K. Smolarkiewicz
2012-04-09
This project had goals of advancing the performance capabilities of the numerical general circulation model EULAG and using it to produce a fully operational atmospheric global climate model (AGCM) that can employ either static or dynamic grid stretching for targeted phenomena. The resulting AGCM combined EULAG's advanced dynamics core with the 'physics' of the NCAR Community Atmospheric Model (CAM). Effort discussed below shows how we improved model performance and tested both EULAG and the coupled CAM-EULAG in several ways to demonstrate the grid stretching and ability to simulate very well a wide range of scales, that is, multi-scale capability. We leveraged our effort through interaction with an international EULAG community that has collectively developed new features and applications of EULAG, which we exploited for our own work summarized here. Overall, the work contributed to over 40 peer-reviewed publications and over 70 conference/workshop/seminar presentations, many of them invited.
An adaptive PCA fusion method for remote sensing images
NASA Astrophysics Data System (ADS)
Guo, Qing; Li, An; Zhang, Hongqun; Feng, Zhongkui
2014-10-01
The principal component analysis (PCA) method is a popular fusion method used for its efficiency and high spatial resolution improvement. However, the spectral distortion is often found in PCA. In this paper, we propose an adaptive PCA method to enhance the spectral quality of the fused image. The amount of spatial details of the panchromatic (PAN) image injected into each band of the multi-spectral (MS) image is appropriately determined by a weighting matrix, which is defined by the edges of the PAN image, the edges of the MS image and the proportions between MS bands. In order to prove the effectiveness of the proposed method, the qualitative visual and quantitative analyses are introduced. The correlation coefficient (CC), the spectral discrepancy (SPD), and the spectral angle mapper (SAM) are used to measure the spectral quality of each fused band image. Q index is calculated to evaluate the global spectral quality of all the fused bands as a whole. The spatial quality is evaluated by the average gradient (AG) and the standard deviation (STD). Experimental results show that the proposed method improves the spectral quality very much comparing to the original PCA method while maintaining the high spatial quality of the original PCA.
2012-01-01
Background Mortality estimates can measure and monitor the impacts of conflict on a population, guide humanitarian efforts, and help to better understand the public health impacts of conflict. Vital statistics registration and surveillance systems are rarely functional in conflict settings, posing a challenge of estimating mortality using retrospective population-based surveys. Results We present a two-stage cluster sampling method for application in population-based mortality surveys. The sampling method utilizes gridded population data and a geographic information system (GIS) to select clusters in the first sampling stage and Google Earth TM imagery and sampling grids to select households in the second sampling stage. The sampling method is implemented in a household mortality study in Iraq in 2011. Factors affecting feasibility and methodological quality are described. Conclusion Sampling is a challenge in retrospective population-based mortality studies and alternatives that improve on the conventional approaches are needed. The sampling strategy presented here was designed to generate a representative sample of the Iraqi population while reducing the potential for bias and considering the context specific challenges of the study setting. This sampling strategy, or variations on it, are adaptable and should be considered and tested in other conflict settings. PMID:22540266
Grid-Search Location Methods for Ground-Truth Collection from Local and Regional Seismic Networks
Schultz, C A; Rodi, W; Myers, S C
2003-07-24
The objective of this project is to develop improved seismic event location techniques that can be used to generate more and better quality reference events using data from local and regional seismic networks. Their approach is to extend existing methods of multiple-event location with more general models of the errors affecting seismic arrival time data, including picking errors and errors in model-based travel-times (path corrections). Toward this end, they are integrating a grid-search based algorithm for multiple-event location (GMEL) with a new parameterization of travel-time corrections and new kriging method for estimating the correction parameters from observed travel-time residuals. Like several other multiple-event location algorithms, GMEL currently assumes event-independent path corrections and is thus restricted to small event clusters. The new parameterization assumes that travel-time corrections are a function of both the event and station location, and builds in source-receiver reciprocity and correlation between the corrections from proximate paths as constraints. The new kriging method simultaneously interpolates travel-time residuals from multiple stations and events to estimate the correction parameters as functions of position. They are currently developing the algorithmic extensions to GMEL needed to combine the new parameterization and kriging method with the simultaneous location of events. The result will be a multiple-event location method which is applicable to non-clustered, spatially well-distributed events. They are applying the existing components of the new multiple-event location method to a data set of regional and local arrival times from Nevada Test Site (NTS) explosions with known origin parameters. Preliminary results show the feasibility and potential benefits of combining the location and kriging techniques. They also show some preliminary work on generalizing of the error model used in GMEL with the use of mixture
Grid-Search Location Methods for Ground-Truth Collection From Local and Regional Seismic Networks
William Rodi; Craig A. Schultz; Gardar Johannesson; Stephen C. Myers
2005-05-13
This project investigated new techniques for improving seismic event locations derived from regional and local networks. The technqiues include a new approach to empirical travel-time calibration that simultaneously fits data from multiple stations and events, using a generalization of the kriging method, and predicts travel-time corrections for arbitrary event-station paths. We combined this calibration approach with grid-search event location to produce a prototype new multiple-event location method that allows the use of spatially well-distributed events and takes into account correlations between the travel-time corrections from proximate event-station paths. Preliminary tests with a high quality data set from Nevada Test Site explosions indicated that our new calibration/location method offers improvement over the conventional multiple-event location methods now in common use, and is applicable to more general event-station geometries than the conventional methods. The tests were limited, however, and further research is needed to fully evaluate, and improve, the approach. Our project also demonstrated the importance of using a realistic model for observational errors in an event location procedure. We took the initial steps in developing a new error model based on mixture-of-Gaussians probability distributions, which possess the properties necessary to characterize the complex arrival time error processes that can occur when picking low signal-to-noise arrivals. We investigated various inference methods for fitting these distributions to observed travel-time residuals, including a Markov Chain Monte Carlo technique for computing Bayesian estimates of the distribution parameters.
