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NASA NTRS1997

Rapid Decimation for Direct Volume Rendering

An approach for eliminating unnecessary portions of a volume when producing a direct volume rendering is described. This reduction in volume size sacrifices some image quality in the interest of rendering speed. Since volume visualization is often used as an exploratory visualization technique, it is important to reduce rendering times, so the user can effectively explore the volume. The methods presented can speed up rendering by factors of 2 to 3 with minor image degradation. A family of decimation algorithms to reduce the number of primitives in the volume without altering the volume's grid in any way is introduced. This allows the decimation to be computed rapidly, making it easier to change decimation levels on the fly. Further, because very little extra space is required, this method is suitable for the very large volumes that are becoming common. The method is also grid-independent, so it is suitable for multiple overlapping curvilinear and unstructured, as well as regular, grids. The decimation process can proceed automatically, or can be guided by the user so that important regions of the volume are decimated less than unimportant regions. A formal error measure is described based on a three-dimensional analog of the Radon transform. Decimation methods are evaluated based on this metric and on direct comparison with reference images.

Gibbs, Jonathan↗

NASA NTRS1995

Moving and adaptive grid methods for compressible flows

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.

Trepanier, Jean-Yves↗

NASA NTRS2019

Geometry Modeling for Unstructured Mesh Adaptation

The quantification and control of discretization error is critical to obtaining reliable simulation results. Adaptive mesh techniques have the potential to automate discretization error control, but have made limited impact on production analysis workflow. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic mesh adaptation mechanics. However, the poor integration of initial mesh generation and adaptive mesh mechanics to typical sources of geometry has hindered adoption of adaptive mesh techniques, where these geometries are often created in Mechanical Computer- Aided Design (MCAD) systems. The difficulty of this coupling is compounded by two factors: the inherent complexity of the model (e.g., large range of scales, bodies in proximity, details not required for analysis) and unintended geometry construction artifacts (e.g., translation, uneven parameterization, degeneracy, self-intersection, sliver faces, gaps, large tolerances be- tween topological elements, local high curvature to enforce continuity). Manual preparation of geometry is commonly employed to enable fixed-grid and adaptive-grid workflows by reducing the severity and negative impacts of these construction artifacts, but manual process interaction inhibits workflow automation. Techniques to permit the use of complex geometry models and reduce the impact of geometry construction artifacts on unstructured grid workflows are models from the AIAA Sonic Boom and High Lift Prediction are shown to demonstrate the utility of the current approach.

Park, Michael A.↗

NASA NTRS2011

Summary of the First AIAA CFD High Lift Prediction Workshop (invited)

The 1st AIAA CFD High Lift Prediction Workshop was held in Chicago in June 2010. The goals of the workshop included an assessment of the numerical prediction capability of current-generation CFD technology/ codes for swept, medium/high-aspect ratio wings in landing/take-off (high lift) configurations. 21 participants from 8 countries and 18 organizations, submitted a total of 39 datasets of CFD results. A variety of grid systems (both structured and unstructured) were used. Trends due to flap angle were analyzed, and effects of grid family, grid density, solver, and turbulence model were addressed. Some participants also assessed the effects of support brackets used to attach the flap and slat to the main wing. This invited paper describes the combined results from all workshop participants. Comparisons with experimental data are made. A statistical summary of the CFD results is also included.

