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Grid generation research at OSU

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.

Nakamura, S.↗

NASA Workshop on future directions in surface modeling and grid generation

Given here is a summary of the paper sessions and panel discussions of the NASA Workshop on Future Directions in Surface Modeling and Grid Generation held a NASA Ames Research Center, Moffett Field, California, December 5-7, 1989. The purpose was to assess U.S. capabilities in surface modeling and grid generation and take steps to improve the focus and pace of these disciplines within NASA. The organization of the workshop centered around overviews from NASA centers and expert presentations from U.S. corporations and universities. Small discussion groups were held and summarized by group leaders. Brief overviews and a panel discussion by representatives from the DoD were held, and a NASA-only session concluded the meeting. In the NASA Program Planning Session summary there are five recommended steps for NASA to take to improve the development and application of surface modeling and grid generation.

Vandalsem, W. R.↗

Towards Flange-to-Flange Turbopump Simulations for Liquid Rocket Engines

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbopump geometry through numerical simulation will be of significant value toward design. This will help to improve safety of future space missions. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the MPI and MLP versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology. INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbopump simulations, moving boundary capability and an efficient time-accurate integration methods are build in the flow solver. To handle the geometric complexity and moving boundary problems, overset grid scheme is incorporated with the solver that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. The performance of the two time integration schemes for time-accurate computations is investigated. For an unsteady flow which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiterations procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in our computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive. The current geometry for the LOX boost turbopump has various rotating and stationary components, such as inducer, stators, kicker, hydrolic turbine, where the flow is extremely unsteady. Figure 1 shows the geometry and computed surface pressure of the inducer. The inducer and the hydrolic turbine rotate in different rotational speed.

Kiris, Cetin↗

Structural dynamics of a thermally silent triiron( II ) spin crossover defect grid complex

The structural evolution of spin crossover (SCO) complexes during their spin transition at equilibrium and out-of-equilibrium conditions needs to be understood to enable their successful utilisation in displays, actuators and memory components. In this study, diffraction techniques were employed to study the structural changes accompanying the temperature increase and the light irradiation of a defect [2 × 2] triiron(II) metallogrid of the form [Fe II 3 L H 2 (HL H ) 2 ](BF 4 ) 4 ·4MeCN (FE3), L H = 3,5-bis{6-(2,2'-bipyridyl)}pyrazole. Although a multi-temperature crystallographic investigation on single crystals evidenced that the compound does not exhibit a thermal spin transition, the structural analysis of the defect grid suggests that the flexibility of the grid, provided by a metal-devoid vertex, leads to interesting characteristics that can be used for intermolecular cooperativity in related thermally responsive systems. Time-resolved photocrystallography results reveal that upon excitation with a ps laser pulse, the defect grid shows the first two steps of the out-of-equilibrium process, namely the photoinduced and elastic steps, occurring at the ps and ns time scales, respectively. Similar to a previously reported [2 × 2] tetrairon(II) metallogrid, FE3 exhibits a local distortion of the entire grid during the photoinduced step and a long-range distortion of the lattice during the elastic step. Although the lifetime of the pure photoinduced high spin (HS) state is longer in the tetranuclear grid than in the defect grid, suggesting that the global nuclearity plays a crucial role for the lifetime of the photoinduced species, the influence of the co-crystalising solvent on the lifetime of the photoinduced HS state remains unknown. This study sheds light on the out-of-equilibrium dynamics of a thermally silent defect triiron SCO metallogrid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Beyond Energy Efficiency: A clustering approach to embed demand flexibility into building energy benchmarking

The intermittency of carbon-free renewables and the demand changes associated with the widespread push for electrifying the transportation and building sectors provides an opportunity for buildings to go beyond energy efficiency and push towards providing demand flexibility to the electricity grid. The duality of energy efficiency and demand flexibility is necessary for success in a sustainable and reliable energy transition. Current building energy benchmarking models are limited in their ability to integrate concepts of demand flexibility and/or utilize granular smart meter data. Thus, current benchmarking methods are focused annual energy usage and fail to incorporate how the time of use of energy consumption impacts emissions in a quickly changing energy grid. Without a more comprehensive view of energy usage and associated real-time emissions, current benchmarking methods are unlikely to realize the full decarbonization potential of buildings. New emerging data streams provide an opportunity to develop a new generation of benchmarking energy models that embed dimensions of energy efficiency, grid interactivity, and demand flexibility into their analysis. In this paper, we propose a four-step method for embedding grid interactivity and demand flexibility into building benchmarking models that utilizes emerging building and time-series electricity data streams. We first engineer features to produce a mix-type dataset that encompasses many attributes of grid-interactive and efficient buildings, and then we apply K-medoids using Gower's Distance to produce peer-group clusters. We apply the method to a case study of 306 primary and secondary schools in southern California, USA. The results show that the method effectively clusters buildings by attributes of demand flexibility and energy efficiency. The clustering results reveal patterns in inefficient building operations and demand inflexibility at the building peer group level. In conclusion, the interpretation of clusters can serve as an integrated energy efficiency and demand flexibility benchmarking model and inform performance-specific policy targeting for buildings that go beyond traditional efficiency measures.

