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NASA NTRS1991

Three dimensional unstructured multigrid for the Euler equations

The three dimensional Euler equations are solved on unstructured tetrahedral meshes using a multigrid strategy. The driving algorithm consists of an explicit vertex-based finite element scheme, which employs an edge-based data structure to assemble the residuals. The multigrid approach employs a sequence of independently generated coarse and fine meshes to accelerate the convergence to steady-state of the fine grid solution. Variables, residuals and corrections are passed back and forth between the various grids of the sequence using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using linear interpolation. The addresses and weights for interpolation are determined in a preprocessing stage using an efficient graph traversal algorithm. The preprocessing operation is shown to require a negligible fraction of the CPU time required by the overall solution procedure, while gains in overall solution efficiencies greater than an order of magnitude are demonstrated on meshes containing up to 350,000 vertices. Solutions using globally regenerated fine meshes as well as adaptively refined meshes are given.

Mavriplis, D. J.↗

NASA NTRS1990

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Young, David P.↗

NASA NTRS1993

Incompressible viscous flows on adaptive, multi-block grids

Adaptive, multi-block grid solutions to incompressible viscous flows using a pseudocompressibility approach in generalized three-dimensional coordinates are presented. The multi-block approach described in this paper allows the user to compute flows in arbitrary geometries without the necessity of ad hoc modifications to the flow code. Complete grid continuity at block interfaces is assumed and block-to-block connectivity in a domain, including all boundary conditions, is specified by user input through the NAMELIST utility. Therefore, solution continuity across block interfaces is achieved through automatic communication among adjacent blocks. Also, adaptive grid generation is employed to enhance grid quality in response to the evolving solution in order to better resolve the flow field. Several two- and three-dimensional solutions are compared with equivalent non-adaptive solutions and available experimental data to validate the present method for both laminar and turbulent cases.

Kim, Young-Mog↗

DOE OSTI2024

Empowering Rural Electrification in Honduras: An Integrated Assessment of PV/BESS and Productive Uses of Electricity in Gracias a Dios

Honduras faces significant challenges in its energy sector, particularly in rural areas where access to reliable and affordable electricity remains limited. The flagship rural electrification initiative for Honduras Secretary of Energy (SEN) is the Politica de Acceso Universal a la Electricidad (PAUEH - Universal Electricity Access Policy), a key solution for addressing this energy poverty is the deployment of more than 1700 distributed solar and hybrid mini-grid solutions. In late 2023 as a first step towards supporting SEN's electrification efforts, the National Renewable Energy Laboratory (NREL) developed a literature review of SEN electrification policy documents and conducted a series of technical capacity-building workshops with SEN and other energy sector stakeholders in Honduras focused on using NREL's open-source REopt tool to conduct techno-economic assessments and develop least-cost optimizations for potential solar + storage mini-grid systems. Building on some initial capacity building on mini-grid modeling, the National Renewable Energy Laboratory (NREL) worked with SEN to develop a detailed techno-economic assessment for electrifying two schools, a healthcare clinic, and a hospital in a hypothetical community within the department of Gracias a Dios. The analysis also evaluates the business case for cold storage productive use of energy (PUE) applications for the fisheries value chain and how the incorporation of these PUE loads potentially impacts both the viability of the PV+BESS solutions as well as local economic development. By assessing the potential for deployment of integrated PV/BESS systems to both support critical community services like education and healthcare, as well as potential for downstream enterprise and economic development, this analysis represents a first step that can help to inform specific strategies for development of pilot PV+BESS projects aligned with national priorities and sector level planning under PAUEH.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

Fortalecimiento de la Electrificación Rural en Honduras: Una Evaluación Integrada de PV+BESS y Usos Productivos de la Electricidad en Gracias a Dios, Honduras [Empowering Rural Electrification in Honduras: An Integrated Assessment of PV/BESS and Productive Uses of Electricity in Gracias a Dios] (Spanish Translation)

14 SOLAR ENERGY↗

NASA NTRS1985

Numerical solution of transonic wing flows using an Euler/Navier-Stokes zonal approach

Transonic flow fields about wing geometries are computed using an Euler/Navier-Stokes approach in which the flow field is divided into several zones. The grid zones immediately adjacent to the wing surface are suitably clustered and solved with the Navier-Stokes equations. Grid zones removed from the wing are less finely clustered and are solved with the Euler equations. Wind tunnel wall effects are easily and accurately modeled with the new grid-zoning algorithm because the wind tunnel grid is constructed as an exact subset of the corresponding free-air grid. Solutions are obtained that are in good agreement with experiment, including cases with significant wind tunnel wall effects and shock-induced separation on the upper wing surface.