Rumsey, C. L.↗

NASA NTRS2010

TPSAS-NF1676L-10980-DND

We plan to perform the following sets of computations on unadapted (fixed) grids: 1) Structured RANS set 1 (Code: CFL3D, Grid: Str-OnetoOne-A-v1 (supplied by HiLiftPW-1 committee), Turbulence model: Spalart-Allmaras), 2) Structured RANS set 2 (Code: CFL3D, Grid: Str-OnetoOne-A-v1 (supplied by HiLiftPW-1 committee), Turbulence model: Menter SST), 3) Structured RANS set 3 (time permitting) (Code: CFL3D, Grid: Str-OnetoOne-B-v1 (supplied by HiLiftPW-1 committee), Turbulence model: Menter SST), 4) Unstructured RANS set 1 (Code: FUN3D, Grid: Unst-Mixed-FromTet-Nodecentered-A-v1 (supplied by HiLiftPW-1 committee), Turbulence model: Spalart-Allmaras), and 5) Unstructured RANS set 2 (time permitting) (Code: FUN3D, Grid: Unst-Hex-FromOnetoOne-A-v1 (supplied by HiLiftPW-1 committee), Turbulence model: Spalart-Allmaras),. Optional case 3 is not being computed. CFL3D is a structured upwind-biased cell-centered RANS code,1 and FUN3D is an unstructured upwind-biased node-centered RANS code

Elizabeth M Lee-Rausch↗

NASA NTRS2010

TPSAS-NF1676L-10454-DND

C L Rumsey↗

NASA NTRS1997

Sensitivity Analysis and Optimization of Aerodynamic Configurations with Blend Surfaces

A novel (geometrical) parametrization procedure using solutions to a suitably chosen fourth order partial differential equation is used to define a class of airplane configurations. Inclusive in this definition are surface grids, volume grids, and grid sensitivity. The general airplane configuration has wing, fuselage, vertical tail and horizontal tail. The design variables are incorporated into the boundary conditions, and the solution is expressed as a Fourier series. The fuselage has circular cross section, and the radius is an algebraic function of four design parameters and an independent computational variable. Volume grids are obtained through an application of the Control Point Form method. A graphic interface software is developed which dynamically changes the surface of the airplane configuration with the change in input design variable. The software is made user friendly and is targeted towards the initial conceptual development of any aerodynamic configurations. Grid sensitivity with respect to surface design parameters and aerodynamic sensitivity coefficients based on potential flow is obtained using an Automatic Differentiation precompiler software tool ADIFOR. Aerodynamic shape optimization of the complete aircraft with twenty four design variables is performed. Unstructured and structured volume grids and Euler solutions are obtained with standard software to demonstrate the feasibility of the new surface definition.

Thomas, A. M.↗

NASA NTRS2003

Toward Immersed Boundary Simulation of High Reynolds Number Flows

In the immersed boundary (IB) method, the surface of an object is reconstructed with forcing terms in the underlying flow field equations. The surface may split a computational cell removing the constraint of the near wall gridlines to be aligned with the surface. This feature greatly simplifies the grid generation process which is cumbersome and expensive in particular for structured grids and complex geometries. The IB method is ideally suited for Cartesian flow solvers. The flow equations written in Cartesian coordinates appear in a very simple form and several numerical algorithms can be used for an efficient solution of the equations. In addition, the accuracy of numerical algorithms is dependent on the underlying grid and it usually deteriorates when the grid deviates from a Cartesian mesh. The challenge for the IB method lies in the representation of the wall boundaries and in providing an adequate near wall flow field resolution. The issue of enforcing no-slip boundary conditions at the immersed surface has been addressed by several authors by imposing a local reconstruction of the solution. Initial work by Verzicco et al. was based on a simple linear, one-dimensional operator and this approach proved to be accurate for boundaries largely aligned with the grid lines. Majumdar et al. used various multidimensional and high order polynomial interpolations schemes. These high order schemes, however, are keen to introduce wiggles and spurious extrema. Iaccarino & Verzicco and Kalitzin & Iaccarino proposed a tri-linear reconstruction for the velocity components and the turbulent scalars. A modified implementation that has proven to be more robust is reported in this paper. The issue of adequate near wall resolution in a Cartesian framework can initially be addressed by using a non-uniform mesh which is stretched near the surface. In this paper, we investigate an unstructured approach for local grid refinement that utilizes Cartesian mesh features. The computation of high Reynolds number wall bounded flows is particularly challenging as it requires the consideration of thin turbulent boundary layers, i.e. near wall regions with large gradients of the flow field variables. For such flows, the representation of the wall boundary has a large impact on the accuracy of the computation. It is also critical for the robustness and convergence of the flow solver.

