SEARCH · Engineering Papers

Results for “Euler flow”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 667 records · Page 37

All sources NASA NTRS DOE OSTI

NASA NTRS1997

CFD Analysis and Design Optimization Using Parallel Computers

A versatile and efficient multi-block method is presented for the simulation of both steady and unsteady flow, as well as aerodynamic design optimization of complete aircraft configurations. The compressible Euler and Reynolds Averaged Navier-Stokes (RANS) equations are discretized using a high resolution scheme on body-fitted structured meshes. An efficient multigrid implicit scheme is implemented for time-accurate flow calculations. Optimum aerodynamic shape design is achieved at very low cost using an adjoint formulation. The method is implemented on parallel computing systems using the MPI message passing interface standard to ensure portability. The results demonstrate that, by combining highly efficient algorithms with parallel computing, it is possible to perform detailed steady and unsteady analysis as well as automatic design for complex configurations using the present generation of parallel computers.

Martinelli, Luigi↗

NASA NTRS2002

Progress in the Simulation of Steady and Time-Dependent Flows with 3D Parallel Unstructured Cartesian Methods

The proposed paper will present recent extensions in the development of an efficient Euler solver for adaptively-refined Cartesian meshes with embedded boundaries. The paper will focus on extensions of the basic method to include solution adaptation, time-dependent flow simulation, and arbitrary rigid domain motion. The parallel multilevel method makes use of on-the-fly parallel domain decomposition to achieve extremely good scalability on large numbers of processors, and is coupled with an automatic coarse mesh generation algorithm for efficient processing by a multigrid smoother. Numerical results are presented demonstrating parallel speed-ups of up to 435 on 512 processors. Solution-based adaptation may be keyed off truncation error estimates using tau-extrapolation or a variety of feature detection based refinement parameters. The multigrid method is extended to for time-dependent flows through the use of a dual-time approach. The extension to rigid domain motion uses an Arbitrary Lagrangian-Eulerlarian (ALE) formulation, and results will be presented for a variety of two- and three-dimensional example problems with both simple and complex geometry.

Aftosmis, M. J.↗

NASA NTRS1984

User's guide for NASCRIN: A vectorized code for calculating two-dimensional supersonic internal flow fields

A computer program NASCRIN has been developed for analyzing two-dimensional flow fields in high-speed inlets. It solves the two-dimensional Euler or Navier-Stokes equations in conservation form by an explicit, two-step finite-difference method. An explicit-implicit method can also be used at the user's discretion for viscous flow calculations. For turbulent flow, an algebraic, two-layer eddy-viscosity model is used. The code is operational on the CDC CYBER 203 computer system and is highly vectorized to take full advantage of the vector-processing capability of the system. It is highly user oriented and is structured in such a way that for most supersonic flow problems, the user has to make only a few changes. Although the code is primarily written for supersonic internal flow, it can be used with suitable changes in the boundary conditions for a variety of other problems.

Kumar, A.↗

NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

Batina, John T.↗

NASA NTRS1983

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results in substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed.

Johnson, G. M.↗

NASA NTRS1983

Multiple-grid convergence acceleration of viscous and inviscid flow computations

A multiple-grid algorithm for use in efficiently obtaining steady solution to the Euler and Navier-Stokes equations is presented. The convergence of a simple, explicit fine-grid solution procedure is accelerated on a sequence of successively coarser grids by a coarse-grid information propagation method which rapidly eliminates transients from the computational domain. This use of multiple-gridding to increase the convergence rate results is substantially reduced work requirements for the numerical solution of a wide range of flow problems. Computational results are presented for subsonic and transonic inviscid flows and for laminar and turbulent, attached and separated, subsonic viscous flows. Work reduction factors as large as eight, in comparison to the basic fine-grid algorithm, were obtained. Possibilities for further performance improvement are discussed. Previously announced in STAR as N83-21847

Johnson, G. M.↗

NASA NTRS1992

High angle of attack: Aerodynamics

The ability to predict high angle of attack, nonlinear, aerodynamic characteristics of flight vehicles, including aircraft, has made significant progress in the last 25 years using computational tools and analyses. The key technological element which has made these analyses possible is the ability to account for the influence of the shed vortical flow, prevalent in this angle of attack range, on geometries of interest. Using selected analysis techniques, applications have also been made to wing design in order to improve their high speed maneuver performance. Various techniques, associated with different levels of accuracy, exist to model this vortical flow influence. The ones included in this paper cover: suction analogy with extensions; free vortex filaments; free vortex sheet modeling; and Euler and Navier-Stokes solutions. Associated relevant features of vortices are also addressed, including: the wing and flow conditions which cause vortex formation; and how the vortex strength varies with angle of attack and wing sweep.

John E. Lamar↗

NASA NTRS1989

Influence of wing geometry on leading-edge vortices and vortex-induced aerodynamics at supersonic speeds

An assessment of the influence of wing geometry on wing leading-edge vortex flows at supersonic speeds is discussed as well as the applicability of various aerodynamic codes for predicting these results. A series of delta-wing wind-tunnel models were tested in the NASA Langley Research Center Unitary Plan Wind Tunnel over a Mach number range from 1.6 to 4.6. The data show that wing airfoil has a significant impact on the localized loading on the wing. The experimental data for the flat wings were compared with results from full-potential, Euler, and Parabolized Navier-Stokes (PNS) computer codes. The theoretical evaluation showed that the full-potential analysis predicted accurate results for the attached-flow (alpha = 0 deg) conditions and that the Euler and PNS analyses made reasonable predictions for both attached and separated flow conditions.

