A Method for Projecting Uncertainty from Sparse Samples of Discrete Random Functions - Example of Multiple Stress-Strain Curves.
Abstract Not Provided
Romero, Vicente J↗
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A Quadratic Programming Based Flux FIxup Method for Arbitrarily High-Order Discontinuous Galerkin Discretizations of the SN Transport Equations
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Mathematics and Computing↗
A Quadratic Programming Based Flux Fixup Method for Arbitrarily High-Order Discontinuous Galerkin Discretizations of the SN Transport Equations
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Mathematics and Computing↗
Model of brittle matrix composite toughening based on discrete fiber reinforcement
An analytical approach for the analysis of the effectiveness of fiber reinforcement in brittle matrix composites is presented. The analytical method allows consideration of discrete fiber distribution and examination of the development of crack growth parameters on microscale. The problem associated with the bridging zone development is addressed here; therefore, the bridging zone is considered to be smaller than the main preexisting crack, and the small scale approach is used. The mechanics of the reinforcement is accurately accounted for in the process zone of a growing crack. Closed form solutions characterizing the initial failure process are presented for linear and nonlinear force - fiber pullout displacement relationships. The implicit exact solution for the extended bridging zone is presented as well.
Rubinstein, Asher A.↗
Large-eddy simulation of turbulent cavitating flow in a micro channel
Large-eddy simulations (LES) of cavitating flow of a Diesel-fuel-like fluid in a generic throttle geometry are presented. Two-phase regions are modeled by a parameter-free thermodynamic equilibrium mixture model, and compressibility of the liquid and the liquid-vapor mixture is taken into account. The Adaptive Local Deconvolution Method (ALDM), adapted for cavitating flows, is employed for discretizing the convective terms of the Navier-Stokes equations for the homogeneous mixture. ALDM is a finite-volume-based implicit LES approach that merges physically motivated turbulence modeling and numerical discretization. Validation of the numerical method is performed for a cavitating turbulent mixing layer. Comparisons with experimental data of the throttle flow at two different operating conditions are presented. The LES with the employed cavitation modeling predicts relevant flow and cavitation features accurately within the uncertainty range of the experiment. The turbulence structure of the flow is further analyzed with an emphasis on the interaction between cavitation and coherent motion, and on the statistically averaged-flow evolution.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
High order multi-grid methods to solve the Poisson equation
High order multigrid methods based on finite difference discretization of the model problem are examined. The following methods are described: (1) a fixed high order FMG-FAS multigrid algorithm; (2) the high order methods; and (3) results are presented on four problems using each method with the same underlying fixed FMG-FAS algorithm.
Schaffer, S.↗
Optimal pre-scheduling of problem remappings
A large class of scientific computational problems can be characterized as a sequence of steps where a significant amount of computation occurs each step, but the work performed at each step is not necessarily identical. Two good examples of this type of computation are: (1) regridding methods which change the problem discretization during the course of the computation, and (2) methods for solving sparse triangular systems of linear equations. Recent work has investigated a means of mapping such computations onto parallel processors; the method defines a family of static mappings with differing degrees of importance placed on the conflicting goals of good load balance and low communication/synchronization overhead. The performance tradeoffs are controllable by adjusting the parameters of the mapping method. To achieve good performance it may be necessary to dynamically change these parameters at run-time, but such changes can impose additional costs. If the computation's behavior can be determined prior to its execution, it can be possible to construct an optimal parameter schedule using a low-order-polynomial-time dynamic programming algorithm. Since the latter can be expensive, the performance is studied of the effect of a linear-time scheduling heuristic on one of the model problems, and it is shown to be effective and nearly optimal.
Nicol, David M.↗
Optimization methods, flux conserving methods for steady state Navier-Stokes equation
Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.
Adeyeye, John↗
Fourier-spectral element approximation of the ion–electron Braginskii system with application to tokamak edge plasma in divertor configuration
Due to the extreme conditions required to produce energy by nuclear fusion in tokamaks, simulating the plasma behavior is an important but challenging task. We focus on the edge part of the plasma, where fluid approaches are probably the best suited, and our approach relies on the Braginskii ion–electron model. Assuming that the electric field is electrostatic, this yields a set of 10 strongly coupled and non-linear conservation equations that exhibit multiscale and anisotropy features. The computational domain is a torus of complex geometrical section, that corresponds to the divertor configuration, i.e. with an “X-point” in the magnetic surfaces. To capture the complex physics that is involved, high order methods are used: The time-discretization is based on a Strang splitting, that combines implicit and explicit high order Runge–Kutta schemes, and the space discretization makes use of the spectral element method in the poloidal plane together with Fourier expansions in the toroidal direction. The paper thoroughly describes the algorithms that have been developed, provides some numerical validations of the key algorithms and exhibits the results of preliminary numerical experiments. In particular, we point out that the highest frequency of the system is intermediate between the ion and electron cyclotron frequencies.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Unstructured Adaptive Meshes: Bad for Your Memory?
This viewgraph presentation explores the need for a NASA Advanced Supercomputing (NAS) parallel benchmark for problems with irregular dynamical memory access. This benchmark is important and necessary because: 1) Problems with localized error source benefit from adaptive nonuniform meshes; 2) Certain machines perform poorly on such problems; 3) Parallel implementation may provide further performance improvement but is difficult. Some examples of problems which use irregular dynamical memory access include: 1) Heat transfer problem; 2) Heat source term; 3) Spectral element method; 4) Base functions; 5) Elemental discrete equations; 6) Global discrete equations. Nonconforming Mesh and Mortar Element Method are covered in greater detail in this presentation.