Novel Campylobacter isolation method using hydrophobic grid membrane filter and semisolid medium.
Valdivieso-Garcia, Alfonso; Harris, Kathleen; Riche, Edward; Campbell, Stephanie; Jarvie, Anne; Popa, Maria; Deckert, Anne; Reid-Smith, Richard; Rahn, Kris
2007-02-01
Culture procedures for isolation of thermophilic campylobacters from food matrices are complex, labor intensive, and time-consuming. Most available methods include the use of antibiotics as selective agents to prevent the growth of competing microflora. A simple procedure for isolation of thermophilic campylobacters after enrichment in Rosef's enrichment broth was developed using a hydrophobic grid membrane filter (HGMF) on semisolid medium (SSM). SSM contains no antibiotics, and the HGMF physically separates Campylobacter from the enrichment broth, allowing isolation based on differential motility. The HGMF-SSM method was compared to the Agriculture and Agri-Food Canada Food Safety Procedures Manual (FSPM-10) method (Isolation of Thermophilic Campylobacters from Fresh Pork, Beef Veal, Poultry and Ready-to-Eat Meat Products), which includes the use of selective antibiotics. During the initial study, after enrichment the HGMF-SSM method yielded pure cultures of campylobacters after 16 to 18 h (overnight) compared with 48 h for the FSPM-10 method. Ninety-four turkey samples collected at local retail stores and 38 frozen pig fecal samples were processed by both methods. Thirty-five samples (26.5%) were positive by the HGMF-SSM method; 24 (18.2%) of these positive samples contained Campylobacter jejuni and 11 (8.3%) contained Campylobacter coli. With the FSPM-10 method, 25 samples (18.9%) were positive: 21 (15.9%) with C. jejuni and 4 (3%) with C. coli. For a subsequent field study, only the HGMF-SSM method was used to isolate Campylobacter from 1,200 chicken samples and 454 turkey samples sold at retail. Analysis of five subisolates from various samples indicated that only one type of Campylobacter was recovered by the HGMF-SSM method, as ascertained by MICs for 10 antimicrobials, sequencing of the short variable region of the flaA gene, and fingerprinting based on amplified fragment length polymorphism. The absence of antibiotics in the SSM may explain the higher
Robust image registration using adaptive coherent point drift method
NASA Astrophysics Data System (ADS)
Yang, Lijuan; Tian, Zheng; Zhao, Wei; Wen, Jinhuan; Yan, Weidong
2016-04-01
Coherent point drift (CPD) method is a powerful registration tool under the framework of the Gaussian mixture model (GMM). However, the global spatial structure of point sets is considered only without other forms of additional attribute information. The equivalent simplification of mixing parameters and the manual setting of the weight parameter in GMM make the CPD method less robust to outlier and have less flexibility. An adaptive CPD method is proposed to automatically determine the mixing parameters by embedding the local attribute information of features into the construction of GMM. In addition, the weight parameter is treated as an unknown parameter and automatically determined in the expectation-maximization algorithm. In image registration applications, the block-divided salient image disk extraction method is designed to detect sparse salient image features and local self-similarity is used as attribute information to describe the local neighborhood structure of each feature. The experimental results on optical images and remote sensing images show that the proposed method can significantly improve the matching performance.
NASA Astrophysics Data System (ADS)
Paget, A. C.; Brodzik, M. J.; Gotberg, J.; Hardman, M.; Long, D. G.
2014-12-01
Spanning over 35 years of Earth observations, satellite passive microwave sensors have generated a near-daily, multi-channel brightness temperature record of observations. Critical to describing and understanding Earth system hydrologic and cryospheric parameters, data products derived from the passive microwave record include precipitation, soil moisture, surface water, vegetation, snow water equivalent, sea ice concentration and sea ice motion. While swath data are valuable to oceanographers due to the temporal scales of ocean phenomena, gridded data are more valuable to researchers interested in derived parameters at fixed locations through time and are widely used in climate studies. We are applying recent developments in image reconstruction methods to produce a systematically reprocessed historical time series NASA MEaSUREs Earth System Data Record, at higher spatial resolutions than have previously been available, for the entire SMMR, SSM/I-SSMIS and AMSR-E record. We take advantage of recently released, recalibrated SSM/I-SSMIS swath format Fundamental Climate Data Records. Our presentation will compare and contrast the two candidate image reconstruction techniques we are evaluating: Backus-Gilbert (BG) interpolation and a radiometer version of Scatterometer Image Reconstruction (SIR). Both BG and SIR use regularization to trade off noise and resolution. We discuss our rationale for the respective algorithm parameters we have selected, compare results and computational costs, and include prototype SSM/I images at enhanced resolutions of up to 3 km. We include a sensitivity analysis for estimating sensor measurement response functions critical to both methods.