Wood, Richard M.↗

NASA NTRS2009

Adiabatic Shock Capturing in Perfect Gas Hypersonic Flows

This paper considers the streamline-upwind Petrov/Galerkin (SUPG) method applied to the compressible Euler and Navier-Stokes equations in conservation-variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, is briefly reviewed. Of particular interest is the behavior of the shock capturing operator, which is required to regularize the scheme in the presence of strong, shock-induced gradients. A standard shock capturing operator which has been widely used in previous studies by several authors is presented and discussed. Specific modifications are then made to this standard operator which are designed to produce a more physically consistent discretization in the presence of strong shock waves. The actual implementation of the term in a finite dimensional approximation is also discussed. The behavior of the standard and modified scheme is then compared for several supersonic/hypersonic flows. The modified shock capturing operator is found to preserve enthalpy in the inviscid portion of the flowfield substantially better than the standard operator.

Kirk, Benjamin S.↗

NASA NTRS1989

Vector potential methods

Vector potential and related methods, for the simulation of both inviscid and viscous flows over aerodynamic configurations, are briefly reviewed. The advantages and disadvantages of several formulations are discussed and alternate strategies are recommended. Scalar potential, modified potential, alternate formulations of Euler equations, least-squares formulation, variational principles, iterative techniques and related methods, and viscous flow simulation are discussed.

Hafez, M.↗

NASA NTRS1990

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Batina, John T.↗

NASA NTRS1985

An implicit, conservative, zonal-boundary scheme for Euler equation calculations

A zonal, or patched, grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative, zonal boundary condition that could be used with explicit schemes was extended so that it can be used with existing second order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, M. M.↗

NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

A method for accurately solving inviscid compressible flow in the subcritical and supercritical regimes about complex configurations is presented. The method is based on the use of unstructured triangular meshes in two dimensions, and special emphasis is placed on the accuracy and efficiency of the solutions. High accuracy is achieved by careful scaling of the artificial dissipation terms, and by reformulating the inner and outer boundary conditions for both the convective and dissipative operators. An adaptive grid refinement strategy is presented which enhances the solution accuracy for complex flows. When coupled with an unstructured multigrid algorithm, this method is shown to produce an efficient solver for flows about arbitrary configurations.

Mavriplis, Dimitri J.↗

NASA NTRS1988

Accurate multigrid solution of the Euler equations on unstructured and adaptive meshes

Mavriplis, Dimitri J.↗

NASA NTRS1991

A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

Scott, James R.↗

NASA NTRS1990

Theory on instability and transition

The fundamental fluid dynamics governing instability and transition to turbulence in boundary layers are considered, and attention is focused on the key aspects of nonlinear dynamics central to the transition process and to turbulent boundary-layer phenomena. Emphasis is placed on truly nonlinear theories, in which the boundary layer mean-flow profile is completely altered from its original form. Nonlinear TS transitions, Euler-stage interactions, and vortex/wave interactions are discussed, and compressible boundary layers are analyzed. Connections with experiments and computations are outlined, along with overall trends including the extension of the nonlinear theory and the advancement in the compressible and other flow regimes.

Smith, Frank T.↗

NASA NTRS1988

High-resolution shock-capturing schemes for inviscid and viscous hypersonic flows

A class of implicit Total Variation Diminishing (TVD) type algorithms suitable for transonic and supersonic multidimensional Euler and Navier-Stokes equations was extended to hypersonic computations. The improved conservative shock-capturing schemes are spatially second- and third-order, and are fully implicit. They can be first- or second-order accurate in time and are suitable for either steady or unsteady calculations. Enhancement of stability and convergence rate for hypersonic flows is discussed. With the proper choice of the temporal discretization and suitable implicit linearization, these schemes are fairly efficient and accurate for very complex two-dimensional hypersonic inviscid and viscous shock interactions. This study is complimented by a variety of steady and unsteady viscous and inviscid hypersonic blunt-body flow computations. Due to the inherent stiffness of viscous flow problems, numerical experiments indicated that the convergence rate is in general slower for viscous flows than for inviscid steady flows.

Yee, H. C.↗

NASA NTRS1992

A numerical resolution study of high order essentially non-oscillatory schemes applied to incompressible flow

High order essentially non-oscillatory (ENO) schemes, originally designed for compressible flow and in general for hyperbolic conservation laws, are applied to incompressible Euler and Navier-Stokes equations with periodic boundary conditions. The projection to divergence-free velocity fields is achieved by fourth order central differences through Fast Fourier Transforms (FFT) and a mild high-order filtering. The objective of this work is to assess the resolution of ENO schemes for large scale features of the flow when a coarse grid is used and small scale features of the flow, such as shears and roll-ups, are not fully resolved. It is found that high-order ENO schemes remain stable under such situations and quantities related to large-scale features, such as the total circulation around the roll-up region, are adequately resolved.

Weinan, E.↗