Biswas, Rupak↗
Substructure coupling in the frequency domain
Frequency domain analysis was found to be a suitable method for determining the transient response of systems subjected to a wide variety of loads. However, since a large number of calculations are performed within the discrete frequency loop, the method loses it computational efficiency if the loads must be represented by a large number of discrete frequencies. It was also discovered that substructure coupling in the frequency domain work particularly well for analyzing structural system with a small number of interface and loaded degrees of freedom. It was discovered that substructure coupling in the frequency domain can lead to an efficient method of obtaining natural frequencies of undamped structures. It was also found that the damped natural frequencies of a system may be determined using frequency domain techniques.
Source record↗
A projection method for particle resampling
Particle discretizations of partial differential equations are advantageous for high-dimensional kinetic models in phase-space due to their better scalability than continuum approaches with respect to dimension. Complex processes collectively referred to as particle noise hamper long time simulations with particle methods. One approach to address this problem is particle mesh adaptivity, or remapping, known as particle resampling and remeshing. Here, this work introduces a resampling method that projects particles to and from a (finite element) function space. The method is simple, using standard sparse linear algebra and finite element techniques, and it preserves all moments up to the order of a polynomial represented exactly by the continuum function space. It is distinguished from most other mesh-based methods in that new particle positions and number are decoupled from the mesh, allowing particle and continuum meshes to be adapted relatively independently. While this work is developed with structured particle and continuum phase-space grids on 1X + 1V Vlasov-Poisson models of Landau damping and two-stream instability, the method is well-suited to unstructured grids. Stable long time dynamics are demonstrated up to time T = 500. Reproducibility artifacts and data are publicly available.
Kinetic methods↗
Flow behavior of hydraulic fractured tight formations considering Pre-Darcy flow using EDFM
For tight reservoirs/formations, flow in fracture and matrix obey different flow patterns. Pre-Darcy flow always exists in low permeability subsurface porous media while Darcy flow can be applied in fracture. It is an outstanding challenge to understand the flow behavior coupling different flow mechanisms. As numerical simulation can predict field-scale performance so the development of efficient simulation method becomes a key issue to evaluate the flow behavior. In this paper, we develop an improved discrete fracture model based on the widely used embedded discrete facture model (EDFM) to simulate the transport both in homogenous and heterogeneous porous media in the presence of Pre-Darcy flow. The conservation equations are derived for fracture and matrix firstly and then discretized by fully implicit method. The transmissibility of different connection types is defined and the detailed calculation workflow is presented as well. The proposed model is verified through the comparison with the model using local grid refined (LGR) method. It is discovered that our simulation method exhibits good accuracy when analyzing the effect of Pre-Darcy flow. Some examples are shown including 1D scalar transport, 2D heterogeneous, 3D flow, complex fracture system and multiple well system problems with fully-coupled flow in fracture and matrix. The pressure distribution and well flux are demonstrated to analyze the Pre-Darcy flow characteristics. Results indicate that the new model works robustly for different flow problems which provide further insight into the Pre-Darcy flow in low permeability media.
02 PETROLEUM↗
Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods
Abstract In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.
Klima, Matej↗
Exploring new topography-based subgrid spatial structures for improving land surface modeling
Topography plays an important role in land surface processes through its influence on atmospheric forcing, soil and vegetation properties, and river network topology and drainage area. Land surface models with a spatial structure that captures spatial heterogeneity, which is directly affected by topography, may improve the representation of land surface processes. Previous studies found that land surface modeling, using subbasins instead of structured grids as computational units, improves the scalability of simulated runoff and streamflow processes. In this study, new land surface spatial structures are explored by further dividing subbasins into subgrid structures based on topographic properties, including surface elevation, slope and aspect. Two methods (local and global) of watershed discretization are applied to derive two types of subgrid structures (geo-located and non-geo-located) over the topographically diverse Columbia River basin in the northwestern United States. In the global method, a fixed elevation classification scheme is used to discretize subbasins. The local method utilizes concepts of hypsometric analysis to discretize each subbasin, using different elevation ranges that also naturally account for slope variations. The relative merits of the two methods and subgrid structures are investigated for their ability to capture topographic heterogeneity and the implications of this on representations of atmospheric forcing and land cover spatial patterns. Results showed that the local method reduces the standard deviation (SD) of subgrid surface elevation in the study domain by 17 to 19 % compared to the global method, highlighting the relative advantages of the local method for capturing subgrid topographic variations. The comparison between the two types of subgrid structures showed that the non-geo-located subgrid structures are more consistent across different area threshold values than the geo-located subgrid structures. Altogether the local method and non-geo-located subgrid structures effectively and robustly capture topographic, climatic and vegetation variability, which is important for land surface modeling.
58 GEOSCIENCES↗
Nuclear rocket shielding methods, modification, updating, and input data preparation. Volume 4 - One-dimensional, discrete ordinates transport technique Final progress report
One dimensional, discrete ordinates transport technique for use with nuclear rocket shielding methods, modification, updating, and data input preparation - Vol. 4
Disney, R. K.↗
Nuclear rocket shielding methods, modification, updating, and input data preparation. Volume 5 - Two-dimensional, discrete ordinates transport technique Final progress report
Two dimensional, discrete ordinates transport technique for use with nuclear rocket shielding methods, modification, updating, and data input preparation - Vol. 5
Disney, R. K.↗
A Method to Represent a Well in a Three‐Dimensional Discrete Fracture Network Model
Abstract In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three‐dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high‐resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real‐world case study.
Pham, Hai (ORCID:0000000310164394)↗