NASA Technical Reports Server (NTRS)
Treiber, David A.; Muilenburg, Dennis A.
1995-01-01
The viability of applying a state-of-the-art Euler code to calculate the aerodynamic forces and moments through maximum lift coefficient for a generic sharp-edge configuration is assessed. The OVERFLOW code, a method employing overset (Chimera) grids, was used to conduct mesh refinement studies, a wind-tunnel wall sensitivity study, and a 22-run computational matrix of flow conditions, including sideslip runs and geometry variations. The subject configuration was a generic wing-body-tail geometry with chined forebody, swept wing leading-edge, and deflected part-span leading-edge flap. The analysis showed that the Euler method is adequate for capturing some of the non-linear aerodynamic effects resulting from leading-edge and forebody vortices produced at high angle-of-attack through C(sub Lmax). Computed forces and moments, as well as surface pressures, match well enough useful preliminary design information to be extracted. Vortex burst effects and vortex interactions with the configuration are also investigated.
Parallel Processing Method for Airborne Laser Scanning Data Using a PC Cluster and a Virtual Grid.
Han, Soo Hee; Heo, Joon; Sohn, Hong Gyoo; Yu, Kiyun
2009-01-01
In this study, a parallel processing method using a PC cluster and a virtual grid is proposed for the fast processing of enormous amounts of airborne laser scanning (ALS) data. The method creates a raster digital surface model (DSM) by interpolating point data with inverse distance weighting (IDW), and produces a digital terrain model (DTM) by local minimum filtering of the DSM. To make a consistent comparison of performance between sequential and parallel processing approaches, the means of dealing with boundary data and of selecting interpolation centers were controlled for each processing node in parallel approach. To test the speedup, efficiency and linearity of the proposed algorithm, actual ALS data up to 134 million points were processed with a PC cluster consisting of one master node and eight slave nodes. The results showed that parallel processing provides better performance when the computational overhead, the number of processors, and the data size become large. It was verified that the proposed algorithm is a linear time operation and that the products obtained by parallel processing are identical to those produced by sequential processing. PMID:22574032
NASA Astrophysics Data System (ADS)
Stanic, Milos; Nordlund, Markus; Kuczaj, Arkadiusz; Frederix, Edoardo; Geurts, Bernard
2014-11-01
Porous media flows can be found in a large number of fields ranging from engineering to medical applications. A volume-averaged approach to simulating porous media is often used because of its practicality and computational efficiency. Derivation of the volume-averaged porous flow equations introduces additional porous resistance terms to the momentum equation. When discretized these porous resistance terms create a body force discontinuity at the porous-fluid interface, which may lead to spurious oscillations if not accounted for properly. A variety of numerical techniques has been proposed to solve this problem, but few of them have concentrated on collocated grids and segregated solvers, which have wide applications in academia and industry. In this work we discuss the source of the spurious oscillations, quantify their amplitude and apply interface treatments methods that successfully remove the oscillations. The interface treatment methods are tested in a variety of realistic scenarios, including the porous plug and Beaver-Joseph test cases and show excellent results, minimizing or entirely removing the spurious oscillations at the porous-fluid interface. This research was financially supported by Philip Morris Products S.A.
Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method.
Mathiowetz, A. M.; Goddard, W. A.
1995-01-01
Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better. PMID:7549885
NASA Astrophysics Data System (ADS)
Jayalakshmi, N. S.; Gaonkar, D. N.
2016-08-01
The output power obtained from solar-wind hybrid system fluctuates with changes in weather conditions. These power fluctuations cause adverse effects on the voltage, frequency and transient stability of the utility grid. In this paper, a control method is presented for power smoothing of grid integrated PV/wind hybrid system using ultracapacitors in a DC coupled structure. The power fluctuations of hybrid system are mitigated and smoothed power is supplied to the utility grid. In this work both photovoltaic (PV) panels and the wind generator are controlled to operate at their maximum power point. The grid side inverter control strategy presented in this paper maintains DC link voltage constant while injecting power to the grid at unity power factor considering different operating conditions. Actual solar irradiation and wind speed data are used in this study to evaluate the performance of the developed system using MATLAB/Simulink software. The simulation results show that output power fluctuations of solar-wind hybrid system can be significantly mitigated using the ultracapacitor based storage system.
Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics
NASA Astrophysics Data System (ADS)
Kraczek, B.; Miller, S. T.; Haber, R. B.; Johnson, D. D.
2010-03-01
We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1d×time and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals
Adaptive spacetime method using Riemann jump conditions for coupled atomistic-continuum dynamics
Kraczek, B. Miller, S.T. Haber, R.B. Johnson, D.D.
