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At least 613 records · Page 34

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NASA NTRS1998

Perfectly Matched Layer for Linearized Euler Equations in Open and Ducted Domains

Recently, perfectly matched layer (PML) as an absorbing boundary condition has widespread applications. The idea was first introduced by Berenger for electromagnetic waves computations. In this paper, it is shown that the PML equations for the linearized Euler equations support unstable solutions when the mean flow has a component normal to the layer. To suppress such unstable solutions so as to render the PML concept useful for this class of problems, it is proposed that artificial selective damping terms be added to the discretized PML equations. It is demonstrated that with a proper choice of artificial mesh Reynolds number, the PML equations can be made stable. Numerical examples are provided to illustrate that the stabilized PML performs well as an absorbing boundary condition. In a ducted environment, the wave mode are dispersive. It will be shown that the group velocity and phase velocity of these modes can have opposite signs. This results in a confined environment, PML may not be suitable as an absorbing boundary condition.

Tam, Christopher K. W.↗

NASA NTRS1999

Computational Assessment of Aft-Body Closure for the HSR Reference H Configuration

A study has been conducted to determine how well the USM3D unstructured Euler solver can be utilized to predict the flow over the High Speed Research (HSR) Reference H configuration with an ultimate goal of prediction of Sting interference so after body closure effects may be evaluated. This study has shown that the code can be used to predict the interference effects of a lower mounted blade sting with a high degree of confidence. It has been shown that wing and fuselage pressures, both levels and trends, can be predicted well. Force and moment levels are not predicted well but experimental trends are predicted. Based upon this, predicted force and moment increments are assumed to be predicted accurately. Deflection of the horizontal tail was found to cause a non-linear increment from the non-deflected sting interference effects.

Londenberg, W. Kelly↗

NASA NTRS1998

An Astronomical Test of CCD Photometric Precision

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques. we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Koch, David↗

NASA NTRS1999

A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems

This article considers a posteriori error estimation of specified functionals for first-order systems of conservation laws discretized using the discontinuous Galerkin (DG) finite element method. Using duality techniques, we derive exact error representation formulas for both linear and nonlinear functionals given an associated bilinear or nonlinear variational form. Weighted residual approximations of the exact error representation formula are then proposed and numerically evaluated for Ringleb flow, an exact solution of the 2-D Euler equations.

Larson, Mats G.↗

NASA NTRS1995

A Hybrid Parallel Preconditioning Algorithm For CFD

A new hybrid preconditioning algorithm will be presented which combines the favorable attributes of incomplete lower-upper (ILU) factorization with the favorable attributes of the approximate inverse method recently advocated by numerous researchers. The quality of the preconditioner is adjustable and can be increased at the cost of additional computation while at the same time the storage required is roughly constant and approximately equal to the storage required for the original matrix. In addition, the preconditioning algorithm suggests an efficient and natural parallel implementation with reduced communication. Sample calculations will be presented for the numerical solution of multi-dimensional advection-diffusion equations. The matrix solver has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The full paper will show numerous examples in CFD to demonstrate the efficiency and robustness of the method.

Barth,Timothy J.↗

NASA NTRS1996

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗

NASA NTRS1995

CFD-Based Design Optimization Tool Developed for Subsonic Inlet

The traditional approach to the design of engine inlets for commercial transport aircraft is a tedious process that ends with a less-than-optimum design. With the advent of high-speed computers and the availability of more accurate and reliable computational fluid dynamics (CFD) solvers, numerical optimization processes can effectively be used to design an aerodynamic inlet lip that enhances engine performance. The designers' experience at Boeing Corporation showed that for a peak Mach number on the inlet surface beyond some upper limit, the performance of the engine degrades excessively. Thus, our objective was to optimize efficiency (minimize the peak Mach number) at maximum cruise without compromising performance at other operating conditions. Using a CFD code NPARC, the NASA Lewis Research Center, in collaboration with Boeing, developed an integrated procedure at Lewis to find the optimum shape of a subsonic inlet lip and a numerical optimization code, ADS. We used a GRAPE-based three-dimensional grid generator to help automate the optimization procedure. The inlet lip shape at the crown and the keel was described as a superellipse, and the superellipse exponents and radii ratios were considered as design variables. Three operating conditions: cruise, takeoff, and rolling takeoff, were considered in this study. Three-dimensional Euler computations were carried out to obtain the flow field. At the initial design, the peak Mach numbers for maximum cruise, takeoff, and rolling takeoff conditions were 0.88, 1.772, and 1.61, respectively. The acceptable upper limits on the takeoff and rolling takeoff Mach numbers were 1.55 and 1.45. Since the initial design provided by Boeing was found to be optimum with respect to the maximum cruise condition, the sum of the peak Mach numbers at takeoff and rolling takeoff were minimized in the current study while the maximum cruise Mach number was constrained to be close to that at the existing design. With this objective, the optimum design satisfied the upper limits at takeoff and rolling takeoff while retaining the desirable cruise performance. Further studies are being conducted to include static and cross-wind operating conditions in the design optimization procedure. This work was carried out in collaboration with Dr. E.S. Reddy of NYMA, Inc.

