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.
An Adaptive VOF Method on Unstructured Grid
NASA Astrophysics Data System (ADS)
Wu, L. L.; Huang, M.; Chen, B.
2011-09-01
In order to improve the accuracy of interface capturing and keeping the computational efficiency, an adaptive VOF method on unstructured grid is proposed in this paper. The volume fraction in each cell is regarded as the criterion to locally refine the interface cell. With the movement of interface, new interface cells (0 ≤ f ≤ 1) are subdivided into child cells, while those child cells that no longer contain interface will be merged back into the original parent cell. In order to avoid the complicated redistribution of volume fraction during the subdivision and amalgamation procedure, a predictor-corrector algorithm is proposed to implement the subdivision and amalgamation procedures only in empty or full cell ( f = 0 or 1). Thus volume fraction in the new cell can take the value from the original cell directly, and the interpolation of the interface is avoided. The advantage of this method is that the re-generation of the whole grid system is not necessary, so its implementation is very efficient. Moreover, an advection flow test of a hollow square was performed, and the relative shape error of the result obtained by adaptive mesh is smaller than those by non-refined grid, which verifies the validation of our method.
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.
Development of a dynamically adaptive grid method for multidimensional problems
NASA Astrophysics Data System (ADS)
Holcomb, J. E.; Hindman, R. G.
1984-06-01
An approach to solution adaptive grid generation for use with finite difference techniques, previously demonstrated on model problems in one space dimension, has been extended to multidimensional problems. The method is based on the popular elliptic steady grid generators, but is 'dynamically' adaptive in the sense that a grid is maintained at all times satisfying the steady grid law driven by a solution-dependent source term. Testing has been carried out on Burgers' equation in one and two space dimensions. Results appear encouraging both for inviscid wave propagation cases and viscous boundary layer cases, suggesting that application to practical flow problems is now possible. In the course of the work, obstacles relating to grid correction, smoothing of the solution, and elliptic equation solvers have been largely overcome. Concern remains, however, about grid skewness, boundary layer resolution and the need for implicit integration methods. Also, the method in 3-D is expected to be very demanding of computer resources.
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.
Methods for prismatic/tetrahedral grid generation and adaptation
NASA Astrophysics Data System (ADS)
Kallinderis, Y.
1995-10-01
The present work involves generation of 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 a method 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 High Speed Civil Transport (HSCT) type of aircraft geometry is considered. The generated hybrid grid required only 170 K tetrahedra instead of an estimated two million had a tetrahedral mesh been used in the prisms region as well. A solution adaptive scheme for viscous computations on hybrid grids is also presented. 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 3-D, isotropic division of tetrahedra and 2-D, directional division of prisms.
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.
Fast adaptive composite grid methods on distributed parallel architectures
NASA Technical Reports Server (NTRS)
Lemke, Max; Quinlan, Daniel
1992-01-01
The fast adaptive composite (FAC) grid method is compared with the adaptive composite method (AFAC) under variety of conditions including vectorization and parallelization. Results are given for distributed memory multiprocessor architectures (SUPRENUM, Intel iPSC/2 and iPSC/860). It is shown that the good performance of AFAC and its superiority over FAC in a parallel environment is a property of the algorithm and not dependent on peculiarities of any machine.
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.
Adaptive grid methods for RLV environment assessment and nozzle analysis
NASA Technical Reports Server (NTRS)
Thornburg, Hugh J.
1996-01-01
Rapid access to highly accurate data about complex configurations is needed for multi-disciplinary optimization and design. In order to efficiently meet these requirements a closer coupling between the analysis algorithms and the discretization process is needed. In some cases, such as free surface, temporally varying geometries, and fluid structure interaction, the need is unavoidable. In other cases the need is to rapidly generate and modify high quality grids. Techniques such as unstructured and/or solution-adaptive methods can be used to speed the grid generation process and to automatically cluster mesh points in regions of interest. Global features of the flow can be significantly affected by isolated regions of inadequately resolved flow. These regions may not exhibit high gradients and can be difficult to detect. Thus excessive resolution in certain regions does not necessarily increase the accuracy of the overall solution. Several approaches have been employed for both structured and unstructured grid adaption. The most widely used involve grid point redistribution, local grid point enrichment/derefinement or local modification of the actual flow solver. However, the success of any one of these methods ultimately depends on the feature detection algorithm used to determine solution domain regions which require a fine mesh for their accurate representation. Typically, weight functions are constructed to mimic the local truncation error and may require substantial user input. Most problems of engineering interest involve multi-block grids and widely disparate length scales. Hence, it is desirable that the adaptive grid feature detection algorithm be developed to recognize flow structures of different type as well as differing intensity, and adequately address scaling and normalization across blocks. These weight functions can then be used to construct blending functions for algebraic redistribution, interpolation functions for unstructured grid generation
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.
A multigrid method for steady Euler equations on unstructured adaptive grids
NASA Technical Reports Server (NTRS)
Riemslagh, Kris; Dick, Erik
1993-01-01
A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.
Grid quality improvement by a grid adaptation technique
NASA Technical Reports Server (NTRS)
Lee, K. D.; Henderson, T. L.; Choo, Y. K.
1991-01-01
A grid adaptation technique is presented which improves grid quality. The method begins with an assessment of grid quality by defining an appropriate grid quality measure. Then, undesirable grid properties are eliminated by a grid-quality-adaptive grid generation procedure. The same concept has been used for geometry-adaptive and solution-adaptive grid generation. The difference lies in the definition of the grid control sources; here, they are extracted from the distribution of a particular grid property. Several examples are presented to demonstrate the versatility and effectiveness of the method.
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.
NASA Astrophysics Data System (ADS)
Tang, Qiuyan; Wang, Jing; Lv, Pin; Sun, Quan
2015-10-01
Propagation simulation method and choosing mesh grid are both very important to get the correct propagation results in wave optics simulation. A new angular spectrum propagation method with alterable mesh grid based on the traditional angular spectrum method and the direct FFT method is introduced. With this method, the sampling space after propagation is not limited to propagation methods no more, but freely alterable. However, choosing mesh grid on target board influences the validity of simulation results directly. So an adaptive mesh choosing method based on wave characteristics is proposed with the introduced propagation method. We can calculate appropriate mesh grids on target board to get satisfying results. And for complex initial wave field or propagation through inhomogeneous media, we can also calculate and set the mesh grid rationally according to above method. Finally, though comparing with theoretical results, it's shown that the simulation result with the proposed method coinciding with theory. And by comparing with the traditional angular spectrum method and the direct FFT method, it's known that the proposed method is able to adapt to a wider range of Fresnel number conditions. That is to say, the method can simulate propagation results efficiently and correctly with propagation distance of almost zero to infinity. So it can provide better support for more wave propagation applications such as atmospheric optics, laser propagation and so on.
A Lagrangian-Eulerian finite element method with adaptive gridding for advection-dispersion problems
Ijiri, Y.; Karasaki, K.
1994-02-01
In the present paper, a Lagrangian-Eulerian finite element method with adaptive gridding for solving advection-dispersion equations is described. The code creates new grid points in the vicinity of sharp fronts at every time step in order to reduce numerical dispersion. The code yields quite accurate solutions for a wide range of mesh Peclet numbers and for mesh Courant numbers well in excess of 1.
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.
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 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
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.
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.
Adaptive-grid methods for time-dependent partial differential equations
Hedstrom, G.W.; Rodrique, G.H.
1981-01-01
This paper contains a survey of recent developments of adaptive-grid algorithms for time-dependent partial differential equations. Two lines of research are discussed. One involves the automatic selection of moving grids to follow propagating waves. The other is based on stationary grids but uses local mesh refinement in both space and time. Advantages and disadvantages of both approaches are discussed. The development of adaptive-grid schemes shows promise of greatly increasing our ability to solve problems in several spatial dimensions.
Adaptive-Grid Methods for Phase Field Models of Microstructure Development
NASA Technical Reports Server (NTRS)
Provatas, Nikolas; Goldenfeld, Nigel; Dantzig, Jonathan A.
1999-01-01
In this work the authors show how the phase field model can be solved in a computationally efficient manner that opens a new large-scale simulational window on solidification physics. Our method uses a finite element, adaptive-grid formulation, and exploits the fact that the phase and temperature fields vary significantly only near the interface. We illustrate how our method allows efficient simulation of phase-field models in very large systems, and verify the predictions of solvability theory at intermediate undercooling. We then present new results at low undercoolings that suggest that solvability theory may not give the correct tip speed in that regime. We model solidification using the phase-field model used by Karma and Rappel.
Adaptive multi-grid method for a periodic heterogeneous medium in 1-D
Fish, J.; Belsky, V.
1995-12-31
A multi-grid method for a periodic heterogeneous medium in 1-D is presented. Based on the homogenization theory special intergrid connection operators have been developed to imitate a low frequency response of the differential equations with oscillatory coefficients. The proposed multi-grid method has been proved to have a fast rate of convergence governed by the ratio q/(4-q), where oadaptive multiscale computational scheme is developed. By this technique a computational model entirely constructed on the scale of material heterogeneity is only used where it is necessary to do so, or as indicated by so called Microscale Reduction Error (MRE) indicators, while in the remaining portion of the problem domain, the medium is treated as homogeneous with effective properties. Such a posteriori MRE indicators and estimators are developed on the basis of assessing the validity of two-scale asymptotic expansion.
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.
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.
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.
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.
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)
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 Astrophysics Data System (ADS)
Ma, Xiang; Zabaras, Nicholas
2009-03-01
A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media.
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.
NASA Technical Reports Server (NTRS)
Olynick, David P.; Hassan, H. A.; Moss, James N.
1988-01-01
A grid generation and adaptation procedure based on the method of transfinite interpolation is incorporated into the Direct Simulation Monte Carlo Method of Bird. In addition, time is advanced based on a local criterion. The resulting procedure is used to calculate steady flows past wedges and cones. Five chemical species are considered. In general, the modifications result in a reduced computational effort. Moreover, preliminary results suggest that the simulation method is time step dependent if requirements on cell sizes are not met.
Adaptive analog-SSOR iterative method for solving grid equations with nonselfadjoint operators
NASA Astrophysics Data System (ADS)
Alekseenko, Elena; Sukhinov, Alexander; Chistyakov, Alexander; Shishenya, Alexander; Roux, Bernard
2013-04-01
Motion models of wave processes in the coastal zone are highly demanded in the projection and construction of coastal surface structures and breakwaters, and also as a component of other models. The most common of the grid approaches is currently vof-method. A significant drawback of this method is in the necessity to solve the convection equation to find fullness of cells. The numerical solution of this equation leads to a strong grid viscosity and "smearing" of the interface. In this paper, we propose a method, which is based on the idea of using a fill, as in vof method, but its conversion is not required to solve the equation of convection. Thus in this work, a mathematical model for the wave hydrodynamics problem, describing wash ashore and taking into account such physical parameters as turbulent exchange, complexity of domain and coastal line geometry, and bottom friction is developed. For the given mathematical model a discrete model is constructed, taking into account dynamical changing of the calculation domain. Discretization of the model is performed on the structured rectangular grid with a new developed finite-volume technique that takes into account fullness of the grid cells that allows describing geometry more accurate. Proposed technique allows improving the real accuracy of a solution in case of complex domain geometry, by improving approximation of the boundary. A software implementation and numerical experiments of the posed problem of the wave hydrodynamics is performed. The results of numerical experiments show the feasibility of using discrete mathematical models of processes that take into account fullness of grid cells, for the simulation of systems with complex geometry of the border. Numerical experiments show that the use of this technique sufficiently smooth solutions are obtained even on coarse grids.
NASA Astrophysics Data System (ADS)
Guseva, T. S.
2016-01-01
A numerical technique of computing shock waves in compressible media with movable deforming interphase boundaries including those of the gas-liquid type has been realized. The approach without explicit separation of the interphase boundary is applied. The CIP-CUP method is used for integrating the equations of gas dynamics. An adaptive grid of special kind (the soroban-grid) is utilized. Some results of testing the technique using one- and two-dimensional problems are given. Results of computation of impact of a jet on a thin liquid layer on a wall are presented.
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.
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.
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.
SAGE - MULTIDIMENSIONAL SELF-ADAPTIVE GRID CODE
NASA Technical Reports Server (NTRS)
Davies, C. B.
1994-01-01
SAGE, Self Adaptive Grid codE, is a flexible tool for adapting and restructuring both 2D and 3D grids. Solution-adaptive grid methods are useful tools for efficient and accurate flow predictions. In supersonic and hypersonic flows, strong gradient regions such as shocks, contact discontinuities, shear layers, etc., require careful distribution of grid points to minimize grid error and produce accurate flow-field predictions. SAGE helps the user obtain more accurate solutions by intelligently redistributing (i.e. adapting) the original grid points based on an initial or interim flow-field solution. The user then computes a new solution using the adapted grid as input to the flow solver. The adaptive-grid methodology poses the problem in an algebraic, unidirectional manner for multi-dimensional adaptations. The procedure is analogous to applying tension and torsion spring forces proportional to the local flow gradient at every grid point and finding the equilibrium position of the resulting system of grid points. The multi-dimensional problem of grid adaption is split into a series of one-dimensional problems along the computational coordinate lines. The reduced one dimensional problem then requires a tridiagonal solver to find the location of grid points along a coordinate line. Multi-directional adaption is achieved by the sequential application of the method in each coordinate direction. The tension forces direct the redistribution of points to the strong gradient region. To maintain smoothness and a measure of orthogonality of grid lines, torsional forces are introduced that relate information between the family of lines adjacent to one another. The smoothness and orthogonality constraints are direction-dependent, since they relate only the coordinate lines that are being adapted to the neighboring lines that have already been adapted. Therefore the solutions are non-unique and depend on the order and direction of adaption. Non-uniqueness of the adapted grid is
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.
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.
NASA Astrophysics Data System (ADS)
Harris, Robert Evan
2008-10-01
An efficient implementation of the high-order spectral volume (SV) method is presented for multi-dimensional conservation laws on unstructured grids. In the SV method, each simplex cell is called a spectral volume (SV), and the SV is further subdivided into polygonal (2D), or polyhedral (3D) control volumes (CVs) to support high-order data reconstructions. In the traditional implementation, Gauss quadrature formulas are used to approximate the flux integrals on all faces. In the new approach, a nodal set is selected and used to reconstruct a high-order polynomial approximation for the flux vector, and then the flux integrals on the internal faces are computed analytically, without the need for Gauss quadrature formulas. This gives a significant advantage over the traditional SV method in efficiency and ease of implementation. Fundamental properties of the new SV implementation are studied and high-order accuracy is demonstrated for linear and nonlinear advection equations, and the Euler equations. The new quadrature-free approach is then extended to handle local adaptive hp-refinement (grid and order refinement). Efficient edge-based adaptation utilizing a binary tree search algorithm is employed. Several different adaptation criteria which focus computational effort near high gradient regions are presented. Both h- and p-refinements are presented in a general framework where it is possible to perform either or both on any grid cell at any time. Several well-known inviscid flow test cases, subjected to various levels of adaptation, are utilized to demonstrate the effectiveness of the method. An analysis of the accuracy and stability properties of the spectral volume (SV) method is then presented. The current work seeks to address the issue of stability, as well as polynomial quality, in the design of SV partitions. A new approach is presented, which efficiently locates stable partitions by means of constrained minimization. Once stable partitions are located, a
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.
Neely, Michael; Bartroff, Jay; van Guilder, Michael; Yamada, Walter; Bayard, David; Jelliffe, Roger; Leary, Robert; Chubatiuk, Alyona; Schumitzky, Alan
2013-01-01
Population pharmacokinetic (PK) modeling methods can be statistically classified as either parametric or nonparametric (NP). Each classification can be divided into maximum likelihood (ML) or Bayesian (B) approazches. In this paper we discuss the nonparametric case using both maximum likelihood and Bayesian approaches. We present two nonparametric methods for estimating the unknown joint population distribution of model parameter values in a pharmacokinetic/pharmacodynamic (PK/PD) dataset. The first method is the NP Adaptive Grid (NPAG). The second is the NP Bayesian (NPB) algorithm with a stick-breaking process to construct a Dirichlet prior. Our objective is to compare the performance of these two methods using a simulated PK/PD dataset. Our results showed excellent performance of NPAG and NPB in a realistically simulated PK study. This simulation allowed us to have benchmarks in the form of the true population parameters to compare with the estimates produced by the two methods, while incorporating challenges like unbalanced sample times and sample numbers as well as the ability to include the covariate of patient weight. We conclude that both NPML and NPB can be used in realistic PK/PD population analysis problems. The advantages of one versus the other are discussed in the paper. NPAG and NPB are implemented in R and freely available for download within the Pmetrics package from www.lapk.org. PMID:23404393
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.
Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations
NASA Technical Reports Server (NTRS)
Moon, Young J.; Liou, Meng-Sing
1989-01-01
Conservative algorithms for boundaray interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.
Conservative treatment of boundary interfaces for overlaid grids and multi-level grid adaptations
NASA Technical Reports Server (NTRS)
Moon, Young J.; Liou, Meng-Sing
1989-01-01
Conservative algorithms for boundary interfaces of overlaid grids are presented. The basic method is zeroth order, and is extended to a higher order method using interpolation and subcell decomposition. The present method, strictly based on a conservative constraint, is tested with overlaid grids for various applications of unsteady and steady supersonic inviscid flows with strong shock waves. The algorithm is also applied to a multi-level grid adaptation in which the next level finer grid is overlaid on the coarse base grid with an arbitrary orientation.
Adaptive grid embedding for the two-dimensional Euler equations
NASA Technical Reports Server (NTRS)
Warren, Gary P.
1990-01-01
A numerical algorithm is presented for solving the two-dimensional 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 an NACA 0012 airfoil in a freestream with Mach numbers of 0.95 and 1.054. Excellent resolution of the shock structures is obtained with the adaptive grid embedding method with significantly fewer grid points than the comparable structured grid.
Conservative Smoothing on an Adaptive Quadrilateral Grid
NASA Astrophysics Data System (ADS)
Sun, M.; Takayama, K.