2010-03-20
We combine the Spacetime Discontinuous Galerkin (SDG) method for elastodynamics with the mathematically consistent Atomistic Discontinuous Galerkin (ADG) method in a new scheme that concurrently couples continuum and atomistic models of dynamic response in solids. The formulation couples non-overlapping continuum and atomistic models across sharp interfaces by weakly enforcing jump conditions, for both momentum balance and kinematic compatibility, using Riemann values to preserve the characteristic structure of the underlying hyperbolic system. Momentum balances to within machine-precision accuracy over every element, on each atom, and over the coupled system, with small, controllable energy dissipation in the continuum region that ensures numerical stability. When implemented on suitable unstructured spacetime grids, the continuum SDG model offers linear computational complexity in the number of elements and powerful adaptive analysis capabilities that readily bridge between atomic and continuum scales in both space and time. A special trace operator for the atomic velocities and an associated atomistic traction field enter the jump conditions at the coupling interface. The trace operator depends on parameters that specify, at the scale of the atomic spacing, the position of the coupling interface relative to the atoms. In a key finding, we demonstrate that optimizing these parameters suppresses spurious reflections at the coupling interface without the use of non-physical damping or special boundary conditions. We formulate the implicit SDG-ADG coupling scheme in up to three spatial dimensions, and describe an efficient iterative solution scheme that outperforms common explicit schemes, such as the Velocity Verlet integrator. Numerical examples, in 1dxtime and employing both linear and nonlinear potentials, demonstrate the performance of the SDG-ADG method and show how adaptive spacetime meshing reconciles disparate time steps and resolves atomic-scale signals in
Hwang, Wei-Chin
2010-01-01
How do we culturally adapt psychotherapy for ethnic minorities? Although there has been growing interest in doing so, few therapy adaptation frameworks have been developed. The majority of these frameworks take a top-down theoretical approach to adapting psychotherapy. The purpose of this paper is to introduce a community-based developmental approach to modifying psychotherapy for ethnic minorities. The Formative Method for Adapting Psychotherapy (FMAP) is a bottom-up approach that involves collaborating with consumers to generate and support ideas for therapy adaptation. It involves 5-phases that target developing, testing, and reformulating therapy modifications. These phases include: (a) generating knowledge and collaborating with stakeholders (b) integrating generated information with theory and empirical and clinical knowledge, (c) reviewing the initial culturally adapted clinical intervention with stakeholders and revising the culturally adapted intervention, (d) testing the culturally adapted intervention, and (e) finalizing the culturally adapted intervention. Application of the FMAP is illustrated using examples from a study adapting psychotherapy for Chinese Americans, but can also be readily applied to modify therapy for other ethnic groups. PMID:20625458
Mukherjee, Sudipto; Rizzo, Robert C.
2014-01-01
Scoring functions are a critically important component of computer-aided screening methods for the identification of lead compounds during early stages of drug discovery. Here, we present a new multi-grid implementation of the footprint similarity (FPS) scoring function that was recently developed in our laboratory which has proven useful for identification of compounds which bind to a protein on a per-residue basis in a way that resembles a known reference. The grid-based FPS method is much faster than its Cartesian-space counterpart which makes it computationally tractable for on-the-fly docking, virtual screening, or de novo design. In this work, we establish that: (i) relatively few grids can be used to accurately approximate Cartesian space footprint similarity, (ii) the method yields improved success over the standard DOCK energy function for pose identification across a large test set of experimental co-crystal structures, for crossdocking, and for database enrichment, and (iii) grid-based FPS scoring can be used to tailor construction of new molecules to have specific properties, as demonstrated in a series of test cases targeting the viral protein HIVgp41. The method will be made available in the program DOCK6. PMID:23436713
NASA Astrophysics Data System (ADS)
Moortgat, J.; Firoozabadi, A.
2013-12-01
Most problems of interest in hydrogeology and subsurface energy resources involve complex heterogeneous geological formations. Such domains are most naturally represented in numerical reservoir simulations by unstructured computational grids. Finite element methods are a natural choice to describe fluid flow on unstructured meshes, because the governing equations can be readily discretized for any grid-element geometry. In this work, we consider the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by tetrahedra, prisms, or hexahedra, and compare to simulations on 3D structured grids. We employ a combination of mixed hybrid finite element methods to solve for the pressure and flux fields in a fractional flow formulation, and higher-order discontinuous Galerkin methods for the mass transport equations. These methods are well suited to simulate flow in heterogeneous and fractured reservoirs, because they provide a globally continuous pressure and flux field, while allowing for sharp discontinuities in the phase properties, such as compositions and saturations. The increased accuracy from using higher-order methods improves the modeling of highly non-linear flow, such as gravitational and viscous fingering. We present several numerical examples to study convergence rates and the (lack of) sensitivity to gridding/mesh orientation, and mesh quality. These examples consider gravity depletion, water and gas injection in oil saturated subsurface reservoirs with species exchange between up to three fluid phases. The examples demonstrate the wide applicability of our chosen finite element methods in the study of challenging multiphase flow problems in porous, geometrically complex, subsurface media.
2015-09-14
GridDyn is a part of power grid simulation toolkit. The code is designed using modern object oriented C++ methods utilizing C++11 and recent Boost libraries to ensure compatibility with multiple operating systems and environments.