Holst, T. L.↗

NASA NTRS1994

A grid generation and flow solution method for the Euler equations on unstructured grids

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.

Anderson, W. Kyle↗

NASA NTRS2010

Updates to Multi-Dimensional Flux Reconstruction for Hypersonic Simulations on Tetrahedral Grids

The quality of simulated hypersonic stagnation region heating with tetrahedral meshes is investigated by using an updated three-dimensional, upwind reconstruction algorithm for the inviscid flux vector. An earlier implementation of this algorithm provided improved symmetry characteristics on tetrahedral grids compared to conventional reconstruction methods. The original formulation however displayed quantitative differences in heating and shear that were as large as 25% compared to a benchmark, structured-grid solution. The primary cause of this discrepancy is found to be an inherent inconsistency in the formulation of the flux limiter. The inconsistency is removed by employing a Green-Gauss formulation of primitive gradients at nodes to replace the previous Gram-Schmidt algorithm. Current results are now in good agreement with benchmark solutions for two challenge problems: (1) hypersonic flow over a three-dimensional cylindrical section with special attention to the uniformity of the solution in the spanwise direction and (2) hypersonic flow over a three-dimensional sphere. The tetrahedral cells used in the simulation are derived from a structured grid where cell faces are bisected across the diagonal resulting in a consistent pattern of diagonals running in a biased direction across the otherwise symmetric domain. This grid is known to accentuate problems in both shock capturing and stagnation region heating encountered with conventional, quasi-one-dimensional inviscid flux reconstruction algorithms. Therefore the test problems provide a sensitive indicator for algorithmic effects on heating. Additional simulations on a sharp, double cone and the shuttle orbiter are then presented to demonstrate the capabilities of the new algorithm on more geometrically complex flows with tetrahedral grids. These results provide the first indication that pure tetrahedral elements utilizing the updated, three-dimensional, upwind reconstruction algorithm may be used for the simulation of heating and shear in hypersonic flows in upwind, finite volume formulations.

Gnoffo, Peter A.↗

NASA NTRS1991

Zonal analysis of two high-speed inlets

Using a zonal technique, thin layer Navier-Stokes solutions for two high speed inlet geometries are presented and compared with experimental data. The first configuration consists of a 3-D inlet preceded by a sharp flat plate. Results with two different grids demonstrate the importance of adequate grid refinement in high speed internal flow computations. The fine grid solution has reasonably good agreement with experimental heat transfer and pressure values inside the inlet. The other configuration consists of a 3-D inlet mounted on a research hypersonic forebody. Numerical results for this configuration have good agreement with experimental pressure data along the forebody, but not inside the inlet. A more refined grid calculation is currently being done to better predict the flowfield in the inlet.

Dilley, A. D.↗

NASA NTRS2007

Enhanced Elliptic Grid Generation

Method and system for generating an elliptic grid in generalized coordinates in two or three dimensions, where one or more decay parameters near a boundary segment of a grid are determined as part of the grid solution, rather than being prescribed initially by a user. The decay parameters may vary with one or more generalized coordinates and determine the rate(s) at which separation distances between adjacent grid lines change as one moves toward or away from a grid boundary segment.

Kaul, Upender K.↗

NASA NTRS1984

Multigrid techniques for the numerical solution of the diffusion equation

An accurate numerical solution of diffusion problems containing large local gradients can be obtained with a significant reduction in computational time by using a multigrid computational scheme. The spatial domain is covered with sets of uniform square grids of different sizes. The finer grid patterns overlap the coarse grid patterns. The finite-difference expressions for each grid pattern are solved independently by iterative techniques. Two interpolation methods were used to establish the values of the potential function on the fine grid boundaries with information obtained from the coarse grid solution. The accuracy and computational requirements for solving a test problem by a simple multigrid and a multilevel-multigrid method were compared. The multilevel-multigrid method combined with a Taylor series interpolation scheme was found to be best.