1999-03-01
The Lax-Wendroff scheme can be freed of spurious oscillations by introducing conservative smoothing. In this paper the approach is first tested in 1-D modeling equations and then extended to multidimensional flows by the finite volume method. The scheme is discretized by a space-splitting method on an adaptive quadrilateral grid. The artificial viscosity coefficients in the conservative smoothing step are specially designed to capture slipstreams and vortices. Algorithms are programmed using a vectorizable data structure, under which not only the flow solver but also the adaptation procedure is well vectorized. The good resolution and high efficiency of the approach are demonstrated in calculating both unsteady and steady compressible flows with either weak or strong shock waves.
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.
Rapid Structured Volume Grid Smoothing and Adaption Technique
NASA Technical Reports Server (NTRS)
Alter, Stephen J.
2004-01-01
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 reduction 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.
NASA Astrophysics Data System (ADS)
Chen, Peng; Quarteroni, Alfio
2015-10-01
In this work we develop an adaptive and reduced computational algorithm based on dimension-adaptive sparse grid approximation and reduced basis methods for solving high-dimensional uncertainty quantification (UQ) problems. In order to tackle the computational challenge of "curse of dimensionality" commonly faced by these problems, we employ a dimension-adaptive tensor-product algorithm [16] and propose a verified version to enable effective removal of the stagnation phenomenon besides automatically detecting the importance and interaction of different dimensions. To reduce the heavy computational cost of UQ problems modelled by partial differential equations (PDE), we adopt a weighted reduced basis method [7] and develop an adaptive greedy algorithm in combination with the previous verified algorithm for efficient construction of an accurate reduced basis approximation. The efficiency and accuracy of the proposed algorithm are demonstrated by several numerical experiments.
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.
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
Load Balancing Sequences of Unstructured Adaptive Grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Oliker, Leonid
1997-01-01
Mesh adaption is a powerful tool for efficient unstructured grid computations but causes load imbalance on multiprocessor systems. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. This paper makes several important additions to our previous work. First, a new remapping cost model is presented and empirically validated on an SP2. Next, our load balancing strategy is applied to sequences of dynamically adapted unstructured grids. Results indicate that our framework is effective on many processors for both steady and unsteady problems with several levels of adaption. Additionally, we demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required for a fine initial mesh. Finally, we show that the data remapping overhead can be significantly reduced by applying our heuristic processor reassignment algorithm.
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
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
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 Astrophysics Data System (ADS)
Kallinderis, Yannis; Khawaja, Aly; McMorris, Harlan
1995-03-01
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.
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.
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.
A novel hyperbolic grid generation procedure with inherent adaptive dissipation
Tai, C.H.; Yin, S.L.; Soong, C.Y.
1995-01-01
This paper reports a novel hyperbolic grid-generation with an inherent adaptive dissipation (HGAD), which is capable of improving the oscillation and overlapping of grid lines. In the present work upwinding differencing is applied to discretize the hyperbolic system and, thereby, to develop the adaptive dissipation coefficient. Complex configurations with the features of geometric discontinuity, exceptional concavity and convexity are used as the test cases for comparison of the present HGAD procedure with the conventional hyerbolic and elliptic ones. The results reveal that the HGAD method is superior in orthogonality and smoothness of the grid system. In addition, the computational efficiency of the flow solver may be improved by using the present HGAD procedure. 15 refs., 8 figs.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
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.
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.
Dynamic mesh adaption for triangular and tetrahedral grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1993-01-01
The following topics are discussed: requirements for dynamic mesh adaption; linked-list data structure; edge-based data structure; adaptive-grid data structure; three types of element subdivision; mesh refinement; mesh coarsening; additional constraints for coarsening; anisotropic error indicator for edges; unstructured-grid Euler solver; inviscid 3-D wing; and mesh quality for solution-adaptive grids. The discussion is presented in viewgraph form.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
1988-08-01
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.
Three-dimensional adaptive grid generation for body-fitted coordinate system
NASA Astrophysics Data System (ADS)
Chen, S. C.
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.
Large-Scale Liquid Simulation on Adaptive Hexahedral Grids.
Ferstl, Florian; Westermann, Rudiger; Dick, Christian
2014-10-01
Regular grids are attractive for numerical fluid simulations because they give rise to efficient computational kernels. However, for simulating high resolution effects in complicated domains they are only of limited suitability due to memory constraints. In this paper we present a method for liquid simulation on an adaptive octree grid using a hexahedral finite element discretization, which reduces memory requirements by coarsening the elements in the interior of the liquid body. To impose free surface boundary conditions with second order accuracy, we incorporate a particular class of Nitsche methods enforcing the Dirichlet boundary conditions for the pressure in a variational sense. We then show how to construct a multigrid hierarchy from the adaptive octree grid, so that a time efficient geometric multigrid solver can be used. To improve solver convergence, we propose a special treatment of liquid boundaries via composite finite elements at coarser scales. We demonstrate the effectiveness of our method for liquid simulations that would require hundreds of millions of simulation elements in a non-adaptive regime. PMID:26357387
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.
Fast transport simulation with an adaptive grid refinement.
Haefner, Frieder; Boy, Siegrun
2003-01-01
One of the main difficulties in transport modeling and calibration is the extraordinarily long computing times necessary for simulation runs. Improved execution time is a prerequisite for calibration in transport modeling. In this paper we investigate the problem of code acceleration using an adaptive grid refinement, neglecting subdomains, and devising a method by which the Courant condition can be ignored while maintaining accurate solutions. Grid refinement is based on dividing selected cells into regular subcells and including the balance equations of subcells in the equation system. The connection of coarse and refined cells satisfies the mass balance with an interpolation scheme that is implicitly included in the equation system. The refined subdomain can move with the average transport velocity of the subdomain. Very small time steps are required on a fine or a refined grid, because of the combined effect of the Courant and Peclet conditions. Therefore, we have developed a special upwind technique in small grid cells with high velocities (velocity suppression). We have neglected grid subdomains with very small concentration gradients (zero suppression). The resulting software, MODCALIF, is a three-dimensional, modularly constructed FORTRAN code. For convenience, the package names used by the well-known MODFLOW and MT3D computer programs are adopted, and the same input file structure and format is used, but the program presented here is separate and independent. Also, MODCALIF includes algorithms for variable density modeling and model calibration. The method is tested by comparison with an analytical solution, and illustrated by means of a two-dimensional theoretical example and three-dimensional simulations of the variable-density Cape Cod and SALTPOOL experiments. Crossing from fine to coarse grid produces numerical dispersion when the whole subdomain of interest is refined; however, we show that accurate solutions can be obtained using a fraction of the
JPEG 2000 coding of image data over adaptive refinement grids
NASA Astrophysics Data System (ADS)
Gamito, Manuel N.; Dias, Miguel S.
2003-06-01
An extension of the JPEG 2000 standard is presented for non-conventional images resulting from an adaptive subdivision process. Samples, generated through adaptive subdivision, can have different sizes, depending on the amount of subdivision that was locally introduced in each region of the image. The subdivision principle allows each individual sample to be recursively subdivided into sets of four progressively smaller samples. Image datasets generated through adaptive subdivision find application in Computational Physics where simulations of natural processes are often performed over adaptive grids. It is also found that compression gains can be achieved for non-natural imagery, like text or graphics, if they first undergo an adaptive subdivision process. The representation of adaptive subdivision images is performed by first coding the subdivision structure into the JPEG 2000 bitstream, ina lossless manner, followed by the entropy coded and quantized transform coefficients. Due to the irregular distribution of sample sizes across the image, the wavelet transform must be applied on irregular image subsets that are nested across all the resolution levels. Using the conventional JPEG 2000 coding standard, adaptive subdivision images would first have to be upsampled to the smallest sample size in order to attain a uniform resolution. The proposed method for coding adaptive subdivision images is shown to perform better than conventional JPEG 2000 for medium to high bitrates.
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.
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.
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.
Automation of assertion testing - Grid and adaptive techniques
NASA Technical Reports Server (NTRS)
Andrews, D. M.
1985-01-01
Assertions can be used to automate the process of testing software. Two methods for automating the generation of input test data are described in this paper. One method selects the input values of variables at regular intervals in a 'grid'. The other, adaptive testing, uses assertion violations as a measure of errors detected and generates new test cases based on test results. The important features of assertion testing are that: it can be used throughout the entire testing cycle; it provides automatic notification of error conditions; and it can be used with automatic input generation techniques which eliminate the subjectivity in choosing test data.
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.
A generic efficient adaptive grid scheme for rocket propulsion modeling
NASA Technical Reports Server (NTRS)
Mo, J. D.; Chow, Alan S.
1993-01-01
The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.
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 sparse grid expansions of the vibrational Hamiltonian
NASA Astrophysics Data System (ADS)
Strobusch, D.; Scheurer, Ch.
2014-02-01
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.
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.
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
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.
Volumetric Rendering of Geophysical Data on Adaptive Wavelet Grid
NASA Astrophysics Data System (ADS)
Vezolainen, A.; Erlebacher, G.; Vasilyev, O.; Yuen, D. A.
2005-12-01
Numerical modeling of geological phenomena frequently involves processes across a wide range of spatial and temporal scales. In the last several years, transport phenomena governed by the Navier-Stokes equations have been simulated in wavelet space using second generation wavelets [1], and most recently on fully adaptive meshes. Our objective is to visualize this time-dependent data using volume rendering while capitalizing on the available sparse data representation. We present a technique for volumetric ray casting of multi-scale datasets in wavelet space. Rather of working with the wavelets at the finest possible resolution, we perform a partial inverse wavelet transform as a preprocessing step to obtain scaling functions on a uniform grid at a user-prescribed resolution. As a result, a function in physical space is represented by a superposition of scaling functions on a coarse regular grid and wavelets on an adaptive mesh. An efficient and accurate ray casting algorithm is based just on these scaling functions. Additional detail is added during the ray tracing by taking an appropriate number of wavelets into account based on support overlap with the interpolation point, wavelet amplitude, and other characteristics, such as opacity accumulation (front to back ordering) and deviation from frontal viewing direction. Strategies for hardware implementation will be presented if available, inspired by the work in [2]. We will pressent error measures as a function of the number of scaling and wavelet functions used for interpolation. Data from mantle convection will be used to illustrate the method. [1] Vasilyev, O.V. and Bowman, C., Second Generation Wavelet Collocation Method for the Solution of Partial Differential Equations. J. Comp. Phys., 165, pp. 660-693, 2000. [2] Guthe, S., Wand, M., Gonser, J., and Straßer, W. Interactive rendering of large volume data sets. In Proceedings of the Conference on Visualization '02 (Boston, Massachusetts, October 27 - November
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.
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)
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.
NASA Astrophysics Data System (ADS)
Kopera, Michal A.; Giraldo, Francis X.
2015-09-01
We perform a comparison of mass conservation properties of the continuous (CG) and discontinuous (DG) Galerkin methods on non-conforming, dynamically adaptive meshes for two atmospheric test cases. The two methods are implemented in a unified way which allows for a direct comparison of the non-conforming edge treatment. We outline the implementation details of the non-conforming direct stiffness summation algorithm for the CG method and show that the mass conservation error is similar to the DG method. Both methods conserve to machine precision, regardless of the presence of the non-conforming edges. For lower order polynomials the CG method requires additional stabilization to run for very long simulation times. We addressed this issue by using filters and/or additional artificial viscosity. The mathematical proof of mass conservation for CG with non-conforming meshes is presented in Appendix B.
The emergence of grid cells: Intelligent design or just adaptation?
Kropff, Emilio; Treves, Alessandro
2008-01-01
Individual medial entorhinal cortex (mEC) 'grid' cells provide a representation of space that appears to be essentially invariant across environments, modulo simple transformations, in contrast to multiple, rapidly acquired hippocampal maps; it may therefore be established gradually during rodent development. We explore with a simplified mathematical model the possibility that the self-organization of multiple grid fields into a triangular grid pattern may be a single-cell process, driven by firing rate adaptation and slowly varying spatial inputs. A simple analytical derivation indicates that triangular grids are favored asymptotic states of the self-organizing system, and computer simulations confirm that such states are indeed reached during a model learning process, provided it is sufficiently slow to effectively average out fluctuations. The interactions among local ensembles of grid units serve solely to stabilize a common grid orientation. Spatial information, in the real mEC network, may be provided by any combination of feedforward cortical afferents and feedback hippocampal projections from place cells, since either input alone is likely sufficient to yield grid fields. PMID:19021261
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.
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.
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.
Visual Methods for Model and Grid Validation
NASA Technical Reports Server (NTRS)
Pang, Alex
1998-01-01
This joint research interchange proposal allowed us to contribute in two directions that are of interest to NASA. These are: (a) data level comparative visualization of experimental and computational fluid flow, and (b) visualization tools for analysis of adaptively refined Cartesian grids.
Adaptive Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
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.
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.
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.
X3D moving grid methods for semiconductor applications
Kuprat, A.; Cartwright, D.; Gammel, J.T.; George, D.; Kendrick, B.; Kilcrease, D.; Trease, H.; Walker, R.
1997-11-01
The Los Alamos 3D grid toolbox handles grid maintenance chores and provides access to a sophisticated set of optimization algorithms for unstructured grids. The application of these tools to semiconductor problems is illustrated in three examples: grain growth, topographic deposition and electrostatics. These examples demonstrate adaptive smoothing, front tracking, and automatic, adaptive refinement/derefinement.
AN OPTIMAL ADAPTIVE LOCAL GRID REFINEMENT APPROACH TO MODELING CONTAMINANT TRANSPORT
A Lagrangian-Eulerian method with an optimal adaptive local grid refinement is used to model contaminant transport equations. pplication of this approach to two bench-mark problems indicates that it completely resolves difficulties of peak clipping, numerical diffusion, and spuri...
Accelerated adaptive integration method.
Kaus, Joseph W; Arrar, Mehrnoosh; McCammon, J Andrew
2014-05-15
Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083
Accelerated Adaptive Integration Method
2015-01-01
Conformational changes that occur upon ligand binding may be too slow to observe on the time scales routinely accessible using molecular dynamics simulations. The adaptive integration method (AIM) leverages the notion that when a ligand is either fully coupled or decoupled, according to λ, barrier heights may change, making some conformational transitions more accessible at certain λ values. AIM adaptively changes the value of λ in a single simulation so that conformations sampled at one value of λ seed the conformational space sampled at another λ value. Adapting the value of λ throughout a simulation, however, does not resolve issues in sampling when barriers remain high regardless of the λ value. In this work, we introduce a new method, called Accelerated AIM (AcclAIM), in which the potential energy function is flattened at intermediate values of λ, promoting the exploration of conformational space as the ligand is decoupled from its receptor. We show, with both a simple model system (Bromocyclohexane) and the more complex biomolecule Thrombin, that AcclAIM is a promising approach to overcome high barriers in the calculation of free energies, without the need for any statistical reweighting or additional processors. PMID:24780083
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.
Grid generation strategies for turbomachinery configurations
NASA Astrophysics Data System (ADS)
Lee, K. D.; Henderson, T. L.
1991-01-01
Turbomachinery flow fields involve unique grid generation issues due to their geometrical and physical characteristics. Several strategic approaches are discussed to generate quality grids. The grid quality is further enhanced through blending and adapting. Grid blending smooths the grids locally through averaging and diffusion operators. Grid adaptation redistributes the grid points based on a grid quality assessment. These methods are demonstrated with several examples.
Self-adaptive Fault-Tolerance of HLA-Based Simulations in the Grid Environment
NASA Astrophysics Data System (ADS)
Huang, Jijie; Chai, Xudong; Zhang, Lin; Li, Bo Hu
The objects of a HLA-based simulation can access model services to update their attributes. However, the grid server may be overloaded and refuse the model service to handle objects accesses. Because these objects have been accessed this model service during last simulation loop and their medium state are stored in this server, this may terminate the simulation. A fault-tolerance mechanism must be introduced into simulations. But the traditional fault-tolerance methods cannot meet the above needs because the transmission latency between a federate and the RTI in grid environment varies from several hundred milliseconds to several seconds. By adding model service URLs to the OMT and expanding the HLA services and model services with some interfaces, this paper proposes a self-adaptive fault-tolerance mechanism of simulations according to the characteristics of federates accessing model services. Benchmark experiments indicate that the expanded HLA/RTI can make simulations self-adaptively run in the grid environment.
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.
Grid generation and flow solution method for Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1992-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme, which uses Delaunay triangulation, generates the field points for the mesh based on cell aspect ratios and allows clustering of grid points near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss-Seidel procedure that is completely vectorizable. Also, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for an NACA 0012 airfoil as well as a two element configuration. Flow solution results are shown for a two dimensional flow over the NACA 0012 airfoil and for a two element configuration in which the solution was obtained through an adaptation procedure and compared with an exact solution. Preliminary three dimensional results also are shown in which the subsonic flow over a business jet is computed.
A grid spacing control technique for algebraic grid generation methods
NASA Technical Reports Server (NTRS)
Smith, R. E.; Kudlinski, R. A.; Everton, E. L.
1982-01-01
A technique which controls the spacing of grid points in algebraically defined coordinate transformations is described. The technique is based on the generation of control functions which map a uniformly distributed computational grid onto parametric variables defining the physical grid. The control functions are smoothed cubic splines. Sets of control points are input for each coordinate directions to outline the control functions. Smoothed cubic spline functions are then generated to approximate the input data. The technique works best in an interactive graphics environment where control inputs and grid displays are nearly instantaneous. The technique is illustrated with the two-boundary grid generation algorithm.
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.
Modeling scramjet combustor flowfields with a grid adaptation scheme
NASA Technical Reports Server (NTRS)
Ramakrishnan, R.; Singh, D. J.
1994-01-01
The accurate description of flow features associated with the normal injection of fuel into supersonic primary flows is essential in the design of efficient engines for hypervelocity aerospace vehicles. The flow features in such injections are complex with multiple interactions between shocks and between shocks boundary layers. Numerical studies of perpendicular sonic N2 injection and mixing in a Mach 3.8 scramjet combustor environment are discussed. A dynamic grid adaptation procedure based on the equilibration of spring-mass system is employed to enhanced the description of the complicated flow features. Numerical results are compared with experimental measurements and indicate that the adaptation procedure enhances the capability of the modeling procedure to describe the flow features associated with scramjet combustor components.