Adaptive Ripple Down Rules Method based on Description Length
NASA Astrophysics Data System (ADS)
Yoshida, Tetsuya; Wada, Takuya; Motoda, Hiroshi; Washio, Takashi
A knowledge acquisition method Ripple Down Rules (RDR) can directly acquire and encode knowledge from human experts. It is an incremental acquisition method and each new piece of knowledge is added as an exception to the existing knowledge base. Past researches on RDR method assume that the problem domain is stable. This is not the case in reality, especially when an environment changes. Things change over time. This paper proposes an adaptive Ripple Down Rules method based on the Minimum Description Length Principle aiming at knowledge acquisition in a dynamically changing environment. We consider the change in the correspondence between attribute-values and class labels as a typical change in the environment. When such a change occurs, some pieces of knowledge previously acquired become worthless, and the existence of such knowledge may hinder acquisition of new knowledge. In our approach knowledge deletion is carried out as well as knowledge acquisition so that useless knowledge is properly discarded to ensure efficient knowledge acquisition while maintaining the prediction accuracy for future data. Furthermore, pruning is incorporated into the incremental knowledge acquisition in RDR to improve the prediction accuracy of the constructed knowledge base. Experiments were conducted by simulating the change in the correspondence between attribute-values and class labels using the datasets in UCI repository. The results are encouraging.
Adaptive Mesh Refinement in Computational Astrophysics -- Methods and Applications
NASA Astrophysics Data System (ADS)
Balsara, D.
2001-12-01
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so because the physics associated with astrophysical phenomena evolves in multi-scale fashion and we wish to arrive at a multi-scale simulational capability to represent the physics. Because astrophysical systems have magnetic fields, multi-scale magnetohydrodynamics (MHD) is of especial interest. In this paper we first discuss general issues in adaptive mesh refinement (AMR). We then focus on the important issues in carrying out divergence-free AMR-MHD and catalogue the progress we have made in that area. We show that AMR methods lend themselves to easy parallelization. We then discuss applications of the RIEMANN framework for AMR-MHD to problems in computational astophysics.
Methods of integrating a high penetration photovoltaic power plant into a micro grid.
Stein, Joshua S.; Johnson, Lars; Nelson, Lauren; Lenox, Carl; Johnson, Robert.
2010-06-01
The island of Lanai is currently one of the highest penetration PV micro grids in the world, with the 1.2 MWAC La Ola Solar Farm operating on a grid with a peak net load of 4.7 MW. This facility interconnects to one of Lanai's three 12.47 kV distribution circuits. An initial interconnection requirements study (IRS) determined that several control and performance features are necessary to ensure safe and reliable operation of the island grid. These include power curtailment, power factor control, over/under voltage and frequency ride through, and power ramp rate limiting. While deemed necessary for stable grid operation, many of these features contradict the current IEEE 1547 interconnection requirements governing distributed generators. These controls have been successfully implemented, tested, and operated since January 2009. Currently, the system is producing power in a curtailed mode according to the requirements of a power purchase agreement (PPA).
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
Rieben, R N; Rodrigue, G H; White, D A
2004-03-09
We present a mixed vector finite element method for solving the time dependent coupled Ampere and Faraday laws of Maxwell's equations on unstructured hexahedral grids that employs high order discretization in both space and time. The method is of arbitrary order accuracy in space and up to 5th order accurate in time, making it well suited for electrically large problems where grid anisotropy and numerical dispersion have plagued other methods. In addition, the method correctly models both the jump discontinuities and the divergence-free properties of the electric and magnetic fields, is charge and energy conserving, conditionally stable, and free of spurious modes. Several computational experiments are performed to demonstrate the accuracy, efficiency and benefits of the method.
A Reduced Grid Method for a Parallel Global Ocean General Circulation Model
Wickett, M.E.
1999-12-01
A limitation of many explicit finite-difference global climate models is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. A computational grid in which the number of cells in the longitudinal direction is reduced toward high-latitudes, keeping the longitudinal width of the resulting cells as uniform as possible and increasing the allowable timestep, is applied to a three-dimensional primitive equation ocean-climate model. This ''reduced'' grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. Algorithms are developed to extend the finite difference techniques to this interface, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The reduced grid eliminates the common alternative of filtering high-frequency modes from the solution at high-latitudes to allow a larger timestep and reduces execution time per model step by roughly 20 percent. The reduced grid model is implemented for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results comparable to those of the original model. Both idealized and realistic model runs are presented to show the effect of the interface numerics on the model solution. First, a rectangular, mid-latitude, at-bottomed basin with vertical walls at the boundaries is driven only by surface wind stress to compare three resolutions of the standard grid to reduced grid cases which use various interface conditions. Next, a similar basin with wind stress, heat, and fresh water forcing is used to compare the results of a reduced grid with those of a standard grid result while exercising the full set of model equations. Finally, global model runs, with topography, forcing, and physical parameters similar to
A reduced-grid method for a parallel global ocean general circulation model
NASA Astrophysics Data System (ADS)
Wickett, Michael Everett
A limitation of many explicit finite-difference global climate models is the timestep restriction caused by the decrease in cell size associated with the convergence of meridians near the poles. A computational grid in which the number of cells in the longitudinal direction is reduced toward high- latitudes, keeping the longitudinal width of the resulting cells as uniform as possible and increasing the allowable timestep, is applied to a three- dimensional primitive equation ocean-climate model. This ``reduced'' grid consists of subgrids which interact at interfaces along their northern and southern boundaries, where the resolution changes by a factor of three. Algorithms are developed to extend the finite difference techniques to this interface, focusing on the conservation required to perform long time integrations, while preserving the staggered spatial arrangement of variables and the numerics used on subgrids. The reduced grid eliminates the common alternative of filtering high- frequency modes from the solution at high-latitudes to allow a larger timestep and reduces execution time per model step by roughly 20 percent. The reduced grid model is implemented for parallel computer architectures with two-dimensional domain decomposition and message passing, with speedup results comparable to those of the original model. Both idealized and realistic model runs are presented to show the effect of the interface numerics on the model solution. First, a rectangular, mid-latitude, flat-bottomed basin with vertical walls at the boundaries is driven only by surface wind stress to compare three resolutions of the standard grid to reduced grid cases which use various interface conditions. Next, a similar basin with wind stress, heat, and fresh water forcing is used to compare the results of a reduced grid with those of a standard grid result while exercising the full set of model equations. Finally, global model runs, with topography, forcing, and physical parameters
Kelkar, K.M.; Choudhury, D.; Minkowycz, W.J.