Source record↗

NASA NTRS2017

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

This paper presents results from numerical experiments for controlling the error caused by a damping layer boundary treatment when simulating the propagation of an acoustic signal from a continuous pressure source. The computations are with the 2D Linearized Euler Equations (LEE) for both a uniform mean flow and a steady parallel jet. The numerical experiments are with algorithms that are third, fifth, seventh and ninth order accurate in space and time. The numerical domain is enclosed in a damping layer boundary treatment. The damping is implemented in a time accurate manner, with simple polynomial damping profiles of second, fourth, sixth and eighth power. At the outer boundaries of the damping layer the propagating solution is uniformly set to zero. The complete boundary treatment is remarkably simple and intrinsically independant from the dimension of the spatial domain. The reported results show the relative effect on the error from the boundary treatment by varying the damping layer width, damping profile power, damping amplitude, propagtion time, grid resolution and algorithm order. The issue that is being addressed is not the accuracy of the numerical solution when compared to a mathematical solution, but the effect of the complete boundary treatment on the numerical solution, and to what degree the error in the numerical solution from the complete boundary treatment can be controlled. We report maximum relative absolute errors from just the boundary treatment that range from O[10-2] to O[10-7].

Algorithm↗

NASA NTRS2017

Numerical Experiments in Error Control for Sound Propagation Using a Damping Layer Boundary Treatment

Computational Aeroacoustics↗

NASA NTRS1975

Upwind second-order difference schemes and applications in unsteady aerodynamic flows

Explicit second-order upwind difference schemes in combination with spatially symmetric schemes can produce larger stability bounds and better numerical resolution than symmetric schemes alone. However, if conservation form is essential, a special operator is required for transition between schemes. An operational approach has been devised for deriving transition operators so that strict conservation and local consistency are maintained. Various aspects of hybrid schemes are studied numerically for model linear and nonlinear equations. To demonstrate the utility of combining two different algorithms, MacCormack's explicit, noncentered, second-order method is combined with a completely upwind version, and numerical solutions of the Euler equations are obtained for two-dimensional, transonic flows with embedded supersonic regions and shock waves. The general utility of the operational approach for combining schemes is emphasized by deriving a second-order conservative scheme for the steady transonic small-disturbance potential equation.

Warming, R. F.↗

NASA NTRS1983

A finite element solution of three-dimensional inviscid rotational flows through curved ducts

A previously developed two-dimensional finite element algorithm for the solution of steady Euler equations is extended to three-dimensional problems. Starting with the general three-dimensional problem, the formulation of steady, rotational flows is presented. The boundary conditions for steady flows where the rotationality is introduced through entropy or total enthalpy gradients are introduced. A three-dimensional flow through a curved duct is analyzed as a sample problem, demonstrating the efficiency of the relaxation scheme. The accuracy of the numerical results is investigated by calculating the velocity and vorticity distributions at different sections of the channel, including the exit.

Ecer, A.↗

NASA NTRS1981

Treatment of conical and nonconical supersonic flows by an implicit marching scheme applied to the full potential equation

An aerodynamic prediction technique based on the full potential equation in conservation form is developed for the treatment of supersonic flows. This technique bridges the gap between simplistic linear theory methods and complex Euler solvers. A novel local density linearization concept and a second order accurate retarded density scheme, both producing the correct artificial viscosity, are introduced in developing an implicit marching scheme for solving the scalar potential. Results for conical flows over delta wings and a wing-body combination and for non-conical flows over bodies of revolution at angles of attack are compared with Euler and nonconservative full potential calculations and experimental data. The present formulation requires an order of magnitude less computer time and significantly less computer memory over Euler codes and exhibits a considerable improvement in computational efficiency and generality over an existing nonconservative full potential code.