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.
A finite volume method for numerical grid generation
NASA Astrophysics Data System (ADS)
Beale, S. B.
1999-07-01
A novel method to generate body-fitted grids based on the direct solution for three scalar functions is derived. The solution for scalar variables , and is obtained with a conventional finite volume method based on a physical space formulation. The grid is adapted or re-zoned to eliminate the residual error between the current solution and the desired solution, by means of an implicit grid-correction procedure. The scalar variables are re-mapped and the process is reiterated until convergence is obtained. Calculations are performed for a variety of problems by assuming combined Dirichlet-Neumann and pure Dirichlet boundary conditions involving the use of transcendental control functions, as well as functions designed to effect grid control automatically on the basis of boundary values. The use of dimensional analysis to build stable exponential functions and other control functions is demonstrated. Automatic procedures are implemented: one based on a finite difference approximation to the Cristoffel terms assuming local-boundary orthogonality, and another designed to procure boundary orthogonality. The performance of the new scheme is shown to be comparable with that of conventional inverse methods when calculations are performed on benchmark problems through the application of point-by-point and whole-field solution schemes. Advantages and disadvantages of the present method are critically appraised. Copyright
A grid generation and flow solution method for the Euler equations on unstructured grids
NASA Technical Reports Server (NTRS)
Anderson, W. Kyle
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set of equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a National Advisory Committee for Aeronautics (NACA) 0012 airfoil as well as a two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed.
A grid generation and flow solution method for the Euler equations on unstructured grids
Anderson, W.K. )
1994-01-01
A grid generation and flow solution algorithm for the Euler equations on unstructured grids is presented. The grid generation scheme utilizes Delaunay triangulation and self-generates the field points for the mesh based on cell aspect ratios and allows for clustering near solid surfaces. The flow solution method is an implicit algorithm in which the linear set or equations arising at each time step is solved using a Gauss Seidel procedure which is completely vectorizable. In addition, a study is conducted to examine the number of subiterations required for good convergence of the overall algorithm. Grid generation results are shown in two dimensions for a NACA 0012 airfoil as well as two-element configuration. Flow solution results are shown for two-dimensional flow over the NACA 0012 airfoil and for a two-element configuration in which the solution has been obtained through an adaptation procedure and compared to an exact solution. Preliminary three-dimensional results are also shown in which subsonic flow over a business jet is computed. 31 refs. 30 figs.
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.
Advancing-layers method for generation of unstructured viscous grids
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A novel approach for generating highly stretched grids which is based on a modified advancing-front technique and benefits from the generality, flexibility, and grid quality of the conventional advancing-front-based Euler grid generators is presented. The method is self-sufficient for the insertion of grid points in the boundary layer and beyond. Since it is based on a totally unstructured grid strategy, the method alleviates the difficulties stemming from the structural limitations of the prismatic techniques.
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.
Structured background grids for generation of unstructured grids by advancing front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1991-01-01
A new method of background grid construction is introduced for generation of unstructured tetrahedral grids using the advancing-front technique. Unlike the conventional triangular/tetrahedral background grids which are difficult to construct and usually inadequate in performance, the new method exploits the simplicity of uniform Cartesian meshes and provides grids of better quality. The approach is analogous to solving a steady-state heat conduction problem with discrete heat sources. The spacing parameters of grid points are distributed over the nodes of a Cartesian background grid by interpolating from a few prescribed sources and solving a Poisson equation. To increase the control over the grid point distribution, a directional clustering approach is used. The new method is convenient to use and provides better grid quality and flexibility. Sample results are presented to demonstrate the power of the method.
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.
Fundamental differences between SPH and grid methods
NASA Astrophysics Data System (ADS)
Agertz, Oscar; Moore, Ben; Stadel, Joachim; Potter, Doug; Miniati, Francesco; Read, Justin; Mayer, Lucio; Gawryszczak, Artur; Kravtsov, Andrey; Nordlund, Åke; Pearce, Frazer; Quilis, Vicent; Rudd, Douglas; Springel, Volker; Stone, James; Tasker, Elizabeth; Teyssier, Romain; Wadsley, James; Walder, Rolf
2007-09-01
We have carried out a comparison study of hydrodynamical codes by investigating their performance in modelling interacting multiphase fluids. The two commonly used techniques of grid and smoothed particle hydrodynamics (SPH) show striking differences in their ability to model processes that are fundamentally important across many areas of astrophysics. Whilst Eulerian grid based methods are able to resolve and treat important dynamical instabilities, such as Kelvin-Helmholtz or Rayleigh-Taylor, these processes are poorly or not at all resolved by existing SPH techniques. We show that the reason for this is that SPH, at least in its standard implementation, introduces spurious pressure forces on particles in regions where there are steep density gradients. This results in a boundary gap of the size of an SPH smoothing kernel radius over which interactions are severely damped.
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.
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.
Three-dimensional grid generation method based on a variational principle
NASA Astrophysics Data System (ADS)
Jacquotte, O.-P.; Cabello, J.
This paper reviews the main stages of construction of a variational method to optimize and adapt two- and three-dimensional grids. A measure of the cell deformation can be built on the basis of geometric axioms. The grid is optimized with respect to a global measure of the mesh quality obtained by summation of the elementary contributions. A convexity property is also prescribed that ensures the optimization problem is correctly stated, and that the solver is efficient. Mechanical and geometric interpretations of the method are given. In particular, a volume control term can be used to adapt grids according to a given criterion. Several examples of optimized and adapted grids are presented, to show the method's possibilities.
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.
Unstructured viscous grid generation by advancing-front method
NASA Technical Reports Server (NTRS)
Pirzadeh, Shahyar
1993-01-01
A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.
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
Generation and adaptation of 3-D unstructured grids for transient problems
NASA Technical Reports Server (NTRS)
Loehner, Rainald
1990-01-01
Grid generation and adaptive refinement techniques suitable for the simulation of strongly unsteady flows past geometrically complex bodies in 3-D are described. The grids are generated using the advancing front technique. Emphasis is placed not to generate elements that are too small, as this would severely increase the cost of simulations with explicit flow solvers. The grids are adapted to an evolving flowfield using simple h-refinement. A grid change is performed every 5 to 10 timesteps, and only one level of refinement/coarsening is allowed per mesh change.
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.
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.
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
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.
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.
Time-dependent grid adaptation for meshes of triangles and tetrahedra
NASA Technical Reports Server (NTRS)
Rausch, Russ D.
1993-01-01
This paper presents in viewgraph form a method of optimizing grid generation for unsteady CFD flow calculations that distributes the numerical error evenly throughout the mesh. Adaptive meshing is used to locally enrich in regions of relatively large errors and to locally coarsen in regions of relatively small errors. The enrichment/coarsening procedures are robust for isotropic cells; however, enrichment of high aspect ratio cells may fail near boundary surfaces with relatively large curvature. The enrichment indicator worked well for the cases shown, but in general requires user supervision for a more efficient solution.
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
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.
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.
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
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
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.
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.
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
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.
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.
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.
An adaptive discretization of incompressible flow using a multitude of moving Cartesian grids
NASA Astrophysics Data System (ADS)
English, R. Elliot; Qiu, Linhai; Yu, Yue; Fedkiw, Ronald
2013-12-01
We present a novel method for discretizing the incompressible Navier-Stokes equations on a multitude of moving and overlapping Cartesian grids each with an independently chosen cell size to address adaptivity. Advection is handled with first and second order accurate semi-Lagrangian schemes in order to alleviate any time step restriction associated with small grid cell sizes. Likewise, an implicit temporal discretization is used for the parabolic terms including Navier-Stokes viscosity which we address separately through the development of a method for solving the heat diffusion equations. The most intricate aspect of any such discretization is the method used in order to solve the elliptic equation for the Navier-Stokes pressure or that resulting from the temporal discretization of parabolic terms. We address this by first removing any degrees of freedom which duplicately cover spatial regions due to overlapping grids, and then providing a discretization for the remaining degrees of freedom adjacent to these regions. We observe that a robust second order accurate symmetric positive definite readily preconditioned discretization can be obtained by constructing a local Voronoi region on the fly for each degree of freedom in question in order to obtain both its stencil (logically connected neighbors) and stencil weights. Internal curved boundaries such as at solid interfaces are handled using a simple immersed boundary approach which is directly applied to the Voronoi mesh in both the viscosity and pressure solves. We independently demonstrate each aspect of our approach on test problems in order to show efficacy and convergence before finally addressing a number of common test cases for incompressible flow with stationary and moving solid bodies.
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.
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.
Error-measure for anisotropic grid-adaptation in turbulence-resolving simulations
NASA Astrophysics Data System (ADS)
Toosi, Siavash; Larsson, Johan
2015-11-01
Grid-adaptation requires an error-measure that identifies where the grid should be refined. In the case of turbulence-resolving simulations (DES, LES, DNS), a simple error-measure is the small-scale resolved energy, which scales with both the modeled subgrid-stresses and the numerical truncation errors in many situations. Since this is a scalar measure, it does not carry any information on the anisotropy of the optimal grid-refinement. The purpose of this work is to introduce a new error-measure for turbulence-resolving simulations that is capable of predicting nearly-optimal anisotropic grids. Turbulent channel flow at Reτ ~ 300 is used to assess the performance of the proposed error-measure. The formulation is geometrically general, applicable to any type of unstructured grid.
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.
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.
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.
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.
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.
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.
The Neural Network Method of Corrosion Diagnosis for Grounding Grid
Hou Zaien; Duan Fujian; Zhang Kecun
2008-11-06
Safety of persons, protection of equipment and continuity of power supply are the main objectives of the grounding system of a large electrical installation. For its accurate working status, it is essential to determine every branch resistance in the system. In this paper, we present a neural network method of corrosion diagnosis for the grounding grid based on the neural network theory. The feasibility of this method is discussed by means of its application to a simulant grounding grid.
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.
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).
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.
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.
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.
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
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.
Supersampling method for efficient grid-based electronic structure calculations.
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. PMID:26957151
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.
Application of unstructured grid methods to steady and unsteady aerodynamic problems
NASA Technical Reports Server (NTRS)
Batina, John T.
1989-01-01
The purpose is to describe the development of unstructured grid methods which have several advantages when compared to methods which make use of structured grids. Unstructured grids, for example, easily allow the treatment of complex geometries, allow for general mesh movement for realistic motions and structural deformations of complete aircraft configurations which is important for aeroelastic analysis, and enable adaptive mesh refinement to more accurately resolve the physics of the flow. Steady Euler calculations for a supersonic fighter configuration to demonstrate the complex geometry capability; unsteady Euler calculations for the supersonic fighter undergoing harmonic oscillations in a complete-vehicle bending mode to demonstrate the general mesh movement capability; and vortex-dominated conical-flow calculations for highly-swept delta wings to demonstrate the adaptive mesh refinement capability are discussed. The basic solution algorithm is a multi-stage Runge-Kutta time-stepping scheme with a finite-volume spatial discretization based on an unstructured grid of triangles in 2D or tetrahedra in 3D. The moving mesh capability is a general procedure which models each edge of each triangle (2D) or tetrahedra (3D) with a spring. The resulting static equilibrium equations which result from a summation of forces are then used to move the mesh to allow it to continuously conform to the instantaneous position or shape of the aircraft. The adaptive mesh refinement procedure enriches the unstructured mesh locally to more accurately resolve the vortical flow features. These capabilities are described in detail along with representative results which demonstrate several advantages of unstructured grid methods. The applicability of the unstructured grid methodology to steady and unsteady aerodynamic problems and directions for future work are discussed.
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
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.
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.
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 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.
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.
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.
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.
The development and application of the self-adaptive grid code, SAGE
NASA Astrophysics Data System (ADS)
Davies, Carol B.
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.
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.
Self-calibration method of two-dimensional grid plate
NASA Astrophysics Data System (ADS)
Ding, Guoqing; Chen, Xin; Wang, Lihua; Lei, Lihua; Li, Yuan
2011-12-01
A two-dimensional grid plate can offer an X-Y position standard where grids are aligned orthogonal to each other. It is important to ensure the positional accuracy of the grid plate when the grid plate is used to calibrate planar movement systems, such as vision measuring machines and scanning probe microscopes. Existing algorithms for self-calibration employ the discrete Fourier transform, which is complicated and has poor noise suppression capability. We have developed an algorithm that can achieve exact self-calibration for a two-dimensional grid plate using the least squares method when there is no random noise. In the presence of random noise, the algorithm still presents an excellent capability for noise suppression. As an extension of the classic three-location measurement, the algorithm can be applied to four- or five-location measurements, which reduce measurement uncertainties. The error propagation characteristic of the random errors has been investigated in the case of different measurement strategies. According to the simulation results, the mean error propagation ratios are less than 1 when the array size of the grid plate is less than 32×32. Finally, the influence of the scale errors of the planar movement system is discussed.
Adaptive wavelet collocation method simulations of Rayleigh-Taylor instability
NASA Astrophysics Data System (ADS)
Reckinger, S. J.; Livescu, D.; Vasilyev, O. V.
2010-12-01
Numerical simulations of single-mode, compressible Rayleigh-Taylor instability are performed using the adaptive wavelet collocation method (AWCM), which utilizes wavelets for dynamic grid adaptation. Due to the physics-based adaptivity and direct error control of the method, AWCM is ideal for resolving the wide range of scales present in the development of the instability. The problem is initialized consistent with the solutions from linear stability theory. Non-reflecting boundary conditions are applied to prevent the contamination of the instability growth by pressure waves created at the interface. AWCM is used to perform direct numerical simulations that match the early-time linear growth, the terminal bubble velocity and a reacceleration region.
Turbomachinery flow calculation on unstructured grids using finite element method
NASA Astrophysics Data System (ADS)
Koschel, W.; Vornberger, A.
An explicit finite-element scheme based on a two-step Taylor-Galerkin algorithm allows the solution of the Euler and Navier-Stokes equations on unstructured grids. Mesh generation methods for unstructured grids are described which lead to efficient flow calculations. Turbulent flow is calculated by using an algebraic turbulence model. To test the numerical accuracy, a laminar and turbulent flow over a flat plate and the supersonic flow in a corner has been calculated. For validation the method is applied to the simulation of the inviscid flow through a transonic turbine cascade and the viscous flow through a subsonic turbine cascade.
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
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.
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.
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.
A new procedure for dynamic adaption of three-dimensional unstructured grids
NASA Technical Reports Server (NTRS)
Biswas, Rupak; Strawn, Roger
1993-01-01
A new procedure is presented for the simultaneous coarsening and refinement of three-dimensional unstructured tetrahedral meshes. This algorithm allows for localized grid adaption that is used to capture aerodynamic flow features such as vortices and shock waves in helicopter flowfield simulations. The mesh-adaption algorithm is implemented in the C programming language and uses a data structure consisting of a series of dynamically-allocated linked lists. These lists allow the mesh connectivity to be rapidly reconstructed when individual mesh points are added and/or deleted. The algorithm allows the mesh to change in an anisotropic manner in order to efficiently resolve directional flow features. The procedure has been successfully implemented on a single processor of a Cray Y-MP computer. Two sample cases are presented involving three-dimensional transonic flow. Computed results show good agreement with conventional structured-grid solutions for the Euler equations.
Nested Cartesian grid method in incompressible viscous fluid flow
NASA Astrophysics Data System (ADS)
Peng, Yih-Ferng; Mittal, Rajat; Sau, Amalendu; Hwang, Robert R.
2010-09-01
In this work, the local grid refinement procedure is focused by using a nested Cartesian grid formulation. The method is developed for simulating unsteady viscous incompressible flows with complex immersed boundaries. A finite-volume formulation based on globally second-order accurate central-difference schemes is adopted here in conjunction with a two-step fractional-step procedure. The key aspects that needed to be considered in developing such a nested grid solver are proper imposition of interface conditions on the nested-block boundaries, and accurate discretization of the governing equations in cells that are with block-interface as a control-surface. The interpolation procedure adopted in the study allows systematic development of a discretization scheme that preserves global second-order spatial accuracy of the underlying solver, and as a result high efficiency/accuracy nested grid discretization method is developed. Herein the proposed nested grid method has been widely tested through effective simulation of four different classes of unsteady incompressible viscous flows, thereby demonstrating its performance in the solution of various complex flow-structure interactions. The numerical examples include a lid-driven cavity flow and Pearson vortex problems, flow past a circular cylinder symmetrically installed in a channel, flow past an elliptic cylinder at an angle of attack, and flow past two tandem circular cylinders of unequal diameters. For the numerical simulations of flows past bluff bodies an immersed boundary (IB) method has been implemented in which the solid object is represented by a distributed body force in the Navier-Stokes equations. The main advantages of the implemented immersed boundary method are that the simulations could be performed on a regular Cartesian grid and applied to multiple nested-block (Cartesian) structured grids without any difficulty. Through the numerical experiments the strength of the solver in effectively
Iso-deviant 2D gridding with efficient adaptive gridder for littoral environments (EAGLE)
NASA Astrophysics Data System (ADS)
Rike, Erik R.; Delbalzo, Donald R.
2005-09-01
Transmission loss (TL) computations in littoral areas require a dense spatial and azimuthal grid to achieve acceptable accuracy and detail. The computational cost of accurate predictions led to a new concept, OGRES (Objective Grid/Radials using Environmentally-sensitive Selection), which produces sparse, irregular acoustic grids, with controlled accuracy. Recent work to further increase accuracy and efficiency with better metrics and interpolation led to EAGLE (Efficient Adaptive Gridder for Littoral Environments). On each iteration, EAGLE produces grids with approximately constant spatial uncertainty (hence, iso-deviance), yielding predictions with ever-increasing resolution and accuracy. The EAGLE point-selection mechanism is tested using the predictive error metric and 2D synthetic data sets created from combinations of simple signal functions (e.g., polynomials, sines, cosines, exponentials), along with white and chromatic noise. The speed, efficiency, fidelity, and iso-deviance of EAGLE are determined for each combination of signal, noise, and interpolator. The results show significant efficiency enhancements compared to uniform grids of the same accuracy. [Work sponsored by NAVAIR.