1997-01-01
Flows in many engineering applications occur in devices that exhibit geometric periodicity, giving rise to flow characteristics that are spatially periodic. This periodicity can be of two types, translational and rotational. Since the geometries encountered in practice are often complex, periodic boundary-fitted grids are used over a typical module to predict such flows. Nonstaggered grids are frequently used for discretizing the equations governing the flow. These methods employ Cartesian velocities as the primary unknowns. In rotationally periodic geometries, these components themselves are not periodic, necessitating special considerations in incorporating the periodicity conditions over the periodic modules. The aim of the present study is to propose modifications to the conventional nonstaggered grid methods for computations of spatially periodic flows, so that geometric periodicities can be treated in a unified manner. The proposed formulation represents a generalization of the existing formulations for nonstaggered grids and can be applied for the discretization of the governing equations in domains with or without periodicity. The proposed formulation is first validated by comparing the computed solutions with the exact solutions for Couette flows in a parallel-plate channel and a cylindrical annulus. The method is then applied to three physical situations to illustrate its utility.
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.
NASA Technical Reports Server (NTRS)
Chan, William M.
1995-01-01
Algorithms and computer code developments were performed for the overset grid approach to solving computational fluid dynamics problems. The techniques developed are applicable to compressible Navier-Stokes flow for any general complex configurations. The computer codes developed were tested on different complex configurations with the Space Shuttle launch vehicle configuration as the primary test bed. General, efficient and user-friendly codes were produced for grid generation, flow solution and force and moment computation.
Woven-grid sealed quasi-bipolar lead-acid battery construction and fabricating method
NASA Technical Reports Server (NTRS)
Rippel, Wally E. (Inventor)
1989-01-01
A quasi-bipolar lead-acid battery construction includes a plurality of bipolar cells disposed in side-by-side relation to form a stack, and a pair of monoplanar plates at opposite ends of the stack, the cell stack and monopolar plates being contained within a housing of the battery. Each bipolar cell is loaded with an electrolyte and composed of a bipolar electrode plate and a pair of separator plates disposed on opposite sides of the electrode plate and peripherally sealed thereto. Each bipolar electrode plate is composed of a partition sheet and two bipolar electrode elements folded into a hairpin configuration and applied over opposite edges of the partition sheet so as to cover the opposite surfaces of the opposite halves thereof. Each bipolar electrode element is comprised of a woven grid with a hot-melt strip applied to a central longitudinal region of the grid along which the grid is folded into the hairpin configuration, and layers of negative and positive active material pastes applied to opposite halves of the grid on opposite sides of the central hot-melt strip. The grid is made up of strands of conductive and non-conductive yarns composing the respective transverse and longitudinal weaves of the grid. The conductive yarn has a multi-stranded glass core surrounded and covered by a lead sheath, whereas the non-conductive yarn has a multi-stranded glass core surrounded and covered by a thermally activated sizing.
An overset grid method for large eddy simulation of turbomachinery stages
NASA Astrophysics Data System (ADS)
Wang, Gaofeng; Duchaine, Florent; Papadogiannis, Dimitrios; Duran, Ignacio; Moreau, Stéphane; Gicquel, Laurent Y. M.
2014-10-01
A coupling method based on the overset grid approach has been successfully developed to couple multi-copies of a massively-parallel unstructured compressible LES solver AVBP for turbomachinery applications. As proper LES predictions require minimizing artificial dissipation as well as dispersion of turbulent structures, the numerical treatment of the moving interface between stationary and rotating components has been thoroughly tested on cases involving acoustical wave propagation, vortex propagation through a translating interface and a cylinder wake through a rotating interface. Convergence and stability of the coupled schemes show that a minimum number of overlapping points are required for a given scheme. The current accuracy limitation is locally given by the interpolation scheme at the interface, but with a limited and localized error. For rotor-stator type applications, the moving interface only introduces a spurious weak tone at the rotational frequency provided the latter is correctly sampled. The approach has then been applied to the QinetiQ MT1 high-pressure transonic experimental turbine to illustrate the potential of rotor/stator LES in complex, high Reynolds-number industrial turbomachinery configurations. Both wave propagation and generation are considered. Mean LES statistics agree well with experimental data and bring improvement over previous RANS or URANS results.
Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods
NASA Technical Reports Server (NTRS)
Swanson, R. C.; Langer, S.
2016-01-01
In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.
Adaptive-Grid Methods for Phase Field Models of Microstructure Development
NASA Technical Reports Server (NTRS)
Dantzig, Jonathan A.; Goldenfeld, Nigel
2001-01-01
Modeling solidification microstructures has become an area of intense study in recent years. The properties of large scale cast products, ranging from automobile engine blocks to aircraft components and other industrial applications, are strongly dependent on the physics that occur at the mesoscopic and microscopic length scales during solidification. The predominant morphology found in solidification microstructures is the dendrite, a tree-like pattern of solid around which solidification proceeds. The microscopic properties of cast products are determined by the length scales of these dendrites, and their associated segregation profiles. For this reason understanding the mechanisms for pattern selection in dendritic growth has attracted a great deal of interest from the experimental and theoretical communities. In particular, a great deal of research has been undertaken to understand such issues as dendrite morphology, shape and growth speed. Experiments on dendrite evolution in pure materials by Glicksman and coworkers on succinonitrile (SCN), and more recently pivalic acid (PVA), as well as other transparent analogs of metals, have provided tests of theories for dendritic growth, and have stimulated considerable theoretical progress. These experiments have clearly demonstrated that in certain parameter ranges the physics of the dendrite tip can be characterized by a steady value for the dendrite tip velocity, radius of curvature and shape. Away from the tip, the time-dependent dendrite exhibits a characteristic sidebranching as it propagates, which is not yet well understood. These experiments are performed by observing individual dendrites growing into an undercooled melt. The experiments are characterized by the dimensionless undercooling. Most experiments are performed at low undercooling.
NASA Astrophysics Data System (ADS)
Won, Jun Yeon; Ko, Guen Bae; Lee, Jae Sung
2016-10-01
In this paper, we propose a fully time-based multiplexing and readout method that uses the principle of the global positioning system. Time-based multiplexing allows simplifying the multiplexing circuits where the only innate traces that connect the signal pins of the silicon photomultiplier (SiPM) channels to the readout channels are used as the multiplexing circuit. Every SiPM channel is connected to the delay grid that consists of the traces on a printed circuit board, and the inherent transit times from each SiPM channel to the readout channels encode the position information uniquely. Thus, the position of each SiPM can be identified using the time difference of arrival (TDOA) measurements. The proposed multiplexing can also allow simplification of the readout circuit using the time-to-digital converter (TDC) implemented in a field-programmable gate array (FPGA), where the time-over-threshold (ToT) is used to extract the energy information after multiplexing. In order to verify the proposed multiplexing method, we built a positron emission tomography (PET) detector that consisted of an array of 4 × 4 LGSO crystals, each with a dimension of 3 × 3 × 20 mm3, and one- to-one coupled SiPM channels. We first employed the waveform sampler as an initial study, and then replaced the waveform sampler with an FPGA-TDC to further simplify the readout circuits. The 16 crystals were clearly resolved using only the time information obtained from the four readout channels. The coincidence resolving times (CRTs) were 382 and 406 ps FWHM when using the waveform sampler and the FPGA-TDC, respectively. The proposed simple multiplexing and readout methods can be useful for time-of-flight (TOF) PET scanners.
Adaptive mesh generation for edge-element finite element method
NASA Astrophysics Data System (ADS)
Tsuboi, Hajime; Gyimothy, Szabolcs
2001-06-01
An adaptive mesh generation method for two- and three-dimensional finite element methods using edge elements is proposed. Since the tangential component continuity is preserved when using edge elements, the strategy of creating new nodes is based on evaluation of the normal component of the magnetic vector potential across element interfaces. The evaluation is performed at the middle point of edge of a triangular element for two-dimensional problems or at the gravity center of triangular surface of a tetrahedral element for three-dimensional problems. At the boundary of two elements, the error estimator is the ratio of the normal component discontinuity to the maximum value of the potential in the same material. One or more nodes are set at the middle points of the edges according to the value of the estimator as well as the subdivision of elements where new nodes have been created. A final mesh will be obtained after several iterations. Some computation results of two- and three-dimensional problems using the proposed method are shown.
Evaluation of Adaptive Subdivision Method on Mobile Device
NASA Astrophysics Data System (ADS)
Rahim, Mohd Shafry Mohd; Isa, Siti Aida Mohd; Rehman, Amjad; Saba, Tanzila
2013-06-01
Recently, there are significant improvements in the capabilities of mobile devices; but rendering large 3D object is still tedious because of the constraint in resources of mobile devices. To reduce storage requirement, 3D object is simplified but certain area of curvature is compromised and the surface will not be smooth. Therefore a method to smoother selected area of a curvature is implemented. One of the popular methods is adaptive subdivision method. Experiments are performed using two data with results based on processing time, rendering speed and the appearance of the object on the devices. The result shows a downfall in frame rate performance due to the increase in the number of triangles with each level of iteration while the processing time of generating the new mesh also significantly increase. Since there is a difference in screen size between the devices the surface on the iPhone appears to have more triangles and more compact than the surface displayed on the iPad. [Figure not available: see fulltext.