24 POWER TRANSMISSION AND DISTRIBUTION↗

GRAPEVINE: Grids about anything by Poisson's equation in a visually interactive networking environment

A proven 3-D multiple-block elliptic grid generator, designed to run in 'batch mode' on a supercomputer, is improved by the creation of a modern graphical user interface (GUI) running on a workstation. The two parts are connected in real time by a network. The resultant system offers a significant speedup in the process of preparing and formatting input data and the ability to watch the grid solution converge by replotting the grid at each iteration step. The result is a reduction in user time and CPU time required to generate the grid and an enhanced understanding of the elliptic solution process. This software system, called GRAPEVINE, is described, and certain observations are made concerning the creation of such software.

Sorenson, Reese L.↗

Three dimensional unstructured grids for the solution of the Euler equations

The advancing front technique is being used to develop a code to generate grids around complex 3-D configurations for use in computing the invisid flow solutions by the Euler equations. By the advancing front technique points are introduced concurrently with the connectivity information so that a separate library is not required. The generation of a 3-D grid is accomplished in several steps. First the boundaries of the domain to be gridded must be described by two-, three- or four-sided surface patches. Next, a background mesh is required to control the grid spacing and stretching throughout the domain. This coarse tetrahedral grid is not required to conform to any of the boundaries. Next, each of the patches is mapped to 2-D, triangulated by the advancing front technique and mapped back to 3-D. These triangles form the initial front for the generation of the final tetrahedral mesh.

Gumbert, Clyde↗

Design and production of the high voltage electrode grids and electron extraction region for the LZ dual-phase xenon time projection chamber

The dual-phase xenon time projection chamber (TPC) is a powerful tool for direct-detection experiments searching for WIMP dark matter, other dark matter models, and neutrinoless double-beta decay. Successful operation of such a TPC is critically dependent on the ability to hold high electric fields in the bulk liquid, across the liquid surface, and in the gas. Careful design and construction of the electrodes used to establish these fields is therefore required. We present the design and production of the LUX-ZEPLIN (LZ) experiment's high-voltage electrodes, a set of four woven mesh wire grids. Grid design drivers are discussed, with emphasis placed on design of the electron extraction region. Here, we follow this with a description of the grid production process and a discussion of steps taken to validate the LZ grids prior to integration into the TPC.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

General Flow-Solver Code for Turbomachinery Applications

Phantom is a computer code intended primarily for real-fluid turbomachinery problems. It is based on Corsair, an ideal-gas turbomachinery code, developed by the same authors, which evolved from the ROTOR codes from NASA Ames. Phantom is applicable to real and ideal fluids, both compressible and incompressible, flowing at subsonic, transonic, and supersonic speeds. It utilizes structured, overset, O- and H-type zonal grids to discretize flow fields and represent relative motions of components. Values on grid boundaries are updated at each time step by bilinear interpolation from adjacent grids. Inviscid fluxes are calculated to third-order spatial accuracy using Roe s scheme. Viscous fluxes are calculated using second-order-accurate central differences. The code is second-order accurate in time. Turbulence is represented by a modified Baldwin-Lomax algebraic model. The code offers two options for determining properties of fluids: One is based on equations of state, thermodynamic departure functions, and corresponding state principles. The other, which is more efficient, is based on splines generated from tables of properties of real fluids. Phantom currently contains fluid-property routines for water, hydrogen, oxygen, nitrogen, kerosene, methane, and carbon monoxide as well as ideal gases.