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
Features of CPB: A Poisson-Boltzmann Solver that Uses an Adaptive Cartesian Grid
Harris, Robert C.; Mackoy, Travis
2014-01-01
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other PBE solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software. PMID:25430617
Features of CPB: a Poisson-Boltzmann solver that uses an adaptive Cartesian grid.
Fenley, Marcia O; Harris, Robert C; Mackoy, Travis; Boschitsch, Alexander H
2015-02-01
The capabilities of an adaptive Cartesian grid (ACG)-based Poisson-Boltzmann (PB) solver (CPB) are demonstrated. CPB solves various PB equations with an ACG, built from a hierarchical octree decomposition of the computational domain. This procedure decreases the number of points required, thereby reducing computational demands. Inside the molecule, CPB solves for the reaction-field component (ϕrf ) of the electrostatic potential (ϕ), eliminating the charge-induced singularities in ϕ. CPB can also use a least-squares reconstruction method to improve estimates of ϕ at the molecular surface. All surfaces, which include solvent excluded, Gaussians, and others, are created analytically, eliminating errors associated with triangulated surfaces. These features allow CPB to produce detailed surface maps of ϕ and compute polar solvation and binding free energies for large biomolecular assemblies, such as ribosomes and viruses, with reduced computational demands compared to other Poisson-Boltzmann equation solvers. The reader is referred to http://www.continuum-dynamics.com/solution-mm.html for how to obtain the CPB software. PMID:25430617
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.
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
NASA Astrophysics Data System (ADS)
Wu, Heng
2000-10-01
In this thesis, an a-posteriori error estimator is presented and employed for solving viscous incompressible flow problems. In an effort to detect local flow features, such as vortices and separation, and to resolve flow details precisely, a velocity angle error estimator e theta which is based on the spatial derivative of velocity direction fields is designed and constructed. The a-posteriori error estimator corresponds to the antisymmetric part of the deformation-rate-tensor, and it is sensitive to the second derivative of the velocity angle field. Rationality discussions reveal that the velocity angle error estimator is a curvature error estimator, and its value reflects the accuracy of streamline curves. It is also found that the velocity angle error estimator contains the nonlinear convective term of the Navier-Stokes equations, and it identifies and computes the direction difference when the convective acceleration direction and the flow velocity direction have a disparity. Through benchmarking computed variables with the analytic solution of Kovasznay flow or the finest grid of cavity flow, it is demonstrated that the velocity angle error estimator has a better performance than the strain error estimator. The benchmarking work also shows that the computed profile obtained by using etheta can achieve the best matching outcome with the true theta field, and that it is asymptotic to the true theta variation field, with a promise of fewer unknowns. Unstructured grids are adapted by employing local cell division as well as unrefinement of transition cells. Using element class and node class can efficiently construct a hierarchical data structure which provides cell and node inter-reference at each adaptive level. Employing element pointers and node pointers can dynamically maintain the connection of adjacent elements and adjacent nodes, and thus avoids time-consuming search processes. The adaptive scheme is applied to viscous incompressible flow at different
Adaptive grid artifact reduction in the frequency domain with spatial properties for x-ray images
NASA Astrophysics Data System (ADS)
Kim, Dong Sik; Lee, Sanggyun
2012-03-01
By applying band-rejection filters (BRFs) in the frequency domain, we can efficiently reduce the grid artifacts, which are caused by using the antiscatter grid in obtaining x-ray digital images. However, if the frequency component of the grid artifact is relatively close to that of the object, then simply applying a BRF may seriously distort the object and cause the ringing artifacts. Since the ringing artifacts are quite dependent on the shape of the object to be recovered in the spatial domain, the spatial property of the x-ray image should be considered in applying BRFs. In this paper, we propose an adaptive filtering scheme, which can cooperate such different properties in the spatial domain. In the spatial domain, we compare several approaches, such as the mangnitude, edge, and frequency-modulation (FM) model-based algorithms, to detect the ringing artifact or the grid artifact component. In order to perform a robust detection whether the ringing artifact is strong or not, we employ the FM model for the extracted signal, which corresponds to a specific grid artifact. A detection of the position for the ringing artifact is then conducted based on the slope detection algorithm, which is commonly used as an FM discriminator in the communication area. However, the detected position of the ringing artifact is not accurate. Hence, in order to obtain an accurate detection result, we combine the edge-based approach with the FM model approach. Numerical result for real x-ray images shows that applying BRFs in the frequency domain in conjunction with the spatial property of the ringing artifact can successfully remove the grid artifact, distorting the object less.
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.
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.
A new orientation-adaptive interpolation method.
Wang, Qing; Ward, Rabab Kreidieh
2007-04-01
We propose an isophote-oriented, orientation-adaptive interpolation method. The proposed method employs an interpolation kernel that adapts to the local orientation of isophotes, and the pixel values are obtained through an oriented, bilinear interpolation. We show that, by doing so, the curvature of the interpolated isophotes is reduced, and, thus, zigzagging artifacts are largely suppressed. Analysis and experiments show that images interpolated using the proposed method are visually pleasing and almost artifact free. PMID:17405424
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.
The Method of Adaptive Comparative Judgement
ERIC Educational Resources Information Center
Pollitt, Alastair
2012-01-01
Adaptive Comparative Judgement (ACJ) is a modification of Thurstone's method of comparative judgement that exploits the power of adaptivity, but in scoring rather than testing. Professional judgement by teachers replaces the marking of tests; a judge is asked to compare the work of two students and simply to decide which of them is the better.…
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
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
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.
Multi-off-grid methods in multi-step integration of ordinary differential equations
NASA Technical Reports Server (NTRS)
Beaudet, P. R.
1974-01-01
Description of methods of solving first- and second-order systems of differential equations in which all derivatives are evaluated at off-grid locations in order to circumvent the Dahlquist stability limitation on the order of on-grid methods. The proposed multi-off-grid methods require off-grid state predictors for the evaluation of the n derivatives at each step. Progressing forward in time, the off-grid states are predicted using a linear combination of back on-grid state values and off-grid derivative evaluations. A comparison is made between the proposed multi-off-grid methods and the corresponding Adams and Cowell on-grid integration techniques in integrating systems of ordinary differential equations, showing a significant reduction in the error at larger step sizes in the case of the multi-off-grid integrator.
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.
An automated method for gridding in microarray images.
Giannakeas, Nikolaos; Fotiadis, Dimitrios I; Politou, Anastasia S
2006-01-01
Microarray technology is a powerful tool for analyzing the expression of a large number of genes in parallel. A typical microarray image consists of a few thousands of spots which determine the level of gene expression in the sample. In this paper we propose a method which automatically addresses each spot area in the image. Initially, a preliminary segmentation of the image is produced using a template matching algorithm. Next, grid and spot finding are realized. The position of non-expressed spots is located and finally a Voronoi diagram is employed to fit the grid on the image. Our method has been evaluated in a set of five images consisting of 45960 spots, from the Stanford microarray database and the reported accuracy for spot detection was 93% PMID:17946343
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
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
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.
Corey, I R; Johnson, J R; Vetter, J S
2002-02-25
This study presents a technique that can significantly improve the performance of a distributed application by allowing the application to locally adapt to architectural characteristics of distinct resources in a distributed system. Application performance is sensitive to application parameter--system architecture pairings. In a distributed or Grid enabled applciation, a single parameter configuration for the whole application will not always be optimal for every participating resource. In particular, some configurations can significantly degrade performance. Furthermore, the behavior of a system may change during the course of the run. The technique described here provides an automated mechanism for run-time adaptation of application parameters to the local system architecture. Using a simulation of a Monte Carlo physics code, the authors demonstrate that this technique can achieve speedups of 18%-37% on individual resources in a distributed environment.
A Fully Automatic Method for Gridding Bright Field Images of Bead-Based Microarrays.
Datta, Abhik; Wai-Kin Kong, Adams; Yow, Kin-Choong
2016-07-01
In this paper, a fully automatic method for gridding bright field images of bead-based microarrays is proposed. There have been numerous techniques developed for gridding fluorescence images of traditional spotted microarrays but to our best knowledge, no algorithm has yet been developed for gridding bright field images of bead-based microarrays. The proposed gridding method is designed for automatic quality control during fabrication and assembly of bead-based microarrays. The method begins by estimating the grid parameters using an evolutionary algorithm. This is followed by a grid-fitting step that rigidly aligns an ideal grid with the image. Finally, a grid refinement step deforms the ideal grid to better fit the image. The grid fitting and refinement are performed locally and the final grid is a nonlinear (piecewise affine) grid. To deal with extreme corruptions in the image, the initial grid parameter estimation and grid-fitting steps employ robust search techniques. The proposed method does not have any free parameters that need tuning. The method is capable of identifying the grid structure even in the presence of extreme amounts of artifacts and distortions. Evaluation results on a variety of images are presented. PMID:26011899
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Wagner, B.; Kileng, B.; Alice Collaboration
2014-06-01
The Nordic Tier-1 centre for LHC is distributed over several computing centres. It uses ARC as the internal computing grid middleware. ALICE uses its own grid middleware AliEn to distribute jobs and the necessary software application stack. To make use of most of the AliEn infrastructure and software deployment methods for running ALICE grid jobs on ARC, we are investigating different possible virtualisation technologies. For this a testbed and possible framework for bridging different middleware systems is under development. It allows us to test a variety of virtualisation methods and software deployment technologies in the form of different virtual machines.
Application of the multigrid method to grid generation
NASA Technical Reports Server (NTRS)
Ohring, S.
1980-01-01
The multigrid method (MGM), used to numerically solve the pair of nonlinear elliptic equations commonly used to generate two dimensional boundary-fitted coordinate systems is discussed. Two different geometries are considered: one involving a coordinate system fitted about a circle and the other selected for an impinging jet flow problem. Two different relaxation schemes are tried: one is successive point overrelaxation and the other is a four-color scheme vectorizeable to take advantage of a parallel processor computer for greater computational speed. Results using MGM are compared with those using SOR (doing successive overrelaxations with the corresponding relaxation scheme on the fine grid only). It is found that MGM becomes significantly more effective than SOR as more accuracy is demanded and as more corrective grids, or more grid points, are used. For the accuracy required, it is found that MGM is two to three times faster than SOR in computing time. With the four-color relaxation scheme as applied to the impinging jet problem, the advantage of MGM over SOR is not as great. This may be due to the effect of a poor initial guess on MGM for this problem.
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
NASA Astrophysics Data System (ADS)
Son, Sang-Kil; Chu, Shih-I.
2008-05-01
We introduce a new computational method on unstructured grids in the three-dimensional (3D) spaces to investigate the electronic structure of polyatomic molecules. The Voronoi-cell finite difference (VFD) method realizes a simple discrete Laplacian operator on unstructured grids based on Voronoi cells and their natural neighbors. The feature of unstructured grids enables us to choose intuitive pictures for an optimal molecular grid system. The new VFD method achieves highly adaptability by the Voronoi-cell diagram and yet simplicity by the finite difference scheme. It has no limitation in local refinement of grids in the vicinity of nuclear positions and provides an explicit expression at each grid without any integration. This method augmented by unstructured molecular grids is suitable for solving the Schr"odinger equation with the realistic 3D Coulomb potentials regardless of symmetry of molecules. For numerical examples, we test accuracies for electronic structures of one-electron polyatomic systems: linear H2^+ and triangular H3^++. We also extend VFD to the density functional theory (DFT) for many-electron polyatomic molecules.
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.
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.
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.
On the applications of algebraic grid generation methods based on transfinite interpolation
NASA Technical Reports Server (NTRS)
Nguyen, Hung Lee
1989-01-01
Algebraic grid generation methods based on transfinite interpolation called the two-boundary and four-boundary methods are applied for generating grids with highly complex boundaries. These methods yield grid point distributions that allow for accurate application to regions of sharp gradients in the physical domain or time-dependent problems with small length scale phenomena. Algebraic grids are derived using the two-boundary and four-boundary methods for applications in both two- and three-dimensional domains. Grids are developed for distinctly different geometrical problems and the two-boundary and four-boundary methods are demonstrated to be applicable to a wide class of geometries.
The Managerial Grid as a Predictor of Conflict Resolution Method and Managerial Effectiveness
ERIC Educational Resources Information Center
Bernardin, H. John; Alvares, Kenneth M.
1976-01-01
Hypotheses based on Blake and Mouton's managerial grid were tested and were not supported by the data. Results indicated that grid placement was a poor predictor of either perceived managerial effectiveness or conflict resolution methods employed. (Author)
On the use of a high order overlapping grid method for coupling in CFD/CAA
NASA Astrophysics Data System (ADS)
Desquesnes, G.; Terracol, M.; Manoha, E.; Sagaut, P.
2006-12-01
This paper presents a theoretical analysis and two applications of a high-order overlapping grid method for coupling Cartesian and curvilinear grids, developed in order to simulate aerodynamic noise. First, the overlapping grid method based on Lagrange interpolating polynomials is described and a theoretical analysis of the interpolation operator is then carried out. It shows that the interpolation generates spurious modes that depend on the wavenumbers of the signal. Besides it also gives the optimal conditions in which interpolation can be applied. Then an application to the simulation of the aeroacoustic noise generated by the vortex shedding behind a cylinder is presented. During this simulation, it appears that interpolation can create some spurious acoustic modes in regions where hydrodynamic fluctuations are significant, as predicted by the theoretical analysis. It is shown that these spurious modes disappear when a refined Cartesian grid is used (26 points per wavelength of the vortex shedding were found to be adequate in this study). At last, the simulation of the aerodynamic noise of a three element high-lift wing profile has then been carried out. For this application, the main acoustic source at the slat trailing edge is represented analytically. The propagation of the generated acoustic wave is simulated with a mean flow at rest and with a steady turbulent mean flow computed by RANS. The first application allows us to assess the method by comparing the results to a reference solution. The second one shows that the influence of a non-uniform mean flow on the directivity of an acoustic source can be observed in complex geometries. This application therefore shows that the proposed coupling method is well adapted to complex geometries that are usually met in industrial applications.
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.
PDEs on moving surfaces via the closest point method and a modified grid based particle method
NASA Astrophysics Data System (ADS)
Petras, A.; Ruuth, S. J.
2016-05-01
Partial differential equations (PDEs) on surfaces arise in a wide range of applications. The closest point method (Ruuth and Merriman (2008) [20]) is a recent embedding method that has been used to solve a variety of PDEs on smooth surfaces using a closest point representation of the surface and standard Cartesian grid methods in the embedding space. The original closest point method (CPM) was designed for problems posed on static surfaces, however the solution of PDEs on moving surfaces is of considerable interest as well. Here we propose solving PDEs on moving surfaces using a combination of the CPM and a modification of the grid based particle method (Leung and Zhao (2009) [12]). The grid based particle method (GBPM) represents and tracks surfaces using meshless particles and an Eulerian reference grid. Our modification of the GBPM introduces a reconstruction step into the original method to ensure that all the grid points within a computational tube surrounding the surface are active. We present a number of examples to illustrate the numerical convergence properties of our combined method. Experiments for advection-diffusion equations that are strongly coupled to the velocity of the surface are also presented.
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
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.
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.
Application of Open Loop H-Adaptation to an Unstructured Grid Tidal Flat Model
NASA Astrophysics Data System (ADS)
Cowles, G. W.
2008-12-01
The complex topology of tidal flats presents a challenge to coastal ocean models. Recently, several models have been developed employing unstructured grids, which can provide the flexibility in mesh resolution required to resolve the complex bathymetry and coastline. However, the distribution of element size in the initial mesh can be somewhat arbitrary, and is in general the product of the operator tailoring the resolution to the underlying bathymetry and regions of interest. In this work, the flow solution from an idealized tidal flat application is used to drive an open loop h-adaptation of the mesh. The model used for this work is the Finite Volume Coastal Ocean Model (FVCOM), an open source, terrain following model. A background length scale distribution derived from model output is used to generate a new initial mesh for the model run, thus defining an iteration of the procedure. Several metrics for computing the background length scale will be examined. These include direct estimation of spatial discretization error using Richardson's extrapolation from a sequence of meshes as well as heuristics derived from gradients in the primitive variables. Examination of grid independence, computational efficiency, and performance of the scheme for idealized tidal flats with inclusion of morphodynamics will be discussed.
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)
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 New Adaptive Image Denoising Method
NASA Astrophysics Data System (ADS)
Biswas, Mantosh; Om, Hari
2016-03-01
In this paper, a new adaptive image denoising method is proposed that follows the soft-thresholding technique. In our method, a new threshold function is also proposed, which is determined by taking the various combinations of noise level, noise-free signal variance, subband size, and decomposition level. It is simple and adaptive as it depends on the data-driven parameters estimation in each subband. The state-of-the-art denoising methods viz. VisuShrink, SureShrink, BayesShrink, WIDNTF and IDTVWT are not able to modify the coefficients in an efficient manner to provide the good quality of image. Our method removes the noise from the noisy image significantly and provides better visual quality of an image.
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.
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
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.
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.
The gridding method for image reconstruction by Fourier transformation
Schomberg, H.; Timmer, J.
1995-09-01
This paper explores a computational method for reconstructing an n-dimensional signal f from a sampled version of its Fourier transform {cflx f}. The method involves a window function {cflx w} and proceeds in three steps. First, the convolution {cflx g} = {cflx w} * {cflx f} is computed numerically on a Cartesian grid, using the available samples of {cflx f}. Then, g = wf is computed via the inverse discrete Fourier transform, and finally f is obtained as g/w. Due to the smoothing effect of the convolution, evaluating {cflx w} * {cflx f} is much less error prone than merely interpolating {cflx f}. The method was originally devised for image reconstruction in radio astronomy, but is actually applicable to a broad range of reconstructive imaging methods, including magnetic resonance imaging and computed tomography. In particular, it provides a fast and accurate alternative to the filtered backprojection. The basic method has several variants with other applications, such as the equidistant resampling of arbitrarily sampled signals or the fast computation of the Radon (Hough) transform.