Kalitzin, Georgi↗

NASA NTRS1988

Finite element Euler computations in three dimensions

A two-step explicit FEM solution algorithm for the three-dimensional compressible Euler and Navier-Stokes equations based on unstructured triangular and tetrahedral grids is described and demonstrated. The method represents an extension and refinement of the algorithms presented by Loehner et al. (1984 and 1985), Peraire et al. (1987), and Morgan et al. (1987). The formulation and numerical implementation are outlined; the mesh generation, data structures, and adaptive remeshing are explained; and results for a two-dimensional airfoil, a three-dimensional engine air intake, a B747 in landing configuration, and a generic fighter aircraft are presented in extensive graphics and discussed in detail.

Peraire, Jaime↗

NASA NTRS1989

TranAir: Recent advances and applications

TranAir is a computer code which solves the full-potential equation for transonic flow about very general and complex configurations. Piecewise flat surface panels are used to describe the surface geometry. This paneled definition is then embedded in an unstructured cartesian flow field grid. Finite elements are used in the discretization of the flow field grid in a manner which is fully conservative and second-order accurate. Since geometries may be defined with relative ease, and since the user is not involved in the generation of the flow field grid, computational results may be generated rather quickly for a wide range of geometries. For transonic cases in the cruise angle-of-attack range, TranAir has generated results which are in generally good agreement with both Euler results and wind tunnel data. A typical transonic case runs in 1 to 2 CPU hours on a Cray X-MP. For subcritical cases, the code runs in 15 to 30 CPU minutes, even for geometries in which several thousand surface panels are used in the definition. This ability to rapidly and accurately provide both subsonic and transonic predictions about very complex aircraft configurations gives TranAir the potential of being a very powerful and widely used design tool.

Madson, Michael D.↗

NASA NTRS1992

Finite-element solution scheme for compressible viscous flow

Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.

Hassan, O.↗

NASA NTRS1995

Full-Wave Analysis Of MMICs Using A Generalized Yee Algorithm

Improved method of temporal analysis of propagation of electro-magnetic waves in monolithic microwave integrated circuits (MMICs) implemented by generalized version of traditional Yee algorithm. Provides more accurate mathematical modeling for analysis and design of MMICs. Based on unstructured and otherwise irregular grids. Grids readily fitted to conductive and dielectric circuit elements having realistically complex three-dimensional shapes. Better for modeling important and geometrically complex phenomena like fringing fields.

Lansing, Faiza S.↗

NASA NTRS1996

Computational Study of a McDonnell Douglas Single-Stage-to-Orbit Vehicle Concept for Aerodynamic Analysis

This paper presents the results of a computational flow analysis of the McDonnell Douglas single-stage-to-orbit vehicle concept designated as the 24U. This study was made to determine the aerodynamic characteristics of the vehicle with and without body flaps over an angle of attack range of 20-40 deg. Computations were made at a flight Mach number of 20 at 200,000 ft. altitude with equilibrium air, and a Mach number of 6 with CF4 gas. The software package FELISA (Finite Element Langley imperial College Sawansea Ames) was used for all the computations. The FELISA software consists of unstructured surface and volume grid generators, and inviscid flow solvers with (1) perfect gas option for subsonic, transonic, and low supersonic speeds, and (2) perfect gas, equilibrium air, and CF4 options for hypersonic speeds. The hypersonic flow solvers with equilibrium air and CF4 options were used in the present studies. Results are compared with other computational results and hypersonic CF4 tunnel test data.