Phillips, R. E.↗

NASA NTRS1992

CFD applications in pump flows

The objective of the proposed paper is to develop a computational procedure that solves incompressible Navier-Stokes equations for pump flows. The solution method is based on the pseudo-compressibility approach and uses an implicit-upwind differencing scheme together with the Gauss-Seidel line relaxation method. The equations are solved in steadily rotating reference frames and the centrifugal force and the Coriolis force are added to the equation of motion. As a benchmark problem, the flow through the Rocketdyne inducer is numerically simulated. A coarse grid solution is obtained with a single zone by using an algebraic turbulence model. In multi-zone fine grid computation, a one-equation Baldwin-Barth turbulence model is utilized. Numerical results are compared with experimental measurements and a good agreement is found between the two. The resulting computer code is then applied to the flow analysis inside a two-stage fuel pump impeller operating at 80 percent, 100 percent, and 120 percent of design flow.

Kiris, Cetin↗

NASA NTRS2005

GLIDE: a grid-based light-weight infrastructure for data-intensive environments

The promise of the grid is that it will enable public access and sharing of immense amounts of computational and data resources among dynamic coalitions of individuals and institutions. However, the current grid solutions make several limiting assumptions that curtail their widespread adoption. To address these limitations, we present GLIDE, a prototype light-weight, data-intensive middleware infrastructure that enables access to the robust data and computational power of the grid on DREAM platforms.

PRISM-MW↗

NASA NTRS2001

Generic Aerothermodynamic Database

The aerothermodynamic database consists of Navier-Stokes solutions in PLOT3D format for the spherical-like nose cap of the X-38. These solutions are chosen to follow a reentry trajectory. The Mach number varies from 7.89 to 1.72 while the angle of attack varies from 38.73 degrees to 17.08 degrees. The Reynolds number varies from 4.139E6 to 2.766E7. Coarse, Medium and Fine grid solutions are supplied for each point in the data base. In addition to the flow solutions, a table of force and moment coefficients as well as the maximum heat transfer coefficient is also stored in the database.

Olsen, Thomas H.↗

NASA NTRS1988

Solution of the Neumann pressure problem in general orthogonal coordinates using the multigrid technique

The multigrid (MG) technique has been advanced for use with Neumann boundary-value problems in clustered curvilinear orthogonal coordinates. This comprises an important step in the analysis of incompressible flow using the velocity-pressure formulation of the Navier-Stokes equations. The finite-difference representation of the problem and the formulation of the restriction and coarse-grid correction operators are examined in detail. Maintaining consistency between these and the integral constraint associated with the Neumann problem is found to be critical for the success of the MG technique. The influence of the smoothing operator is examined by employing Gauss-Seidel, alternating-direction implicit, and strongly implicit techniques. The MG procedure enhances the efficiency of fine-grid solutions of the Neumann problem by a factor of 3 to 14, depending on the type of smoothing operator employed and the values of the problem parameters.

Ghia, U.↗

NASA NTRS1989

An adaptive embedded mesh procedure for leading-edge vortex flows

A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.

Powell, Kenneth G.↗

DOE OSTI2025

Grid Architecture Mapping to Understand Transformation (GAMUT): Concept Definition

The electric power system is undergoing significant transformation driven by changes in the generation mix, increasing reliance on information and communication technologies, evolving customer expectations, and a dynamic cyber-physical environment. To address these challenges, substantial investments will be made over the next decade to create a flexible, affordable, secure, reliable, and resilient electric system. In response, the U.S. Department of Energy's Office of Electricity is developing knowledge management tools aimed at systematically documenting technology pilots and demonstration projects. This initiative seeks to improve understanding of operating contexts, planning steps, and integration requirements for innovative grid technologies. The Department of Energy project leverages Grid Architecture principles to collect and organize insights into the interdependencies, requirements, and capabilities of various grid solutions. By employing a systematic approach, the project aims to perform a feasibility study for the development of a software tool that will support stakeholders, including regulators, transmission and distribution system operators, distributed energy resources aggregators, and technology providers. By offering a systematic, software-based framework to document technologies, understand their benefits and impacts, and inform deployment strategies, the proposed Grid Architecture Mapping to Understand Transformation (GAMUT) Tool is intended to reduce costs, enhance decision-making, and facilitate scaling and effective deployment of new technologies. The feasibility study will evaluate the technical and financial viability of the GAMUT Tool, identifying stakeholder needs and assessing risks and mitigation strategies. Ultimately, the GAMUT team aims to develop an initial minimal viable product, followed by staged improvements, to aid in the modernization of the electric grid, contributing to a more sustainable and resilient energy future.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