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.
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.
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.
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.
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
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.
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.
A high-resolution Godunov method for compressible multi-material flow on overlapping grids
NASA Astrophysics Data System (ADS)
Banks, J. W.; Schwendeman, D. W.; Kapila, A. K.; Henshaw, W. D.
2007-04-01
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 the 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 a 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.
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.
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.
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.
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 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.
Adaptive characterization method for desktop color printers
NASA Astrophysics Data System (ADS)
Shen, Hui-Liang; Zheng, Zhi-Huan; Jin, Chong-Chao; Du, Xin; Shao, Si-Jie; Xin, John H.
2013-04-01
With the rapid development of multispectral imaging technique, it is desired that the spectral color can be accurately reproduced using desktop color printers. However, due to the specific spectral gamuts determined by printer inks, it is almost impossible to exactly replicate the reflectance spectra in other media. In addition, as ink densities can not be individually controlled, desktop printers can only be regarded as red-green-blue devices, making physical models unfeasible. We propose a locally adaptive method, which consists of both forward and inverse models, for desktop printer characterization. In the forward model, we establish the adaptive transform between control values and reflectance spectrum on individual cellular subsets by using weighted polynomial regression. In the inverse model, we first determine the candidate space of the control values based on global inverse regression and then compute the optimal control values by minimizing the color difference between the actual spectrum and the predicted spectrum via forward transform. Experimental results show that the proposed method can reproduce colors accurately for different media under multiple illuminants.
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 Technical Reports Server (NTRS)
Golik, W. L.
1996-01-01
A robust solver for the elliptic grid generation equations is sought via a numerical study. The system of PDEs is discretized with finite differences, and multigrid methods are applied to the resulting nonlinear algebraic equations. Multigrid iterations are compared with respect to the robustness and efficiency. Different smoothers are tried to improve the convergence of iterations. The methods are applied to four 2D grid generation problems over a wide range of grid distortions. The results of the study help to select smoothing schemes and the overall multigrid procedures for elliptic grid generation.
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.
NASA Technical Reports Server (NTRS)
Slater, John W.; Liou, Meng-Sing; Hindman, Richard G.
1994-01-01
An approach is presented for the generation of two-dimensional, structured, dynamic grids. The grid motion may be due to the motion of the boundaries of the computational domain or to the adaptation of the grid to the transient, physical solution. A time-dependent grid is computed through the time integration of the grid speeds which are computed from a system of grid speed equations. The grid speed equations are derived from the time-differentiation of the grid equations so as to ensure that the dynamic grid maintains the desired qualities of the static grid. The grid equations are the Euler-Lagrange equations derived from a variational statement for the grid. The dynamic grid method is demonstrated for a model problem involving boundary motion, an inviscid flow in a converging-diverging nozzle during startup, and a viscous flow over a flat plate with an impinging shock wave. It is shown that the approach is more accurate for transient flows than an approach in which the grid speeds are computed using a finite difference with respect to time of the grid. However, the approach requires significantly more computational effort.
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.
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
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.
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.
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.
NASA Astrophysics Data System (ADS)
Lin, Wan-Feng; Chow, Chi-Wai; Yeh, Chien-Hung
2015-03-01
Orthogonal frequency division multiplexing (OFDM) is a promising candidate for light emitting diode (LED)-based optical wireless communication (OWC); however, precise channel estimation is required for synchronization and equalization. In this work, we study and discover that the channel response of the white-lightLED-based OWC was smooth and stable. Hence we propose and demonstrate using a specific and adaptive arrangement of grid-type pilot scheme to estimate the LED OWC channel response. Experimental results show that our scheme can achieve better transmission performance and with some transmission capacity enhancement when compared with the method using training-symbol scheme (also called block-type pilot scheme).
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 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
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.
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.
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
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.
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.
An adaptive SPH method for strong shocks
NASA Astrophysics Data System (ADS)
Sigalotti, Leonardo Di G.; López, Hender; Trujillo, Leonardo
2009-09-01
We propose an alternative SPH scheme to usual SPH Godunov-type methods for simulating supersonic compressible flows with sharp discontinuities. The method relies on an adaptive density kernel estimation (ADKE) algorithm, which allows the width of the kernel interpolant to vary locally in space and time so that the minimum necessary smoothing is applied in regions of low density. We have performed a von Neumann stability analysis of the SPH equations for an ideal gas and derived the corresponding dispersion relation in terms of the local width of the kernel. Solution of the dispersion relation in the short wavelength limit shows that stability is achieved for a wide range of the ADKE parameters. Application of the method to high Mach number shocks confirms the predictions of the linear analysis. Examples of the resolving power of the method are given for a set of difficult problems, involving the collision of two strong shocks, the strong shock-tube test, and the interaction of two blast waves.
Adaptive wavelet methods - Matrix-vector multiplication
NASA Astrophysics Data System (ADS)
Černá, Dana; Finěk, Václav
2012-12-01
The design of most adaptive wavelet methods for elliptic partial differential equations follows a general concept proposed by A. Cohen, W. Dahmen and R. DeVore in [3, 4]. The essential steps are: transformation of the variational formulation into the well-conditioned infinite-dimensional l2 problem, finding of the convergent iteration process for the l2 problem and finally derivation of its finite dimensional version which works with an inexact right hand side and approximate matrix-vector multiplications. In our contribution, we shortly review all these parts and wemainly pay attention to approximate matrix-vector multiplications. Effective approximation of matrix-vector multiplications is enabled by an off-diagonal decay of entries of the wavelet stiffness matrix. We propose here a new approach which better utilize actual decay of matrix entries.
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.
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.
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.
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.
Imbalance-correction grid-refinement method for lattice Boltzmann flow simulations
NASA Astrophysics Data System (ADS)
Kuwata, Y.; Suga, K.
2016-04-01
To enhance the accuracy and applicability of the zonal grid refinement method for the lattice Boltzmann method, a new method which minimizes the interface imbalances of mass and momentum is developed. This method introduces a correction step for the macroscopic flow variables such as the fluid density and velocity to remove their interface discontinuity. To demonstrate and evaluate the presently developed imbalance correction grid refinement method, large eddy simulations of turbulent channel and square cylinder flows are carried out. By changing the grid arrangement in the turbulent channel flows, it is confirmed that the present method reduces the sensitivity to the location of the grid refinement interface and minimizes the unphysically discontinuous profiles satisfactorily. Furthermore, the present method considerably improves mass conservation of the system, which is particularly important for long time periodical flow simulations. It is also confirmed that the present method generally improves the prediction performance of the square cylinder flows.
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.
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.
NASA Technical Reports Server (NTRS)
Moitra, Anutosh
1989-01-01
A fast and versatile procedure for algebraically generating boundary conforming computational grids for use with finite-volume Euler flow solvers is presented. A semi-analytic homotopic procedure is used to generate the grids. Grids generated in two-dimensional planes are stacked to produce quasi-three-dimensional grid systems. The body surface and outer boundary are described in terms of surface parameters. An interpolation scheme is used to blend between the body surface and the outer boundary in order to determine the field points. The method, albeit developed for analytically generated body geometries is equally applicable to other classes of geometries. The method can be used for both internal and external flow configurations, the only constraint being that the body geometries be specified in two-dimensional cross-sections stationed along the longitudinal axis of the configuration. Techniques for controlling various grid parameters, e.g., clustering and orthogonality are described. Techniques for treating problems arising in algebraic grid generation for geometries with sharp corners are addressed. A set of representative grid systems generated by this method is included. Results of flow computations using these grids are presented for validation of the effectiveness of the method.
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…
The Managerial Grid as a Predictor of Conflict Resolution Method and Managerial Effectiveness.
ERIC Educational Resources Information Center
Bernardin, H. John; Alvares, Kenneth
The relationship between ratings of leadership effectiveness and conflict resolution methods was investigated within a large midwestern manufacturing firm. Hypotheses based on Blake and Mouton's managerial grid were tested and were not supported within these data. Results indicated that grid placement was a poor predictor of either perceived…
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.
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)
Heineken, Wolfram; Kunik, Matthias
2008-05-01
A finite volume method with grid adaption is applied to two hyperbolic problems: the ultra-relativistic Euler equations, and a scalar conservation law. Both problems are considered in two space dimensions and share the common feature of moving shock waves. In contrast to the classical Euler equations, the derivation of appropriate initial conditions for the ultra-relativistic Euler equations is a non-trivial problem that is solved using one-dimensional shock conditions and the Lorentz invariance of the system. The discretization of both problems is based on a finite volume method of second order in both space and time on a triangular grid. We introduce a variant of the min-mod limiter that avoids unphysical states for the Euler system. The grid is adapted during the integration process. The frequency of grid adaption is controlled automatically in order to guarantee a fine resolution of the moving shock fronts. We introduce the concept of "width refinement" which enlarges the width of strongly refined regions around the shock fronts; the optimal width is found by a numerical study. As a result we are able to improve efficiency by decreasing the number of adaption steps. The performance of the finite volume scheme is compared with several lower order methods.
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.
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.
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.
Grid generation research at OSU
NASA Technical Reports Server (NTRS)
Nakamura, S.
1992-01-01
In the last two years, effort was concentrated on: (1) surface modeling; (2) surface grid generation; and (3) 3-D flow space grid generation. The surface modeling shares the same objectives as the surface modeling in computer aided design (CAD), so software available in CAD can in principle be used for solid modeling. Unfortunately, however, the CAD software cannot be easily used in practice for grid generation purposes, because they are not designed to provide appropriate data base for grid generation. Therefore, we started developing a generalized surface modeling software from scratch, that provides the data base for the surface grid generation. Generating surface grid is an important step in generating a 3-D space for flow space. To generate a surface grid on a given surface representation, we developed a unique algorithm that works on any non-smooth surfaces. Once the surface grid is generated, a 3-D space can be generated. For this purpose, we also developed a new algorithm, which is a hybrid of the hyperbolic and the elliptic grid generation methods. With this hybrid method, orthogonality of the grid near the solid boundary can be easily achieved without introducing empirical fudge factors. Work to develop 2-D and 3-D grids for turbomachinery blade geometries was performed, and as an extension of this research we are planning to develop an adaptive grid procedure with an interactive grid environment.
Application of a multi-level grid method to transonic flow calculations
NASA Technical Reports Server (NTRS)
South, J. C., Jr.; Brandt, A.
1976-01-01
A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.
NASA Astrophysics Data System (ADS)
Roache, P. J.
1982-08-01
A computational effort to develop computer codes for rapidly and accurately modeling the electric fields within laser cavities is described. Semidirect/marching methods are used both for the generation of two dimensional boundary fitted grids using the elliptic generating equation approach, and for the solution of electric field problems in those coordinate systems. The efficiency of the semidirect/marching methods makes possible interactive design of the laser electrodes using a modest computer. Also described are techniques for high order accuracy, a method for precise grid control at interior points, and applications to the elliptic grid generation problem of computer symbolic manipulation.
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)
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.
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.
NASA Astrophysics Data System (ADS)
Han, Jiafu; Li, Hongsheng; Ma, Liuqing
2009-09-01
High-quality spatially referenced population information plays an important role in many social-demographic fields. This paper focuses on grid transformation method for population data by combining geographic factors and simulated township boundary adjustment. Given the location, area and census data of each town-level administrative unit and national base map (1:25000) in China, 1km*1km gridded population data can be acquired after interpolation and several adjustments. Besides the adjustment based on geographical factors like topography, transport (roads), rivers and settlements, a new adjustment method based on township boundary simulation and total population of the town is proposed in this paper. The Voronoi polygon of town point is generated and rasterized into 1km*1km grids. Considering the area of each township and boundary line of the corresponding country, the collapse or expansion process of the rasterized Voronoi polygon is conducted pixel by pixel to minimize the differences between total count of grids with same township ID and the announced area of the corresponding township iteratively. After boundary simulation, gridded population data is adjusted based on town-level census data. The study indicated that the proposed method can acquire fine-grained grid population surface. It is demonstrated as an effective method to transform census population data into regular grids.
NASA Astrophysics Data System (ADS)
Han, Jiafu; Li, Hongsheng; Ma, Liuqing
2010-11-01
High-quality spatially referenced population information plays an important role in many social-demographic fields. This paper focuses on grid transformation method for population data by combining geographic factors and simulated township boundary adjustment. Given the location, area and census data of each town-level administrative unit and national base map (1:25000) in China, 1km*1km gridded population data can be acquired after interpolation and several adjustments. Besides the adjustment based on geographical factors like topography, transport (roads), rivers and settlements, a new adjustment method based on township boundary simulation and total population of the town is proposed in this paper. The Voronoi polygon of town point is generated and rasterized into 1km*1km grids. Considering the area of each township and boundary line of the corresponding country, the collapse or expansion process of the rasterized Voronoi polygon is conducted pixel by pixel to minimize the differences between total count of grids with same township ID and the announced area of the corresponding township iteratively. After boundary simulation, gridded population data is adjusted based on town-level census data. The study indicated that the proposed method can acquire fine-grained grid population surface. It is demonstrated as an effective method to transform census population data into regular grids.
The Stagger-grid: A grid of 3D stellar atmosphere models. I. Methods and general properties
NASA Astrophysics Data System (ADS)
Magic, Z.; Collet, R.; Asplund, M.; Trampedach, R.; Hayek, W.; Chiavassa, A.; Stein, R. F.; Nordlund, Å.
2013-09-01
Aims: We present the Stagger-grid, a comprehensive grid of time-dependent, three-dimensional (3D), hydrodynamic model atmospheres for late-type stars with realistic treatment of radiative transfer, covering a wide range in stellar parameters. This grid of 3D models is intended for various applications besides studies of stellar convection and atmospheres per se, including stellar parameter determination, stellar spectroscopy and abundance analysis, asteroseismology, calibration of stellar evolution models, interferometry, and extrasolar planet search. In this introductory paper, we describe the methods we applied for the computation of the grid and discuss the general properties of the 3D models as well as of their temporal and spatial averages (here denoted ⟨3D⟩ models). Methods: All our models were generated with the Stagger-code, using realistic input physics for the equation of state (EOS) and for continuous and line opacities. Our ~ 220 grid models range in effective temperature, Teff, from 4000 to 7000 K in steps of 500 K, in surface gravity, log g, from 1.5 to 5.0 in steps of 0.5 dex, and metallicity, [Fe/H], from - 4.0 to + 0.5 in steps of 0.5 and 1.0 dex. Results: We find a tight scaling relation between the vertical velocity and the surface entropy jump, which itself correlates with the constant entropy value of the adiabatic convection zone. The range in intensity contrast is enhanced at lower metallicity. The granule size correlates closely with the pressure scale height sampled at the depth of maximum velocity. We compare the ⟨3D⟩ models with currently widely applied one-dimensional (1D) atmosphere models, as well as with theoretical 1D hydrostatic models generated with the same EOS and opacity tables as the 3D models, in order to isolate the effects of using self-consistent and hydrodynamic modeling of convection, rather than the classical mixing length theory approach. For the first time, we are able to quantify systematically over a broad
An iterative KP1 method for solving the transport equation in 3D domains on unstructured grids
NASA Astrophysics Data System (ADS)
Kokonkov, N. I.; Nikolaeva, O. V.
2015-10-01
A two-step iterative KP1 method for solving systems of grid equations that approximate the integro-differential transport equation in 3D domains on unstructured grids using nodal SN methods is described. Results of testing the efficiency of the proposed method in solving benchmark problems of reactor protection on tetrahedral grids are presented.
Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses
NASA Technical Reports Server (NTRS)
Batina, John T.; Lee, Elizabeth M.; Kleb, William L.; Rausch, Russ D.
1991-01-01
The current status of unstructured grid methods development in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for unsteady aerodynamic and aeroelastic analyses. The flow solvers are highlighted which were developed for the solution of the unsteady Euler equations and selected results are given which show various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy.
Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses
NASA Technical Reports Server (NTRS)
Batina, John T.; Lee, Elizabeth M.; Kleb, William L.; Rausch, Russ D.
1992-01-01
The current status of unstructured grid methods developed in the Unsteady Aerodynamics Branch at NASA Langley Research Center is described. These methods are being developed for unsteady aerodynamic and aeroelastic analyses. Flow solvers that have been developed for the solution of unsteady Euler equations are highlighted. The results demonstrate two and three dimensional applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy.
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.
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.
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.
Efficient 3D Acoustic Numerical modeling in the Logarithmic-grid using the Expanding Domain Method
NASA Astrophysics Data System (ADS)
Hong, B. R.; Chung, W.; Ko, H.; Bae, H. S.
2015-12-01
In the numerical modeling of seismic wave propagation by the use of a discrete computing domain, dispersion analysis is preceded by the determination of the spatial grid spacings in order to ensure accurate modeling results. Grid spacing is a function of wavelength, and the wavelength depends on the minimum velocity and maximum source frequency. Therefore, as the frequency increases, the number of grids increase and this leads to computational overburden. In order to reduce the computing complexity, coordinate transformation techniques such as Riemannian coordinates and logarithmic grid sets are proposed. Riemannian wave-field extrapolation is a way to reformulate the wave-field by expressing it in Riemannian coordinates. In the logarithmic grid, grid spacing changes logarithmically, so this enables us to reduce the number of grids compared to a conventional grid set. Furthermore, this could completely remove boundary reflections by extending the model dimensions. However, numerical modeling in the logarithmic grid is still inefficient because it is performed for whole model at every individual time step. In this study we applied the expanding domain method to the logarithmic modeling in order to improve computational efficiency. This method, based on amplitude comparison, excludes computations for zero wave-fields by considering a non-zero domain boundary. Numerical examples demonstrated that our new modeling method enhances computational efficiency maintaining accuracy compared with conventional modeling methods. In wider and higher-order dimensions, particularly, the efficiency of our modeling method increased. Our new modeling technique could also be applied to the generation of underwater target echo signals requiring high frequency analysis.
