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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

3D Structured Grid Adaptation

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.

Banks, D. W.↗
NASA NTRS2002

On Accuracy of Adaptive Grid Methods for Captured Shocks

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.

Yamaleev, Nail K.↗
NASA NTRS1989

A Simple Algebraic Grid Adaptation Scheme with Applications to Two- and Three-dimensional Flow Problems

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented. The scheme locally adjusts the grid density based on gradients of selected flow variables from either finite difference or finite volume calculations. A user-prescribed grid stretching can be specified such that control of the grid spacing can be maintained in areas of known flowfield behavior. For example, the grid can be clustered near a wall for boundary layer resolution and made coarse near the outer boundary of an external flow. A grid smoothing technique is incorporated into the adaptive grid routine, which is found to be more robust and efficient than the weight function filtering technique employed by other researchers. Since the present algebraic scheme requires no iteration or solution of differential equations, the computer time needed for grid adaptation is trivial, making the scheme useful for three-dimensional flow problems. Applications to two- and three-dimensional flow problems show that a considerable improvement in flowfield resolution can be achieved by using the proposed adaptive grid scheme. Although the scheme was developed with steady flow in mind, it is a good candidate for unsteady flow computations because of its efficiency.

Hsu, Andrew T.↗
NASA NTRS1993

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 NTRS1989

A simple algebraic grid adaptation scheme with applications to two- and three-dimensional flow problems

An algebraic adaptive grid scheme based on the concept of arc equidistribution is presented which provides high flowfield resolution when applied to two-dimensional and three-dimensional flow problems. The present scheme locally adjusts the grid density using gradients of selected flow variables from either finite difference or finite volume calculations, and it can specify user-prescribed grid stretching such that control of the grid spacing can be maintained in areas of known flowfield behavior. A robust and efficient grid smoothing technique has been incorporated into the adaptive grid routine.

Hsu, Andrew T.↗
NASA NTRS2016

Near-Body Grid Adaption for Overset Grids

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.

Buning, Pieter G.↗
NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

Park, Michael A.↗
NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. Laminar flow over a delta wing is verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and pitching moment.

Park, Michael A.↗
NASA NTRS2018

Unstructured Grid Adaptation and Solver Technology for Turbulent Flows

Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.

Park, Michael A.↗
NASA NTRS1991

Grid quality improvement by a grid adaptation technique

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.

Lee, K. D.↗
NASA NTRS1992

Algebraic grid adaptation method using non-uniform rational B-spline surface modeling

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.

Yang, Jiann-Cherng↗
DOE OSTI2025

Adaptive Grid Redistribution for a 1D Model of Turbulence and Clouds

In global atmospheric models, resolving stratocumulus (Sc) in the vertical is computationally expensive. However, Sc appear only under special meteorological conditions. Therefore, there is motivation to refine the vertical grid levels adaptively. In order to facilitate the possibility of parallelization on graphical processing units, our grid adaptation method prescribes the number of vertical levels a priori. Then grid levels are relocated toward altitude ranges in need of refinement. Because the method relocates existing grid levels, rather than adding extra levels, there is a risk of creating regions with overly coarse grid spacing, that is, voids in the grid mesh. To prevent such voids from forming, a simple method is developed to impose a maximum grid spacing. To decide where to place enhanced resolution, the authors develop an empirical mesh refinement criterion. It refines grid spacing near the ground, near strong temperature gradients, and within clouds. Our grid adaptation method is implemented in a single-column model and evaluated on four test cases: decaying stratocumulus, developing shallow cumulus, a quasi-stationary stratocumulus deck, and the diurnal cycle of a dry boundary layer. In the stratocumulus cases, mesh refinement leads to improvements in both the time evolution of fields and their time averages. The other two cases show smaller differences.

Carstensen, Steffen [Univ. of Wisconsin, Milwaukee↗
NASA NTRS1993

General-Purpose Time-Accurate Adaptive-Grid Method

Adaptive-grid method provides for generation of time-accurate grids used to solve wide variety of problems numerically. Intended use in computation of compressible flows. Part of solution method including algebraic grid-movement scheme; algorithm solving, by use of explicit numerical-integration scheme, Euler equations of unsteady flow; and temporal coupling routine utilizing grid-prediction/correction method to link dynamic grid with Euler-equation-solving algorithm. Improves ability to adapt grid to multiple features of solution and involves use of coarse grid in prediction stage of temporal coupling reducing central-processing-unit cost of obtaining new grid.

Bockelie, Michael J.↗
NASA NTRS1994

Stability and error estimation for Component Adaptive Grid methods

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.

Oliger, Joseph↗
NASA NTRS1992

Interactive solution-adaptive grid generation procedure

TURBO-AD is a two dimensional interactive solution adaptive grid generation program. The code uniquely combines a grid adaptation technique that uses parametric mapping with control sources and an algebraic grid generation that uses control points into a single software package. The grid adaptation is achieved by first adapting the control points to a numerical solution in the parametric domain using the control sources obtained from flow properties. Then a new grid is generated from the adapted control net using the control point formulation. The new adapted grid in the parametric domain is then mapped back to the physical domain. 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 grid generation from the adapted control net is an efficient algebraic process.

Choo, Yung K.↗
NASA NTRS1990

Interactive grid adaption

An interactive grid adaption method is developed, discussed and applied to the unsteady flow about an oscillating airfoil. The user is allowed to have direct interaction with the adaption of the grid as well as the solution procedure. Grid points are allowed to adapt simultaneously to several variables. In addition to the theory and results, the hardware and software requirements are discussed.

Abolhassani, Jamshid S.↗
NASA NTRS1997

Load Balancing Sequences of Unstructured Adaptive Grids

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.

Biswas, Rupak↗
NASA NTRS1995

ICASE/LaRC Workshop on Adaptive Grid Methods

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.

South, Jerry C., Jr.↗