Dorney, Daniel↗

Supercomputing Aspects for Simulating Incompressible Flow

The primary objective of this research is to support the design of liquid rocket systems for the Advanced Space Transportation System. Since the space launch systems in the near future are likely to rely on liquid rocket engines, increasing the efficiency and reliability of the engine components is an important task. One of the major problems in the liquid rocket engine is to understand fluid dynamics of fuel and oxidizer flows from the fuel tank to plume. Understanding the flow through the entire turbo-pump geometry through numerical simulation will be of significant value toward design. One of the milestones of this effort is to develop, apply and demonstrate the capability and accuracy of 3D CFD methods as efficient design analysis tools on high performance computer platforms. The development of the Message Passage Interface (MPI) and Multi Level Parallel (MLP) versions of the INS3D code is currently underway. The serial version of INS3D code is a multidimensional incompressible Navier-Stokes solver based on overset grid technology, INS3D-MPI is based on the explicit massage-passing interface across processors and is primarily suited for distributed memory systems. INS3D-MLP is based on multi-level parallel method and is suitable for distributed-shared memory systems. For the entire turbo-pump simulations, moving boundary capability and efficient time-accurate integration methods are built in the flow solver, To handle the geometric complexity and moving boundary problems, an overset grid scheme is incorporated with the solver so that new connectivity data will be obtained at each time step. The Chimera overlapped grid scheme allows subdomains move relative to each other, and provides a great flexibility when the boundary movement creates large displacements. Two numerical procedures, one based on artificial compressibility method and the other pressure projection method, are outlined for obtaining time-accurate solutions of the incompressible Navier-Stokes equations. The performance of the two methods is compared by obtaining unsteady solutions for the evolution of twin vortices behind a flat plate. Calculated results are compared with experimental and other numerical results. For an unsteady flow, which requires small physical time step, the pressure projection method was found to be computationally efficient since it does not require any subiteration procedure. It was observed that the artificial compressibility method requires a fast convergence scheme at each physical time step in order to satisfy the incompressibility condition. This was obtained by using a GMRES-ILU(0) solver in present computations. When a line-relaxation scheme was used, the time accuracy was degraded and time-accurate computations became very expensive.

Kwak, Dochan↗

Optimal Padding for the Two-Dimensional Fast Fourier Transform

One-dimensional Fast Fourier Transform (FFT) operations work fastest on grids whose size is divisible by a power of two. Because of this, padding grids (that are not already sized to a power of two) so that their size is the next highest power of two can speed up operations. While this works well for one-dimensional grids, it does not work well for two-dimensional grids. For a two-dimensional grid, there are certain pad sizes that work better than others. Therefore, the need exists to generalize a strategy for determining optimal pad sizes. There are three steps in the FFT algorithm. The first is to perform a one-dimensional transform on each row in the grid. The second step is to transpose the resulting matrix. The third step is to perform a one-dimensional transform on each row in the resulting grid. Steps one and three both benefit from padding the row to the next highest power of two, but the second step needs a novel approach. An algorithm was developed that struck a balance between optimizing the grid pad size with prime factors that are small (which are optimal for one-dimensional operations), and with prime factors that are large (which are optimal for two-dimensional operations). This algorithm optimizes based on average run times, and is not fine-tuned for any specific application. It increases the amount of times that processor-requested data is found in the set-associative processor cache. Cache retrievals are 4-10 times faster than conventional memory retrievals. The tested implementation of the algorithm resulted in faster execution times on all platforms tested, but with varying sized grids. This is because various computer architectures process commands differently. The test grid was 512 512. Using a 540 540 grid on a Pentium V processor, the code ran 30 percent faster. On a PowerPC, a 256x256 grid worked best. A Core2Duo computer preferred either a 1040x1040 (15 percent faster) or a 1008x1008 (30 percent faster) grid. There are many industries that can benefit from this algorithm, including optics, image-processing, signal-processing, and engineering applications.

Dean, Bruce H.↗

Structured adaptive grid generation using algebraic methods

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 of points to the grid redistribution scheme. The evaluation of the weighting mesh is accomplished by utilizing the weight function representing the solution variation and the equidistribution law. The selection of the weight function plays a key role in grid adaptation. A new weight function utilizing a properly weighted boolean sum of various flowfield characteristics is defined. The redistribution scheme is developed utilizing Non-Uniform Rational B-Splines (NURBS) representation. The application of NURBS representation results in a well distributed smooth grid by maintaining the fidelity of the geometry associated with boundary curves. Several algebraic methods are applied to smooth and/or nearly orthogonalize the grid lines. An elliptic solver is utilized to smooth the grid lines if there are grid crossings. Various computational examples of practical interest are presented to demonstrate the success of these methods.