NASA Astrophysics Data System (ADS)
Gotovac, Hrvoje; Srzic, Veljko
2014-05-01
Contaminant transport in natural aquifers is a complex, multiscale process that is frequently studied using different Eulerian, Lagrangian and hybrid numerical methods. Conservative solute transport is typically modeled using the advection-dispersion equation (ADE). Despite the large number of available numerical methods that have been developed to solve it, the accurate numerical solution of the ADE still presents formidable challenges. In particular, current numerical solutions of multidimensional advection-dominated transport in non-uniform velocity fields are affected by one or all of the following problems: numerical dispersion that introduces artificial mixing and dilution, grid orientation effects, unresolved spatial and temporal scales and unphysical numerical oscillations (e.g., Herrera et al, 2009; Bosso et al., 2012). In this work we will present Eulerian Lagrangian Adaptive Fup Collocation Method (ELAFCM) based on Fup basis functions and collocation approach for spatial approximation and explicit stabilized Runge-Kutta-Chebyshev temporal integration (public domain routine SERK2) which is especially well suited for stiff parabolic problems. Spatial adaptive strategy is based on Fup basis functions which are closely related to the wavelets and splines so that they are also compactly supported basis functions; they exactly describe algebraic polynomials and enable a multiresolution adaptive analysis (MRA). MRA is here performed via Fup Collocation Transform (FCT) so that at each time step concentration solution is decomposed using only a few significant Fup basis functions on adaptive collocation grid with appropriate scales (frequencies) and locations, a desired level of accuracy and a near minimum computational cost. FCT adds more collocations points and higher resolution levels only in sensitive zones with sharp concentration gradients, fronts and/or narrow transition zones. According to the our recent achievements there is no need for solving the large
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
Surface warpage measurement of diamond grid disk by shadow Moiré method
NASA Astrophysics Data System (ADS)
Chen, Terry Yuan-Fang; Chen, Jian-Shiang
2011-12-01
Diamond grid disk dresser is frequently employed to remove the accumulated debris lest the polishing surface glazes. The surface warpage of diamond grid disk must be small enough to assure the flatness of polished wafers during chemical mechanical planarization process. In this study, phase-shifted shadow moiré method was employed to measure the surface warpage of diamond grid disks. To eliminate erroneous bright or black spots caused by the diamond grids, a novel method is proposed by selecting proper threshold values from the addition of four phase-shifted images, and from the grey-level difference between the addition of phases 0 and π images and the addition of phases π/2 and 3π/2 images. Test of the proposed method on real specimens show that the erroneous bright and black spots can be effectively identified and patched. Thereafter the phase can be unwrapped successfully to obtain the surface profile and thus the warpage of specimens.
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.
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.
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.
Three-dimensional unstructured grid method applied to turbomachinery
NASA Technical Reports Server (NTRS)
Kwon, Oh Joon; Hah, Chunill
1993-01-01
This work has three objectives: to develop a three-dimensional flow solver based on unstructured tetrahedral meshes for turbomachinery flows; to validate the solver through comparisons with experimental data; and to apply the solver for better understanding of the flow through turbomachinery geometries and design improvement. The work followed three different approaches: an existing external flow solver/grid generator (USM3D/VGRID) was extensively modified for internal flows; a three-dimensional, finite-volume solver based on Roe's flux-difference splitting and explicit Runge-Kutta time stepping; and three-dimensional unstructured tetrahedral mesh generation using an advancing-front technique. A discussion of these topics is presented in viewgraph form.
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.
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
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.
NASA Astrophysics Data System (ADS)
Zhang, H.-L.; Röttgermann, A.; Wagner, S.
1995-01-01
The Field Panel Method (FPM) with grid stretching technique, presented in this paper, was developed for solving transonic full potential flow around arbitrary airfoils at incidence. In this method, the total potential values are represented by boundary integrals together with a volume integral. The volume integral domain includes both inside and finite outside of the configuration and can be discretisized in a Cartesian grid which may penetrate into the configuration surface. Thus, we avoid the very difficult task of generating body-fitted grids around complex configurations. The boundary potential values are obtained by implementing a standard panel method (symmetrical singularity model), whereas the field potential values are estimated by solving the full potential equation (using AF3 scheme in a Cartesian grid) with approximate inner and proper outer boundary conditions. Furthermore, the grid stretching technique has been utilized that allows to capture the shock waves in a much better quality. It is also shown that both field grid and panel distribution have to be stretched at the same time. Results for transonic potential flows about NACA0012 and RAE2822 airfoils at different Mach numbers and incidences are obtained and compared with other numerical solutions. Great improvement in shock wave quality was achieved by using the present method.
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…
QUEST - A Bayesian adaptive psychometric method
NASA Technical Reports Server (NTRS)
Watson, A. B.; Pelli, D. G.
1983-01-01
An adaptive psychometric procedure that places each trial at the current most probable Bayesian estimate of threshold is described. The procedure takes advantage of the common finding that the human psychometric function is invariant in form when expressed as a function of log intensity. The procedure is simple, fast, and efficient, and may be easily implemented on any computer.
Adaptive method of realizing natural gradient learning for multilayer perceptrons.
Amari, S; Park, H; Fukumizu, K
2000-06-01
The natural gradient learning method is known to have ideal performances for on-line training of multilayer perceptrons. It avoids plateaus, which give rise to slow convergence of the backpropagation method. It is Fisher efficient, whereas the conventional method is not. However, for implementing the method, it is necessary to calculate the Fisher information matrix and its inverse, which is practically very difficult. This article proposes an adaptive method of directly obtaining the inverse of the Fisher information matrix. It generalizes the adaptive Gauss-Newton algorithms and provides a solid theoretical justification of them. Simulations show that the proposed adaptive method works very well for realizing natural gradient learning. PMID:10935719
NASA Astrophysics Data System (ADS)
Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.
2009-04-01
A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.
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.
An adaptive finite element method for convective heat transfer with variable fluid properties
NASA Astrophysics Data System (ADS)
Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois
1993-07-01
This paper presents an adaptive finite element method based on remeshing to solve incompressible viscous flow problems for which fluid properties present a strong temperature dependence. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Two general purpose error estimators, that take into account fluid properties variations, are presented. The methodology is applied to a problem of practical interest: the thermal convection of corn syrup in an enclosure with localized heating. Predictions are in good agreement with experimental measurements. The method leads to improved accuracy and reliability of finite element predictions.
Reduced-rank approximations to the far-field transform in the gridded fast multipole method
NASA Astrophysics Data System (ADS)
Hesford, Andrew J.; Waag, Robert C.
2011-05-01
The fast multipole method (FMM) has been shown to have a reduced computational dependence on the size of finest-level groups of elements when the elements are positioned on a regular grid and FFT convolution is used to represent neighboring interactions. However, transformations between plane-wave expansions used for FMM interactions and pressure distributions used for neighboring interactions remain significant contributors to the cost of FMM computations when finest-level groups are large. The transformation operators, which are forward and inverse Fourier transforms with the wave space confined to the unit sphere, are smooth and well approximated using reduced-rank decompositions that further reduce the computational dependence of the FMM on finest-level group size. The adaptive cross approximation (ACA) is selected to represent the forward and adjoint far-field transformation operators required by the FMM. However, the actual error of the ACA is found to be greater than that predicted using traditional estimates, and the ACA generally performs worse than the approximation resulting from a truncated singular-value decomposition (SVD). To overcome these issues while avoiding the cost of a full-scale SVD, the ACA is employed with more stringent accuracy demands and recompressed using a reduced, truncated SVD. The results show a greatly reduced approximation error that performs comparably to the full-scale truncated SVD without degrading the asymptotic computational efficiency associated with ACA matrix assembly.
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.
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.
Adaptive method for electron bunch profile prediction
NASA Astrophysics Data System (ADS)
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.
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.
Semi-implicit integration factor methods on sparse grids for high-dimensional systems
NASA Astrophysics Data System (ADS)
Wang, Dongyong; Chen, Weitao; Nie, Qing
2015-07-01
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.
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.
Grid base plate for an electrode plate for a storage battery and method of manufacture thereof
Sano, I.; Suzuki, Y.
1981-06-02
A grid base plate and its method of manufacture is described. The method is comprised of intermittently conveying a thin elongated metallic sheet longitudinally in one direction through successive first, second and third stations, the sheet being stopped in each of the stations between successive conveying steps. In the first station , the sheet is bent to form a peripheral upwardly projecting portion in a frame region surrounding an inner grid region. In the second station, a plurality of openings are punched in the grid region and in the third station, the sheet is punched along an outer peripheral edge surface to separate the base plate from the sheet. The upwardly projecting portion forms a space with the grid region which is filled with an active material of a thickness determined by the height of the upwardly projecting portion. The upwardly projecting portion has an outer bend region with an end surface constituting a peripheral edge of the frame which faces laterally outwards and is disposed vertically. The outer bend region has a lower surface disposed in the same horizontal plane as a lower surface of an inner region in the vicinity of the juncture of the projecting portion and the grid region. Thereby, when the base plate is placed on a horizontal planar surface, the peripheral frame region will rest on the horizontal surface along two lines of contact respectively at the bottom of the edge surface and at the lower surface at the juncture of the frame region and the grid region.
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.
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…
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
a Pressure-Based Composite Grid Method for Complex Fluid Flows.
NASA Astrophysics Data System (ADS)
Wright, Jeffrey Allen
In this work, a pressure-based composite grid algorithm is developed for solving the incompressible Navier -Stokes equations on domains composed of an arbitrary number of overlapping subgrids. The governing equations are solved independently within each of the subgrids and a staggered grid is used to store the dependent variables. The primary emphasis is on the development of a conservative interface treatment for transferring information between the subgrids of the system. The differences between the conservative interface scheme developed for a staggered grid and that for a nonstaggered grid are discussed. An organizational scheme is developed in order to provide a general and more flexible means for handling arbitrarily overlain subgrids. In order to provide improved computational efficiency, a multigrid technique previously implemented for a single grid solution algorithm has been adopted for use with the composite grid algorithm. In the current procedure, the composite grid method operates as an independent module within the framework of the outer multigrid shell. Results for simple configurations show that composite gridding has little detrimental effect on overall multigrid performance, and that even for geometrically complex flows the current composite multigrid method can largely maintain its effectiveness. With the extension of the current method to natural convection flows it is demonstrated that a locally conservative procedure for exchanging information between subgrids, for the energy and/or species equations, can allow a non-unique solution jump across block interfaces. A new scheme, based on a linear interpolation with global correction is employed which allows the proper solution continuity across internal block interfaces to be maintained. To demonstrate the overall effectiveness of the technique, the double-diffusive flow in a solar pond-type configuration is computed. With an initially gravitationally stable system consisting of a two
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
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.
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.
NASA Technical Reports Server (NTRS)
Sohn, Andrew; Biswas, Rupak; Simon, Horst D.
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.
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.
Modeling flow through inline tube bundles using an adaptive immersed boundary method
NASA Astrophysics Data System (ADS)
Liang, Chunlei; Luo, Xiaoyu; Griffith, Boyce
2007-11-01
Fluid flow and its exerted forces on the tube bundle cylinders are important in designing mechanical/nuclear heat exchanger facilities. In this paper, we study the vortex structure of the flow around the tube bundle for different tube spacing. An adaptive, formally 2^nd order immersed boundary (IB) method is used to simulate the flow. One advantage of the IB method is its great flexibility and ease in positioning solid bodies in the fluid domain. Our IB approach uses a six-point regularized delta function and is a type of continuous forcing approach. Validation results obtained using the IB method for two-in-tandem cylinders compare well with those obtained using the finite volume or spectral element methods on unstructured grids. Subsequently, we simulated flow through six-row inline tube bundles with pitch-to-diameter ratios of 2.1, 3.2, and 4, respectively, on structured adaptively refined Cartesian grids. The IB method enables us to study the critical tube spacing when the flow regime switches from the vortex reattachment pattern to alternative individual vortex shedding.
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.
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…
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.
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.
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-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...
NASA Astrophysics Data System (ADS)
Roussel, Olivier; Schneider, Kai
2010-03-01
An adaptive mulitresolution method based on a second-order finite volume discretization is presented for solving the three-dimensional compressible Navier-Stokes equations in Cartesian geometry. The explicit time discretization is of second-order and for flux evaluation a 2-4 Mac Cormack scheme is used. Coherent Vortex Simulations (CVS) are performed by decomposing the flow variables into coherent and incoherent contributions. The coherent part is computed deterministically on a locally refined grid using the adaptive multiresolution method while the influence of the incoherent part is neglected to model turbulent dissipation. The computational efficiency of this approach in terms of memory and CPU time compression is illustrated for turbulent mixing layers in the weakly compressible regime and for Reynolds numbers based on the mixing layer thickness between 50 and 200. Comparisons with direct numerical simulations allow to assess the precision and efficiency of CVS.
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.
NASA Astrophysics Data System (ADS)
Ronilaya, Ferdian; Miyauchi, Hajime
2014-10-01
This paper presents a new implementation of a parameter adaptive PID-type fuzzy controller (PAPIDfc) for a grid-supporting inverter of battery to alleviate frequency fluctuations in a wind-diesel power system. A variable speed wind turbine that drives a permanent magnet synchronous generator is assumed for demonstrations. The PAPIDfc controller is built from a set of control rules that adopts the droop method and uses only locally measurable frequency signal. The output control signal is determined from the knowledge base and the fuzzy inference. The input-derivative gain and the output-integral gain of the PAPIDfc are tuned online. To ensure safe battery operating limits, we also propose a protection scheme called intelligent battery protection (IBP). Several simulation experiments are performed by using MATLAB®/SimPowersystems™. Next, to verify the scheme's effectiveness, the simulation results are compared with the results of conventional controllers. The results demonstrate the effectiveness of the PAPIDfc scheme to control a grid-supporting inverter of the battery in the reduction of frequency fluctuations.
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.
Development of unstructured grid methods for steady and unsteady aerodynamic analysis
NASA Technical Reports Server (NTRS)
Batina, John T.
1990-01-01
The current status of the development of unstructured grid methods in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for steady and unsteady aerodynamic applications. The flow solvers that were developed for the solution of the unsteady Euler and Navier-Stokes equations are highlighted and selected results are given which demonstrate various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy.
Development of unstructured grid methods for steady and unsteady aerodynamic analysis
NASA Technical Reports Server (NTRS)
Batina, John T.
1990-01-01
The current status of the development of unstructured grid methods in the Unsteady Aerodynamic Branch at NASA-Langley is described. These methods are being developed for steady and unsteady aerodynamic applications. The flow solvers that were developed for the solution of the unsteady Euler and Navier-Stokes equations are highlighted and selected results are given which demonstrate various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy.
Radiation hydrodynamics including irradiation and adaptive mesh refinement with AZEuS. I. Methods
NASA Astrophysics Data System (ADS)
Ramsey, J. P.; Dullemond, C. P.
2015-02-01
Aims: The importance of radiation to the physical structure of protoplanetary disks cannot be understated. However, protoplanetary disks evolve with time, and so to understand disk evolution and by association, disk structure, one should solve the combined and time-dependent equations of radiation hydrodynamics. Methods: We implement a new implicit radiation solver in the AZEuS adaptive mesh refinement magnetohydrodynamics fluid code. Based on a hybrid approach that combines frequency-dependent ray-tracing for stellar irradiation with non-equilibrium flux limited diffusion, we solve the equations of radiation hydrodynamics while preserving the directionality of the stellar irradiation. The implementation permits simulations in Cartesian, cylindrical, and spherical coordinates, on both uniform and adaptive grids. Results: We present several hydrostatic and hydrodynamic radiation tests which validate our implementation on uniform and adaptive grids as appropriate, including benchmarks specifically designed for protoplanetary disks. Our results demonstrate that the combination of a hybrid radiation algorithm with AZEuS is an effective tool for radiation hydrodynamics studies, and produces results which are competitive with other astrophysical radiation hydrodynamics codes.
Adaptive 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
Adaptive finite-element method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
Adaptive multiscale method for two-dimensional nanoscale adhesive contacts
NASA Astrophysics Data System (ADS)
Tong, Ruiting; Liu, Geng; Liu, Lan; Wu, Liyan
2013-05-01
There are two separate traditional approaches to model contact problems: continuum and atomistic theory. Continuum theory is successfully used in many domains, but when the scale of the model comes to nanometer, continuum approximation meets challenges. Atomistic theory can catch the detailed behaviors of an individual atom by using molecular dynamics (MD) or quantum mechanics, although accurately, it is usually time-consuming. A multiscale method coupled MD and finite element (FE) is presented. To mesh the FE region automatically, an adaptive method based on the strain energy gradient is introduced to the multiscale method to constitute an adaptive multiscale method. Utilizing the proposed method, adhesive contacts between a rigid cylinder and an elastic substrate are studied, and the results are compared with full MD simulations. The process of FE meshes refinement shows that adaptive multiscale method can make FE mesh generation more flexible. Comparison of the displacements of boundary atoms in the overlap region with the results from full MD simulations indicates that adaptive multiscale method can transfer displacements effectively. Displacements of atoms and FE nodes on the center line of the multiscale model agree well with that of atoms in full MD simulations, which shows the continuity in the overlap region. Furthermore, the Von Mises stress contours and contact force distributions in the contact region are almost same as full MD simulations. The method presented combines multiscale method and adaptive technique, and can provide a more effective way to multiscale method and to the investigation on nanoscale contact problems.
A grid generation method to calculate the flow field in a three-dimensional cascade of blades
NASA Astrophysics Data System (ADS)
Inoue, Kenji
1992-05-01
A method is described for generating boundary fitted grids to calculate the flow field across a three dimensional cascade of blades placed radially in the axially symmetric space between the hub and casing. Successive application of a series of stretching and conformal transformation maps one-period domain of the cascade onto a box in computational space. The grid in physical space is then obtained by inverse transformation of the grid points in computational space, being an H-type grid and having a periodicity which includes the inclination of grid lines at the periodic boundary.
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.
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.
High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids
NASA Astrophysics Data System (ADS)
McCorquodale, P.; Dorr, M. R.; Hittinger, J. A. F.; Colella, P.