Shankar, V.↗

DOE OSTI2023

A numerical extension of the spatially-filtered Euler equations for contact discontinuities

Solving the spatially-filtered Euler equations with a kinetic energy-preserving centered discretization is an efficient framework for simulating shock-dominated flows. Here, the present work describes a numerical treatment of the spatially-filtered Euler equations to minimize oscillations when simulating contact discontinuities. To counteract dispersive errors inherent to centered schemes, a WENO-like correction term is applied to the enthalpy transport in the energy equation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1991

A multiblock/multigrid Euler analysis of a propfan transport with wing-mounted nacelles, including slipstream effects

A multiblock/multigrid computation of the inviscid flow over a wing-mounted propfan transport with propwash is presented. An explicit multistage scheme drives the integral Euler equations to a steady state solution, while an actuator disk approximates the slipstream effects of the propfan blades. Practical applications of detailed surface gridding, multiple block field grids and multigrid convergence acceleration are demonstrated.

Nishida, Brian A.↗

NASA NTRS1987

Analysis of Scramjet Inlets

NASCRIN program analyzes two-dimensional flow fields in supersoniccombustion ramjet (scramjet) inlets. Solves two-dimensional Euler or Navier-Stokes equations in conservative form by unsplit, explicit, two-step finite-difference method. More recent explicit/implicit, two-step scheme incorporated by analysis of viscous flow. Algebraic, two-layer eddy-viscosity model used for turbulent-flow calculations. Vectorized version, written for CDC CYBER 205, whereas scalar version, can be run on CRAY or other scalar computers.

Kumar, A.↗

NASA NTRS1994

Direct calculations of waves in fluid flows using high-order compact difference scheme

The solution of the unsteady Euler equations by a sixth-order compact difference scheme combined with a fourth-order Runge-Kutta method is investigated. Closed-form expression for the amplification factors and their corresponding dispersion correlations are obtained by Fourier analysis of the fully discretized, two-dimensional Euler equations. The numerical dissipation, dispersion, and anisotropic effects are assessed. It is found that the Courant-Friedrichs-Lewy (CFL) limit for stable calculations is about 0.8. For a CFL number equal to 0.6, the smallest wavelength which is resolved without numerical damping is about six - eight grid nodes. For phase speeds corresponding to acoustic waves, the corresponding time period is resolved by about 200 - 300 time steps. Three numerical examples of waves in compressible flow are included: (1) sound propagation in a duct with linear shear, (2) linear wave growth in a compressible free shear layer, and (3) vortex pairing in a compressible free shear layer perturbed at two frequencies.

Yu, Sheng-Tao↗

NASA NTRS1984

Prediction of the vortex wake for noncircular missiles in supersonic flow

Engineering prediction methods with the capability to calculate induced effects of lee-side separation vorticity associated with circular and noncircular missiles at high angles of attack in supersonic flow are compared. Methods of interest include a discrete vortex cloud technique, concentrated vortex models, and solutions of Euler's equations with specified separation. Comparison of measured and predicted surface pressure distributions and flow field surveys are presented for bodies with circular and elliptic cross sections. Two flow models for computing lee-side vortex-induced effects on control fins in the vicinity of the vortex field are examined, and suggestions regarding the appropriate flow model for specific situations are included.

Mendenhall, M. R.↗

NASA NTRS1983

New implicit boundary procedures - Theory and applications

Analytical techniques for the application of implicit boundary conditions for inviscid flows to shock and body boundary layer conditions involving the Euler equations are presented. The theory of characteristics is used to update boundary points with spatial second order accuracy. The method is useful for implicit schemes which feature approximate factorization, and as such is incorporated into an existing PNS code. Examples are provided in terms of flows over a cone, over a maneuverable reentry vehicle, and over a finned vehicle. Improvements in the convergence rate are demonstrated for the conical flow solutions.

Rai, M. M.↗