Adaptive Elastic Net for Generalized Methods of Moments.
Caner, Mehmet; Zhang, Hao Helen
2014-01-30
Model selection and estimation are crucial parts of econometrics. This paper introduces a new technique that can simultaneously estimate and select the model in generalized method of moments (GMM) context. The GMM is particularly powerful for analyzing complex data sets such as longitudinal and panel data, and it has wide applications in econometrics. This paper extends the least squares based adaptive elastic net estimator of Zou and Zhang (2009) to nonlinear equation systems with endogenous variables. The extension is not trivial and involves a new proof technique due to estimators lack of closed form solutions. Compared to Bridge-GMM of Caner (2009), we allow for the number of parameters to diverge to infinity as well as collinearity among a large number of variables, also the redundant parameters set to zero via a data dependent technique. This method has the oracle property, meaning that we can estimate nonzero parameters with their standard limit and the redundant parameters are dropped from the equations simultaneously. Numerical examples are used to illustrate the performance of the new method.
Webster, Clayton; Tempone, Raul; Nobile, Fabio
2007-12-01
This work describes the convergence analysis of a Smolyak-type sparse grid stochastic collocation method for the approximation of statistical quantities related to the solution of partial differential equations with random coefficients and forcing terms (input data of the model). To compute solution statistics, the sparse grid stochastic collocation method uses approximate solutions, produced here by finite elements, corresponding to a deterministic set of points in the random input space. This naturally requires solving uncoupled deterministic problems and, as such, the derived strong error estimates for the fully discrete solution are used to compare the computational efficiency of the proposed method with the Monte Carlo method. Numerical examples illustrate the theoretical results and are used to compare this approach with several others, including the standard Monte Carlo.
A Full Multi-Grid Method for the Solution of the Cell Vertex Finite Volume Cauchy-Riemann Equations
NASA Technical Reports Server (NTRS)
Borzi, A.; Morton, K. W.; Sueli, E.; Vanmaele, M.
1996-01-01
The system of inhomogeneous Cauchy-Riemann equations defined on a square domain and subject to Dirichlet boundary conditions is considered. This problem is discretised by using the cell vertex finite volume method on quadrilateral meshes. The resulting algebraic problem is overdetermined and the solution is defined in a least squares sense. By this approach a consistent algebraic problem is obtained which differs from the original one by O(h(exp 2)) perturbations of the right-hand side. A suitable cell-based convergent smoothing iteration is presented which is naturally linked to the least squares formulation. Hence, a standard multi-grid algorithm is reported which combines the given smoother and cell-based transfer operators. Some remarkable reduction properties of these operators are shown. A full multi-grid method is discussed which solves the discrete problem to the level of truncation error by employing one multi-grid cycle at each current level of discretisation. Experiments and applications of the full multi-grid scheme are presented.
NASA Astrophysics Data System (ADS)
Jeong, Manhee; Jo, Woo Jin; Kim, Han Soo; Ha, Jang Ho
2015-06-01
A single-polarity charge-sensing method was studied by using a CdZnTe Frisch collar grid detector grown by using a low-pressure Bridgeman furnace at the Korea Atomic Energy Research Institute (KAERI). The Frisch collar grid CdZnTe detector has an active volume of 5 × 5 × 10 mm3, and was fabricated from a single crystal, Teflon tape and copper tape used as a Frisch collar grid. A room-temperature energy resolution of 6% full width at half maximum (FWHM) was obtained for the 662keV peak of Cs-137 without any additional electrical corrections. The detector's fabrication process is described, and its characteristics are discussed. Finally, the charge transport properties and gamma-ray energy resolution of the fabricated Frisch collar grid detector are compared with those of two other Frisch collar detectors grown by using different crystal growth methods and purchased from eV-products and Redlen technology.
Adaptive enhancement method of infrared image based on scene feature
NASA Astrophysics Data System (ADS)
Zhang, Xiao; Bai, Tingzhu; Shang, Fei
2008-12-01
All objects emit radiation in amounts related to their temperature and their ability to emit radiation. The infrared image shows the invisible infrared radiation emitted directly. Because of the advantages, the technology of infrared imaging is applied to many kinds of fields. But compared with visible image, the disadvantages of infrared image are obvious. The characteristics of low luminance, low contrast and the inconspicuous difference target and background are the main disadvantages of infrared image. The aim of infrared image enhancement is to improve the interpretability or perception of information in infrared image for human viewers, or to provide 'better' input for other automated image processing techniques. Most of the adaptive algorithm for image enhancement is mainly based on the gray-scale distribution of infrared image, and is not associated with the actual image scene of the features. So the pertinence of infrared image enhancement is not strong, and the infrared image is not conducive to the application of infrared surveillance. In this paper we have developed a scene feature-based algorithm to enhance the contrast of infrared image adaptively. At first, after analyzing the scene feature of different infrared image, we have chosen the feasible parameters to describe the infrared image. In the second place, we have constructed the new histogram distributing base on the chosen parameters by using Gaussian function. In the last place, the infrared image is enhanced by constructing a new form of histogram. Experimental results show that the algorithm has better performance than other methods mentioned in this paper for infrared scene images.