2015-05-01
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. We demonstrate fourth-order accuracy for the advection equation for multiblock coordinate systems in two and three dimensions.
Multiple grid method for the calculation of potential flow around three dimensional bodies
NASA Astrophysics Data System (ADS)
Wolff, H.
1982-01-01
The classical approach of representation of the solution by means of a doublet distribution on the boundary of the domain is considered. From the boundary condition, a Fredholm integral equation for the doublet distribution, mu, is obtained. By a piecewise constant function, mu is approximated. This numerical method results in a nonsparse system that is solved by a multiple grid iterative process. The convergence rate of this process is discussed and its performance is compared with the Jacobi iterative process. For flow around an ellipsoid, the multiple grid process turns out to be much more efficient than the Jacobi iterative process.
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.
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.
On the grid generation methods in harmonic mapping on plane and curved surfaces
NASA Technical Reports Server (NTRS)
Sritharan, S. S.; Smith, P. W.
1984-01-01
Harmonic grid generation methods for multiply connected plane regions and regions on curved surfaces are discussed. In particular, using a general formulation on an analytic Riemannian manifold, it is proved that these mappings are globally one-to-one and onto.
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.
NASA Astrophysics Data System (ADS)
Schneider, Kai; Roussel, Olivier; Farge, Marie
2007-11-01
Coherent Vortex Simulation is based on the wavelet decomposition of the flow into coherent and incoherent components. An adaptive multiresolution method using second order finite volumes with explicit time discretization, a 2-4 Mac Cormack scheme, allows an efficient computation of the coherent flow on a dynamically adapted grid. Neglecting the influence of the incoherent background models turbulent dissipation. We present CVS computation of three dimensional compressible time developing mixing layer. We show the speed up in CPU time with respect to DNS and the obtained memory reduction thanks to dynamical octree data structures. The impact of different filtering strategies is discussed and it is found that isotropic wavelet thresholding of the Favre averaged gradient of the momentum yields the most effective results.
An adaptive, formally second order accurate version of the immersed boundary method
NASA Astrophysics Data System (ADS)
Griffith, Boyce E.; Hornung, Richard D.; McQueen, David M.; Peskin, Charles S.
2007-04-01
Like many problems in biofluid mechanics, cardiac mechanics can be modeled as the dynamic interaction of a viscous incompressible fluid (the blood) and a (visco-)elastic structure (the muscular walls and the valves of the heart). The immersed boundary method is a mathematical formulation and numerical approach to such problems that was originally introduced to study blood flow through heart valves, and extensions of this work have yielded a three-dimensional model of the heart and great vessels. In the present work, we introduce a new adaptive version of the immersed boundary method. This adaptive scheme employs the same hierarchical structured grid approach (but a different numerical scheme) as the two-dimensional adaptive immersed boundary method of Roma et al. [A multilevel self adaptive version of the immersed boundary method, Ph.D. Thesis, Courant Institute of Mathematical Sciences, New York University, 1996; An adaptive version of the immersed boundary method, J. Comput. Phys. 153 (2) (1999) 509-534] and is based on a formally second order accurate (i.e., second order accurate for problems with sufficiently smooth solutions) version of the immersed boundary method that we have recently described [B.E. Griffith, C.S. Peskin, On the order of accuracy of the immersed boundary method: higher order convergence rates for sufficiently smooth problems, J. Comput. Phys. 208 (1) (2005) 75-105]. Actual second order convergence rates are obtained for both the uniform and adaptive methods by considering the interaction of a viscous incompressible flow and an anisotropic incompressible viscoelastic shell. We also present initial results from the application of this methodology to the three-dimensional simulation of blood flow in the heart and great vessels. The results obtained by the adaptive method show good qualitative agreement with simulation results obtained by earlier non-adaptive versions of the method, but the flow in the vicinity of the model heart valves
A new volume-of-fluid method with a constructed distance function on general structured grids
NASA Astrophysics Data System (ADS)
Wang, Zhaoyuan; Yang, Jianming; Stern, Frederick
2012-05-01
A second-order volume-of-fluid method (VOF) is presented for interface tracking and sharp interface treatment on general structured grids. Central to the new method is a second-order distance function construction scheme on a general structured grid based on the reconstructed interface. A novel technique is developed for evaluating the interface normal vector using the distance function. With the normal vector, the interface is reconstructed from the volume fraction function via a piecewise linear interface calculation (PLIC) scheme on the computational domain. Several numerical tests are conducted to demonstrate the accuracy and efficiency of the present method. In general, the new VOF method is more efficient than both the high-order level set and the coupled level set and volume-of-fluid (CLSVOF) methods. The results from the new method are better than those from the benchmark VOF method, particularly in the under-resolved regions, and are comparable to those from the CLSVOF method. Breaking waves over a submerged bump and around a wedge-shaped bow are simulated to demonstrate the application of the new method and sharp interface treatment in a two-phase flow solver on curvilinear grids. The computational results are in good agreement with the available experimental measurements.
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)
Liao, Fei; Ye, Zhengyin
2015-12-01
Despite significant progress in recent computational techniques, the accurate numerical simulations, such as direct-numerical simulation and large-eddy simulation, are still challenging. For accurate calculations, the high-order finite difference method (FDM) is usually adopted with coordinate transformation from body-fitted grid to Cartesian grid. But this transformation might lead to failure in freestream preservation with the geometric conservation law (GCL) violated, particularly in high-order computations. GCL identities, including surface conservation law (SCL) and volume conservation law (VCL), are very important in discretization of high-order FDM. To satisfy GCL, various efforts have been made. An early and successful approach was developed by Thomas and Lombard [6] who used the conservative form of metrics to cancel out metric terms to further satisfy SCL. Visbal and Gaitonde [7] adopted this conservative form of metrics for SCL identities and satisfied VCL identity through invoking VCL equation to acquire the derivative of Jacobian in computation on moving and deforming grids with central compact schemes derived by Lele [5]. Later, using the metric technique from Visbal and Gaitonde [7], Nonomura et al. [8] investigated the freestream and vortex preservation properties of high-order WENO and WCNS on stationary curvilinear grids. A conservative metric method (CMM) was further developed by Deng et al. [9] with stationary grids, and detailed discussion about the innermost difference operator of CMM was shown with proof and corresponding numerical test cases. Noticing that metrics of CMM is asymmetrical without coordinate-invariant property, Deng et al. proposed a symmetrical CMM (SCMM) [12] by using the symmetric forms of metrics derived by Vinokur and Yee [10] to further eliminate asymmetric metric errors with stationary grids considered only. The research from Abe et al. [11] presented new asymmetric and symmetric conservative forms of time metrics and
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.
An automated method for gridding and clustering-based segmentation of cDNA microarray images.
Giannakeas, Nikolaos; Fotiadis, Dimitrios I
2009-01-01
Microarrays are widely used to quantify gene expression levels. Microarray image analysis is one of the tools, which are necessary when dealing with vast amounts of biological data. In this work we propose a new method for the automated analysis of microarray images. The proposed method consists of two stages: gridding and segmentation. Initially, the microarray images are preprocessed using template matching, and block and spot finding takes place. Then, the non-expressed spots are detected and a grid is fit on the image using a Voronoi diagram. In the segmentation stage, K-means and Fuzzy C means (FCM) clustering are employed. The proposed method was evaluated using images from the Stanford Microarray Database (SMD). The results that are presented in the segmentation stage show the efficiency of our Fuzzy C means-based work compared to the two already developed K-means-based methods. The proposed method can handle images with artefacts and it is fully automated. PMID:19046850
An Adaptive Finite Difference Method for Hyperbolic Systems in OneSpace Dimension
Bolstad, John H.
1982-06-01
Many problems of physical interest have solutions which are generally quite smooth in a large portion of the region of interest, but have local phenomena such as shocks, discontinuities or large gradients which require much more accurate approximations or finer grids for reasonable accuracy. Examples are atmospheric fronts, ocean currents, and geological discontinuities. In this thesis we develop and partially analyze an adaptive finite difference mesh refinement algorithm for the initial boundary value problem for hyperbolic systems in one space dimension. The method uses clusters of uniform grids which can ''move'' along with pulses or steep gradients appearing in the calculation, and which are superimposed over a uniform coarse grid. Such refinements are created, destroyed, merged, separated, recursively nested or moved based on estimates of the local truncation error. We use a four-way linked tree and sequentially allocated deques (double-ended queues) to perform these operations efficiently. The local truncation error in the interior of the region is estimated using a three-step Richardson extrapolation procedure, which can also be considered a deferred correction method. At the boundaries we employ differences to estimate the error. Our algorithm was implemented using a portable, extensible Fortran preprocessor, to which we added records and pointers. The method is applied to three model problems: the first order wave equation, the second order wave equation, and the inviscid Burgers equation. For the first two model problems our algorithm is shown to be three to five times more efficient (in computing time) than the use of a uniform coarse mesh, for the same accuracy. Furthermore, to our knowledge, our algorithm is the only one which adaptively treats time-dependent boundary conditions for hyperbolic systems.
An auto-adaptive background subtraction method for Raman spectra.
Xie, Yi; Yang, Lidong; Sun, Xilong; Wu, Dewen; Chen, Qizhen; Zeng, Yongming; Liu, Guokun
2016-05-15
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. PMID:26950502
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.
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.
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
Track and vertex reconstruction: From classical to adaptive methods
Strandlie, Are; Fruehwirth, Rudolf
2010-04-15
This paper reviews classical and adaptive methods of track and vertex reconstruction in particle physics experiments. Adaptive methods have been developed to meet the experimental challenges at high-energy colliders, in particular, the CERN Large Hadron Collider. They can be characterized by the obliteration of the traditional boundaries between pattern recognition and statistical estimation, by the competition between different hypotheses about what constitutes a track or a vertex, and by a high level of flexibility and robustness achieved with a minimum of assumptions about the data. The theoretical background of some of the adaptive methods is described, and it is shown that there is a close connection between the two main branches of adaptive methods: neural networks and deformable templates, on the one hand, and robust stochastic filters with annealing, on the other hand. As both classical and adaptive methods of track and vertex reconstruction presuppose precise knowledge of the positions of the sensitive detector elements, the paper includes an overview of detector alignment methods and a survey of the alignment strategies employed by past and current experiments.
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.
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.
Introduction to Adaptive Methods for Differential Equations
NASA Astrophysics Data System (ADS)
Eriksson, Kenneth; Estep, Don; Hansbo, Peter; Johnson, Claes
Knowing thus the Algorithm of this calculus, which I call Differential Calculus, all differential equations can be solved by a common method (Gottfried Wilhelm von Leibniz, 1646-1719).When, several years ago, I saw for the first time an instrument which, when carried, automatically records the number of steps taken by a pedestrian, it occurred to me at once that the entire arithmetic could be subjected to a similar kind of machinery so that not only addition and subtraction, but also multiplication and division, could be accomplished by a suitably arranged machine easily, promptly and with sure results. For it is unworthy of excellent men to lose hours like slaves in the labour of calculations, which could safely be left to anyone else if the machine was used. And now that we may give final praise to the machine, we may say that it will be desirable to all who are engaged in computations which, as is well known, are the managers of financial affairs, the administrators of others estates, merchants, surveyors, navigators, astronomers, and those connected with any of the crafts that use mathematics (Leibniz).
The adaptive EVP method for solving the sea ice momentum equation
NASA Astrophysics Data System (ADS)
Kimmritz, Madlen; Danilov, Sergey; Losch, Martin
2016-05-01
Stability and convergence of the modified EVP implementation of the visco-plastic sea ice rheology by Bouillon et al., Ocean Modell., 2013, is analyzed on B- and C-grids. It is shown that the implementation on a B-grid is less restrictive with respect to stability requirements than on a C-grid. On C-grids convergence is sensitive to the discretization of the viscosities. We suggest to adaptively vary the parameters of pseudotime subcycling of the modified EVP scheme in time and space to satisfy local stability constraints. This new approach generally improves the convergence of the modified EVP scheme and hence its numerical efficiency. The performance of the new "adaptive EVP" approach is illustrated in a series of experiments with the sea ice component of the MIT general circulation model (MITgcm) that is formulated on a C-grid.
Peláez, Daniel; Meyer, Hans-Dieter
2013-01-01
In this article, a new method, multigrid POTFIT (MGPF), is presented. MGPF is a grid-based algorithm which transforms a general potential energy surface into product form, that is, a sum of products of one-dimensional functions. This form is necessary to profit from the computationally advantageous multiconfiguration time-dependent Hartree method for quantum dynamics. MGPF circumvents the dimensionality related issues present in POTFIT [A. Jäckle and H.-D. Meyer, J. Chem. Phys. 104, 7974 (1996)], allowing quantum dynamical studies of systems up to about 12 dimensions. MGPF requires the definition of a fine grid and a coarse grid, the latter being a subset of the former. The MGPF approximation relies on a series of underlying POTFIT calculations on grids which are smaller than the fine one and larger than or equal to the coarse one. This aspect makes MGPF a bit less accurate than POTFIT but orders of magnitude faster and orders of magnitude less memory demanding than POTFIT. Moreover, like POTFIT, MGPF is variational and provides an efficient error control. PMID:23298029
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.
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.
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
Adaptive multiscale model reduction with Generalized Multiscale Finite Element Methods
NASA Astrophysics Data System (ADS)
Chung, Eric; Efendiev, Yalchin; Hou, Thomas Y.
2016-09-01
In this paper, we discuss a general multiscale model reduction framework based on multiscale finite element methods. We give a brief overview of related multiscale methods. Due to page limitations, the overview focuses on a few related methods and is not intended to be comprehensive. We present a general adaptive multiscale model reduction framework, the Generalized Multiscale Finite Element Method. Besides the method's basic outline, we discuss some important ingredients needed for the method's success. We also discuss several applications. The proposed method allows performing local model reduction in the presence of high contrast and no scale separation.
NASA Astrophysics Data System (ADS)
Davies, D. R.; Davies, J. H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2007-05-01
An adaptive finite element procedure is presented for improving the quality of solutions to convection-dominated problems in geodynamics. The method adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver, and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code ConMan. An unstructured quadrilateral mesh generator is utilized, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation-based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermochemical problems with well-established benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy while increasing computational efficiency. For thermochemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid-based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies.
NASA Astrophysics Data System (ADS)
Yang, Xiaoquan; Cheng, Jian; Liu, Tiegang; Luo, Hong
2015-11-01
The direct discontinuous Galerkin (DDG) method based on a traditional discontinuous Galerkin (DG) formulation is extended and implemented for solving the compressible Navier-Stokes equations on arbitrary grids. Compared to the widely used second Bassi-Rebay (BR2) scheme for the discretization of diffusive fluxes, the DDG method has two attractive features: first, it is simple to implement as it is directly based on the weak form, and therefore there is no need for any local or global lifting operator; second, it can deliver comparable results, if not better than BR2 scheme, in a more efficient way with much less CPU time. Two approaches to perform the DDG flux for the Navier- Stokes equations are presented in this work, one is based on conservative variables, the other is based on primitive variables. In the implementation of the DDG method for arbitrary grid, the definition of mesh size plays a critical role as the formation of viscous flux explicitly depends on the geometry. A variety of test cases are presented to demonstrate the accuracy and efficiency of the DDG method for discretizing the viscous fluxes in the compressible Navier-Stokes equations on arbitrary grids.
Hong Luo; Luqing Luo; Robert Nourgaliev; Vincent A. Mousseau
2010-09-01
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.
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.
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.
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.
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.
Schwartz, Peter; Barad, Michael; Colella, Phillip; Ligocki, Terry
2004-11-02
We present an algorithm for solving Poisson's equation and the heat equation on irregular domains in three dimensions. Our work uses the Cartesian grid embedded boundary algorithm for 2D problems of Johansen and Colella (1998, J. Comput. Phys. 147(2):60-85) and extends work of McCorquodale, Colella and Johansen (2001, J. Comput. Phys. 173(2):60-85). Our method is based on a finite-volume discretization of the operator, on the control volumes formed by intersecting the Cartesian grid cells with the domain, combined with a second-order accurate discretization of the fluxes. The resulting method provides uniformly second-order accurate solutions and gradients and is amenable to geometric multigrid solvers.
Adaptive computational methods for SSME internal flow analysis
NASA Technical Reports Server (NTRS)
Oden, J. T.
1986-01-01
Adaptive finite element methods for the analysis of classes of problems in compressible and incompressible flow of interest in SSME (space shuttle main engine) analysis and design are described. The general objective of the adaptive methods is to improve and to quantify the quality of numerical solutions to the governing partial differential equations of fluid dynamics in two-dimensional cases. There are several different families of adaptive schemes that can be used to improve the quality of solutions in complex flow simulations. Among these are: (1) r-methods (node-redistribution or moving mesh methods) in which a fixed number of nodal points is allowed to migrate to points in the mesh where high error is detected; (2) h-methods, in which the mesh size h is automatically refined to reduce local error; and (3) p-methods, in which the local degree p of the finite element approximation is increased to reduce local error. Two of the three basic techniques have been studied in this project: an r-method for steady Euler equations in two dimensions and a p-method for transient, laminar, viscous incompressible flow. Numerical results are presented. A brief introduction to residual methods of a-posterior error estimation is also given and some pertinent conclusions of the study are listed.
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)
Wei, Tao; Mu, Shengjing; Nakano, Aiichiro; Shing, Katherine
2009-05-01
Atomistic simulation of protein adsorption on a solid surface in aqueous environment is computationally demanding, therefore the determination of preferred protein orientations on the solid surface usually serves as an initial step in simulation studies. We have developed a hybrid multi-loop genetic-algorithm/simplex/spatial-grid method to search for low adsorption-energy orientations of a protein molecule on a solid surface. In this method, the surface and the protein molecule are treated as rigid bodies, whereas the bulk fluid is represented by spatial grids. For each grid point, an effective interaction region in the surface is defined by a cutoff distance, and the possible interaction energy between an atom at the grid point and the surface is calculated and recorded in a database. In searching for the optimum position and orientation, the protein molecule is translated and rotated as a rigid body with the configuration obtained from a previous Molecular Dynamic simulation. The orientation-dependent protein-surface interaction energy is obtained using the generated database of grid energies. The hybrid search procedure consists of two interlinked loops. In the first loop A, a genetic algorithm (GA) is applied to identify promising regions for the global energy minimum and a local optimizer with the derivative-free Nelder-Mead simplex method is used to search for the lowest-energy orientation within the identified regions. In the second loop B, a new population for GA is generated and competitive solution from loop A is improved. Switching between the two loops is adaptively controlled by the use of similarity analysis. We test the method for lysozyme adsorption on a hydrophobic hydrogen-terminated silicon (110) surface in implicit water (i.e., a continuum distance-dependent dielectric constant). The results show that the hybrid search method has faster convergence and better solution accuracy compared with the conventional genetic algorithm.