Prabhu, Ramadas K.↗

NASA NTRS1999

An Inviscid Computational Study of an X-33 Configuration at Hypersonic Speeds

This report documents the results of a study conducted to compute the inviscid longitudinal aerodynamic characteristics of a simplified X-33 configuration. The major components of the X-33 vehicle, namely the body, the canted fin, the vertical fin, and the body-flap, were simulated in the CFD (Computational Fluid Dynamic) model. The rear-ward facing surfaces at the base including the aerospike engine surfaces were not simulated. The FELISA software package consisting of an unstructured surface and volume grid generator and two inviscid flow solvers was used for this study. Computations were made for Mach 4.96, 6.0, and 10.0 with perfect gas air option, and for Mach 10 with equilibrium air option with flow condition of a typical point on the X-33 flight trajectory. Computations were also made with CF4 gas option at Mach 6.0 to simulate the CF4 tunnel flow condition. An angle of attack range of 12 to 48 deg was covered. The CFD results were compared with available wind tunnel data. Comparison was good at low angles of attack; at higher angles of attack (beyond 25 deg) some differences were found in the pitching moment. These differences progressively increased with increase in angle of attack, and are attributed to the viscous effects. However, the computed results showed the trends exhibited by the wind tunnel data.

Prabhu, Ramadas K.↗

NASA NTRS2011

Summary of the Tandem Cylinder Solutions from the Benchmark Problems for Airframe Noise Computations-I Workshop

Fifteen submissions in the tandem cylinders category of the First Workshop on Benchmark problems for Airframe Noise Computations are summarized. Although the geometry is relatively simple, the problem involves complex physics. Researchers employed various block-structured, overset, unstructured and embedded Cartesian grid techniques and considerable computational resources to simulate the flow. The solutions are compared against each other and experimental data from 2 facilities. Overall, the simulations captured the gross features of the flow, but resolving all the details which would be necessary to compute the noise remains challenging. In particular, how to best simulate the effects of the experimental transition strip, and the associated high Reynolds number effects, was unclear. Furthermore, capturing the spanwise variation proved difficult.

Lockard, David P.↗

NASA NTRS2019

Computational Analysis of the External Aerodynamics of the Unpowered X-57 Mod-III Aircraft

Investigations of the external aerodynamics of the unpowered X-57 Mod-III configuration using computational fluid dynamics are presented. Two different Reynolds-averaged Navier-Stokes flow solvers were used in the analysis: the STAR-CCM+ unstructured solver using polyhedral grid topology, and the Launch Ascent Vehicle Aerodynamics (LAVA) structured curvilinear flow solver using structured overset grid topology. A grid refinement study was conducted and suitable grid resolution was determined by examining the forces and moments of the aircraft. Code-to-code comparison shows that STAR-CCM+ and LAVA are in good agreement both in quantitative values and trends. The angle-of-attack sweep and sideslip-angle sweep were performed. Results indicate that lift coefficients have a sharp drop at stall. At high angle of attack, STAR-CCM+ and LAVA show different flow separation behavior possibly due to differences in the turbulence model. The sideslip-angle sweep results show constant pitching moment from 0° to 15°, then a sharp increase between 15° and 20° sideslip angle.

Yoo, Seung Y.↗

NASA NTRS2019

High-Fidelity Multidisciplinary Sensitivity Analysis Framework for Multipoint Rotorcraft Optimization

A multidisciplinary, gradient-based sensitivity-analysis methodology is evaluated for optimization of rotorcraft configurations. The tightly coupled discipline models include physics-based fluid dynamics and rotorcraft comprehensive analysis. A discretely-consistent adjoint method accounts for sensitivities of the unsteady flow and unstructured, dynamic, over set grids, while sensitivities of structural responses to aerodynamic loads are computed using a complex-variable method. The methodology is applied to optimize the shape of UH-60A Blackhawk helicopter blades for hover and forward flight conditions. The objective of the multipoint design is to simultaneously increase the rotorcraft figure of merit in a hover flight and reduce the rotor power in a forward flight. Trimmed loose-coupling solutions for the baseline configuration are used to initiate the tight-coupling multidisciplinary analysis. Target thrust and rolling and pitching moments are enforced as optimization constraints. The optimized configuration improves the optimization metrics at both design points. The improved performance and all constraints are maintained over many revolutions beyond the optimization interval, satisfying the required flight conditions. Computational cost of the optimization cycle is assessed in a high-performance computing environment and found affordable for design of rotorcraft in general level-flight conditions.

Wang, Li↗

NASA NTRS1990

Adaptive grid embedding for the two-dimensional flux-split Euler equations

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.

Warren, Gary Patrick↗