Yang, Jiann-Cherng↗

NASA Capabilities that Could Impact Terrestrial Smart Grids of the Future

Incremental steps to steadily build, test, refine, and qualify capabilities that lead to affordable flight elements and a deep space capability. Potential Deep Space Vehicle Power system characteristics: power 10 kilowatts average; two independent power channels with multi-level cross-strapping; solar array power 24 plus kilowatts; multi-junction arrays; lithium Ion battery storage 200 plus ampere-hours; sized for deep space or low lunar orbit operation; distribution120 volts secondary (SAE AS 5698); 2 kilowatt power transfer between vehicles.

Power systems↗

Estimation of the Attenuation Caused by Power Line Towers on an E1-HEMP Induced Excitation

In a transmission line, the coupling between a line and a tower above ground is evaluated when the excitation is an E1 high-altitude electromagnetic pulse (HEMP). The model focuses on capturing correctly the effect of the coupling on the peak of the HEMP induced current that propagates along the line. This assessment is necessary to accurately estimate the effect of the excitation on the systems and components of the power grid. This analysis is a step towards a quantitative evaluation of HEMP excitation on the power grid. The results obtained indicate that the effect can be significant, especially for lines heights of 20 meters or more.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Removing numerical pathologies in a turbulence parameterization through convergence testing

Discretized numerical models of the atmosphere are usually intended to faithfully represent an underlying set of continuous equations, but this necessary condition is violated sometimes by subtle pathologies that have crept into the discretized equations. Such pathologies can introduce undesirable artifacts, such as sawtooth noise, into the model solutions. The presence of these pathologies can be detected by numerical convergence testing. This study employs convergence testing to verify the discretization of the Cloud Layers Unified By Binormals (CLUBB) model of clouds and turbulence. That convergence testing identifies two aspects of CLUBB's equation set that contribute to undesirable noise in the solutions. First, numerical limiters (i.e. clipping) used by CLUBB introduce discontinuities or slope discontinuities in model fields. Second, this noise can be amplified by an advective term in CLUBB's background diffusion. Smoothing the limiters and removing the advective component of the background diffusion reduces the noise and restores the expected first-order convergence in CLUBB's solutions. These model reformulations improve the results at coarser, near-operational grid spacing and time step in cumulus cloud and dry turbulence tests. In addition, convergence testing is proved to be a valuable tool for detecting pathologies, including unintended discontinuities and grid dependence, in the model equation set.

Mathematics and Computing, Geosciences↗

Explicit Monotone Stable Super-Time-stepping Methods for Finite Time Singularities

We explore a novel way to numerically resolve the scaling behavior of finite-time singularities in solutions of nonlinear parabolic PDEs. The Runge–Kutta–Legendre (RKL) and Runge–Kutta–Gegenbauer (RKG) super-time-stepping methods were originally developed for nonlinear complex physics problems with diffusion. These are multistage single step second-order, forward-in-time methods with no implicit solves. The advantage is that the time-step size for stability scales with stage number 𝑠 as $\mathcal{O}$⁡(𝑠 2 ). Many interesting nonlinear PDEs have finite-time singularities, and the presence of diffusion often limits one to using implicit or semi-implicit time-step methods for stability constraints. Finite-time singularities are particularly challenging due to the large range of scales that one desires to resolve, often with adaptive spatial grids and adaptive time steps. Here, in this study, we show two examples of nonlinear PDEs for which the self-similar singularity structure has time and space scales that are resolvable using the RKL and RKG methods, without forcing even smaller time steps. Compared to commonly used implicit numerical methods, we achieve a significantly smaller run time while maintaining comparable accuracy. We also prove numerical monotonicity for both the RKL and RKG methods under their linear stability conditions for the constant coefficient heat equation, in the case of infinite domain and periodic boundary condition, leading to a theoretical guarantee of the superiority of the RKL and RKG methods over traditional super-time-stepping methods, such as the Runge-Kutta-Chebyshev and the orthogonal Runge-Kutta-Chebyshev methods. Code can be found at https://github.com/ZT220501/SRK-Singularity.

97 MATHEMATICS AND COMPUTING↗

A CIERRA Gridded Product Climatology for LIS/OTD [Slides]

As a stepping-stone towards developing improved GLM-CIERRA grids, I am testing pixel matching techniques on the LIS/OTD data; The goal is to maintain accuracy while vastly improving computational efficiency; The end result will be standardized grids at the nominal resolution of each instrument (5 km for LIS, 10 km for OTD) that take into account the pixel geometry for each event that comprises a given flash

58 GEOSCIENCES↗

Comparing Anisotropic Output-Based Grid Adaptation Methods by Decomposition

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.

Park, Michael A.↗