B-spline methods and zonal grids for numerical simulations of turbulent flows
NASA Astrophysics Data System (ADS)
Kravchenko, Arthur Grigorievich
1998-12-01
A novel numerical technique is developed for simulations of complex turbulent flows on zonal embedded grids. This technique is based on the Galerkin method with basis functions constructed using B-splines. The technique permits fine meshes to be embedded in physically significant flow regions without placing a large number of grid points in the rest of the computational domain. The numerical technique has been tested successfully in simulations of a fully developed turbulent channel flow. Large eddy simulations of turbulent channel flow at Reynolds numbers up to Rec = 110,000 (based on centerline velocity and channel half-width) show good agreement with the existing experimental data. These tests indicate that the method provides an efficient information transfer between zones without accumulation of errors in the regions of sudden grid changes. The numerical solutions on multi-zone grids are of the same accuracy as those on a single-zone grid but require less computer resources. The performance of the numerical method in a generalized coordinate system is assessed in simulations of laminar flows over a circular cylinder at low Reynolds numbers and three-dimensional simulations at ReD = 300 (based on free-stream velocity and cylinder diameter). The drag coefficients, the size of the recirculation region, and the vortex shedding frequency all agree well with the experimental data and previous simulations of these flows. Large eddy simulations of a flow over a circular cylinder at a sub-critical Reynolds number, ReD = 3900, are performed and compared with previous upwind-biased and central finite-difference computations. In the very near-wake, all three simulations are in agreement with each other and agree fairly well with the PIV experimental data of Lourenco & Shih (1993). Farther downstream, the results of the B- spline computations are in better agreement with the hot- wire experiment of Ong & Wallace (1996) than those obtained in finite-difference simulations
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.
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.
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.…
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…
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.
(Yet) A New Method for the Determination of Flow Directions and Contributing Areas over Gridded DEMs
NASA Astrophysics Data System (ADS)
Shelef, E.; Hilley, G. E.
2012-12-01
Flow routing across real or modeled topography is required to calculate parameters such as water discharge, surface lowering rate, and the likelihood of slope failure. There are a number of ways in which this is accomplished using digital topography, but all distribute flow either down the steepest decent to the surrounding four (D4) or eight (D8) cells, or partition flow between these surrounding cells according to value of downslope magnitude (Dinf and multipel flow direction methods [MFD]). The latter three of these schemes may route flow diagonally to cells through the corners of the elevation cells, which distorts their sourced area and the length they traverse. This non-orthogonal routing produces an inconsistency that may impact models that use these routing schemes. To address this issue, we decompose the elevation grid into a set of right triangular facets anchored at three adjacent grid nodes. These facets are sorted according to mean elevation, and flow from each facet is routed to adjacent facets according to the slope of each triangle. Flow is progressively added and partitioned from highest triangle to lowest, allowing routing to be accomplished in approximately n(log(n)+1) operations (where n is the number of triangular facets). Finally, contributing area is calculated using the mean of the contributing area from the portions of the facets contained within the rectangular grid cell. This methodology allows cell-to-cell dispersion within a kernel of the topography but ultimately distributes flow along orthogonal boundaries of the grid. Thus, this method produces behavior similar to a nine-cell kernel method but has the benefit of routing flow along the gridded directions of the topography. This method was benchmarked against the other commonly used flow routing schemes, and was found to perform similarly to distributive nine-cell kernel methods such as Dinf and MFD methods. Cone tests, which are the common benchmark for these methods, tend to prefer
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.
Adaptive frequency estimation by MUSIC (Multiple Signal Classification) method
NASA Astrophysics Data System (ADS)
Karhunen, Juha; Nieminen, Esko; Joutsensalo, Jyrki
During the last years, the eigenvector-based method called MUSIC has become very popular in estimating the frequencies of sinusoids in additive white noise. Adaptive realizations of the MUSIC method are studied using simulated data. Several of the adaptive realizations seem to give in practice equally good results as the nonadaptive standard realization. The only exceptions are instantaneous gradient type algorithms that need considerably more samples to achieve a comparable performance. A new method is proposed for constructing initial estimates to the signal subspace. The method improves often dramatically the performance of instantaneous gradient type algorithms. The new signal subspace estimate can also be used to define a frequency estimator directly or to simplify eigenvector computation.
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-SiO_{2} model becomes much larger when the dangling-bond state is induced by a defect in the oxygen layer, while that through the (001)Ge-GeO_{2} model is insensitive to the dangling bond state. PMID:26465580
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.
A simple method for fabrication of enhanced fluorescence substrate on TEM copper grid
NASA Astrophysics Data System (ADS)
Dong, Jun; Du, Yabing; Qi, Jianxia; Zhang, Wenwen; Li, Wenyang
2013-09-01
A simple method to fabricate enhanced fluorescence substrates was experimentally demonstrated. The fabricated substrate, consisting of silver dendrites, was manufactured by a modified galvanic displacement process between Ag ions and TEM grid at room temperature. Substrate enhancement efficiency, which was evaluated from fluorescence spectrum intensities of the adsorbed Rhodamine 6G (Rh6G) molecules, was found to increase rapidly with reaction time. The observation highlights the importance of strong coupling effects between silver nanobranches and the variation of SEF efficiency can be qualitatively explained with the local surface plasmon resonance model of coupled silver nanostructures. As a result, with a laser, a spectrometer, some second-hand TEM grids, and simple chemical agents, we can easily fabricate the enhanced substrate, which can be applied to study surface enhanced fluorescence, one of the research focuses currently.
A Laplacian Equation Method for Numerical Generation of Boundary-Fitted 3D Orthogonal Grids
NASA Astrophysics Data System (ADS)
Theodoropoulos, T.; Bergeles, G. C.
1989-06-01
A sethod for generating boundary fitted orthogonal curvilinear grids in 3-dimensional space is described. The mapping between the curvilinear coordinates and the Cartesian coordinates is provided by a set of Laplace equations which, expressed in curvilinear coordinates, involve the components of the metric tensor and are therefore non-linear and coupled. An iterative algorithm is described, which achieves a numerical solution. Grids appropriate for the calculation of flow fields over complex topography or in complex flow passages as those found in turbomachinery, and for other engineering applications can be constructed using the proposed method. Various examples are presented and plotted in perspective, and data for the assessment of the properties of the resulting meshes is provided.
A method of smooth bivariate interpolation for data given on a generalized curvilinear grid
NASA Technical Reports Server (NTRS)
Zingg, David W.; Yarrow, Maurice
1992-01-01
A method of locally bicubic interpolation is presented for data given at the nodes of a two-dimensional generalized curvilinear grid. The physical domain is transformed to a computational domain in which the grid is uniform and rectangular by a generalized curvilinear coordinate transformation. The metrics of the transformation are obtained by finite differences in the computational domain. Metric derivatives are determined by repeated application of the chain rule for partial differentiation. Given the metrics and the metric derivatives, the partial derivatives required to determine a locally bicubic interpolant can be estimated at each data point using finite differences in the computational domain. A bilinear transformation is used to analytically transform the individual quadrilateral cells in the physical domain into unit squares, thus allowing the use of simple formulas for bicubic interpolation.
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
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.
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.
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.
Using deconvolution to improve the metrological performance of the grid method
NASA Astrophysics Data System (ADS)
Grédiac, Michel; Sur, Frédéric; Badulescu, Claudiu; Mathias, Jean-Denis
2013-06-01
The use of various deconvolution techniques to enhance strain maps obtained with the grid method is addressed in this study. Since phase derivative maps obtained with the grid method can be approximated by their actual counterparts convolved by the envelope of the kernel used to extract phases and phase derivatives, non-blind restoration techniques can be used to perform deconvolution. Six deconvolution techniques are presented and employed to restore a synthetic phase derivative map, namely direct deconvolution, regularized deconvolution, the Richardson-Lucy algorithm and Wiener filtering, the last two with two variants concerning their practical implementations. Obtained results show that the noise that corrupts the grid images must be thoroughly taken into account to limit its effect on the deconvolved strain maps. The difficulty here is that the noise on the grid image yields a spatially correlated noise on the strain maps. In particular, numerical experiments on synthetic data show that direct and regularized deconvolutions are unstable when noisy data are processed. The same remark holds when Wiener filtering is employed without taking into account noise autocorrelation. On the other hand, the Richardson-Lucy algorithm and Wiener filtering with noise autocorrelation provide deconvolved maps where the impact of noise remains controlled within a certain limit. It is also observed that the last technique outperforms the Richardson-Lucy algorithm. Two short examples of actual strain fields restoration are finally shown. They deal with asphalt and shape memory alloy specimens. The benefits and limitations of deconvolution are presented and discussed in these two cases. The main conclusion is that strain maps are correctly deconvolved when the signal-to-noise ratio is high and that actual noise in the actual strain maps must be more specifically characterized than in the current study to address higher noise levels with Wiener filtering.
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.
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
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.
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.
NASA Astrophysics Data System (ADS)
Canestrelli, A.; Jagers, B.; Spruyt, A.; Borsboom, M.; Slingerland, R. L.
2014-12-01
In this work we propose an efficient approach to solve morphodynamics in complex river geometries, with a particular emphasis for river deltas. We use a novel immersed boundary method of solution in Delft3D, an open source hydrodynamic model that employs a Cartesian structured grid. Our approach employs a hybrid cut-cell/ghost-cell method: ghost cells are used for the flow momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut-cells are used in the continuity equation in order to conserve mass. The resulting scheme is robust, does not suffer any time step limitation for small cut cells and conserves fluid mass up to machine precision. The model has been coupled with the existing Delft3D morphodynamic module, adapted for the presence of immersed irregular boundaries cutting through the regular grid. A cut-cell technique is proposed for both the bed-load and suspended load components. The bed-load component, without any modification, turns out to trigger bed instability in small cut-cells, especially for high values of the morphodynamic factor. We therefore propose a simple "virtual merging technique" that guarantees stability even for very high values of the morphodynamic factor. A bank erosion module provides for lateral displacement of the immersed boundaries in proportion to excess bank shear stress. The model has been tested against different analytical and reference solutions. Moreover, morphodynamic simulations of river deltas show that deltas with various channel networks arise as a consequence of jet momentum and stability, and sediment size and geotechnical properties.
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.
An adaptive over/under data combination method
NASA Astrophysics Data System (ADS)
He, Jian-Wei; Lu, Wen-Kai; Li, Zhong-Xiao
2013-12-01
The traditional "dephase and sum" algorithms for over/under data combination estimate the ghost operator by assuming a calm sea surface. However, the real sea surface is typically rough, which invalidates the calm sea surface assumption. Hence, the traditional "dephase and sum" algorithms might produce poor-quality results in rough sea conditions. We propose an adaptive over/under data combination method, which adaptively estimates the amplitude spectrum of the ghost operator from the over/under data, and then over/under data combinations are implemented using the estimated ghost operators. A synthetic single shot gather is used to verify the performance of the proposed method in rough sea surface conditions and a real triple over/under dataset demonstrates the method performance.
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.
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.
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
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.
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. PMID:25481821
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
Adaptive [theta]-methods for pricing American options
NASA Astrophysics Data System (ADS)
Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran
2008-12-01
We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.
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
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.
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.
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 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.
Sparse grid discontinuous Galerkin methods for high-dimensional elliptic equations
NASA Astrophysics Data System (ADS)
Wang, Zixuan; Tang, Qi; Guo, Wei; Cheng, Yingda
2016-06-01
This paper constitutes our initial effort in developing sparse grid discontinuous Galerkin (DG) methods for high-dimensional partial differential equations (PDEs). Over the past few decades, DG methods have gained popularity in many applications due to their distinctive features. However, they are often deemed too costly because of the large degrees of freedom of the approximation space, which are the main bottleneck for simulations in high dimensions. In this paper, we develop sparse grid DG methods for elliptic equations with the aim of breaking the curse of dimensionality. Using a hierarchical basis representation, we construct a sparse finite element approximation space, reducing the degrees of freedom from the standard O (h-d) to O (h-1 |log2 h| d - 1) for d-dimensional problems, where h is the uniform mesh size in each dimension. Our method, based on the interior penalty (IP) DG framework, can achieve accuracy of O (hk |log2 h| d - 1) in the energy norm, where k is the degree of polynomials used. Error estimates are provided and confirmed by numerical tests in multi-dimensions.
Adaptive domain decomposition methods for advection-diffusion problems
Carlenzoli, C.; Quarteroni, A.
1995-12-31
Domain decomposition methods can perform poorly on advection-diffusion equations if diffusion is dominated by advection. Indeed, the hyperpolic part of the equations could affect the behavior of iterative schemes among subdomains slowing down dramatically their rate of convergence. Taking into account the direction of the characteristic lines we introduce suitable adaptive algorithms which are stable with respect to the magnitude of the convective field in the equations and very effective on bear boundary value problems.
NASA Astrophysics Data System (ADS)
Domingues, Margarete O.; Gomes, Anna Karina F.; Mendes, Odim; Schneider, Kai
2013-10-01
We present a new adaptive multiresoltion method for the numerical simulation of ideal magnetohydrodynamics. The governing equations, i.e., the compressible Euler equations coupled with the Maxwell equations are discretized using a finite volume scheme on a two-dimensional Cartesian mesh. Adaptivity in space is obtained via multiresolution analysis, which allows the reliable introduction of a locally refined mesh while controlling the error. The explicit time discretization uses a compact Runge-Kutta method for local time stepping and an embedded Runge-Kutta scheme for automatic time step control. An extended generalized Lagrangian multiplier approach with the mixed hyperbolic-parabolic correction type is used to control the incompressibility of the magnetic field. Applications to a two-dimensional problem illustrate the properties of the method. Memory savings and numerical divergences of the magnetic field are reported and the accuracy of the adaptive computations is assessed by comparing with the available exact solution. This work was supported by the contract SiCoMHD (ANR-Blanc 2011-045).
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.
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.
Blandon, Juan; Parker, Gregory A; Madrid, Christopher
2016-02-11
We introduce a hyperspherical coordinate mapping procedure to the slow variable discretization-enhanced renormalized Numerov method that allows for more accurate and cost-effective calculations of cold and ultracold atom-dimer scattering. The mapping procedure allows optimization of the numerical grid point spacing by adjusting to the shape of the interaction potential. We show results for elastic scattering in HeH2 and compare the results to previous MOLSCAT calculations by Forrey et al. [ Phys. Rev. A 1999, 59, 2146 ]. PMID:26797269
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.
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.
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
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.
A novel adaptive force control method for IPMC manipulation
NASA Astrophysics Data System (ADS)
Hao, Lina; Sun, Zhiyong; Li, Zhi; Su, Yunquan; Gao, Jianchao
2012-07-01
IPMC is a type of electro-active polymer material, also called artificial muscle, which can generate a relatively large deformation under a relatively low input voltage (generally speaking, less than 5 V), and can be implemented in a water environment. Due to these advantages, IPMC can be used in many fields such as biomimetics, service robots, bio-manipulation, etc. Until now, most existing methods for IPMC manipulation are displacement control not directly force control, however, under most conditions, the success rate of manipulations for tiny fragile objects is limited by the contact force, such as using an IPMC gripper to fix cells. Like most EAPs, a creep phenomenon exists in IPMC, of which the generated force will change with time and the creep model will be influenced by the change of the water content or other environmental factors, so a proper force control method is urgently needed. This paper presents a novel adaptive force control method (AIPOF control—adaptive integral periodic output feedback control), based on employing a creep model of which parameters are obtained by using the FRLS on-line identification method. The AIPOF control method can achieve an arbitrary pole configuration as long as the plant is controllable and observable. This paper also designs the POF and IPOF controller to compare their test results. Simulation and experiments of micro-force-tracking tests are carried out, with results confirming that the proposed control method is viable.
NASA Astrophysics Data System (ADS)
Wang, Yue
A new variable grid-size and time-step finite-difference (FD) method is developed and applied to three different geophysical problems: simulation of tube waves in boreholes, three-dimensional (3-D) ground-motion simulation in sedimentary basin models, and reverse-time migration of multicomponent data. Unlike the conventional FD method, which uses a fixed grid-size and time-step for the entire model region, spatially variable grid-sizes and time-steps are used to achieve the optimal computational efficiency. For tube wave simulations, a fine grid-spacing is used for simulation inside the borehole region, while a coarse grid is used in the exterior region. While the stability condition requires a very fine time step for the fine grid, a variable time-step method provides coarse time steps for simulation in the coarse grid. Variable grid-size and time-step changes are used to achieve both accuracy and efficiency in the simulations. Numerical tests are performed for the Bayou Choctaw salt-flank model with different borehole models. The results show the important borehole effects on the seismic wavefield for a realistic source bandwidth. The combination of variable grid-size and time-step methods reduces computational costs by several orders of magnitude for the borehole models. Viscoelastic 3-D simulations are performed for a three-layer Salt Lake basin model. The near-surface unconsolidated layer is modeled with a fine grid, and the deep part of the model is modeled by a coarse grid. Simulation results show that the 3-D basin features and the shallow layer significantly affect the amplitude and duration time of the ground motion. In the elastic case, the approximation by 2-D modeling is insufficient to simulate the 3-D ground motion response. A basin model without a shallow low-velocity layer underestimates the ground motion duration and cumulative kinetic energy by 50% or more. The simulation of a Bingham Mine blast suggests that a lower S-velocity should be used to
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.