Engineering topics

Swanson, R. C.

Publications and source records attributed to Swanson, R. C..

At least 19 records

NASA NTRS2016

Comparison of NACA 0012 Laminar Flow Solutions: Structured and Unstructured Grid Methods

In this paper we consider the solution of the compressible Navier-Stokes equations for a class of laminar airfoil flows. The principal objective of this paper is to demonstrate that members of this class of laminar flows have steady-state solutions. These laminar airfoil flow cases are often used to evaluate accuracy, stability and convergence of numerical solution algorithms for the Navier-Stokes equations. In recent years, such flows have also been used as test cases for high-order numerical schemes. While generally consistent steady-state solutions have been obtained for these flows using higher order schemes, a number of results have been published with various solutions, including unsteady ones. We demonstrate with two different numerical methods and a range of meshes with a maximum density that exceeds 8 × 106 grid points that steady-state solutions are obtained. Furthermore, numerical evidence is presented that even when solving the equations with an unsteady algorithm, one obtains steady-state solutions.

Swanson, R. C.↗

NASA NTRS2012

Parametric Study of Decay of Homogeneous Isotropic Turbulence Using Large Eddy Simulation

Numerical simulations of decaying homogeneous isotropic turbulence are performed with both low-order and high-order spatial discretization schemes. The turbulent Mach and Reynolds numbers for the simulations are 0.2 and 250, respectively. For the low-order schemes we use either second-order central or third-order upwind biased differencing. For higher order approximations we apply weighted essentially non-oscillatory (WENO) schemes, both with linear and nonlinear weights. There are two objectives in this preliminary effort to investigate possible schemes for large eddy simulation (LES). One is to explore the capability of a widely used low-order computational fluid dynamics (CFD) code to perform LES computations. The other is to determine the effect of higher order accuracy (fifth, seventh, and ninth order) achieved with high-order upwind biased WENO-based schemes. Turbulence statistics, such as kinetic energy, dissipation, and skewness, along with the energy spectra from simulations of the decaying turbulence problem are used to assess and compare the various numerical schemes. In addition, results from the best performing schemes are compared with those from a spectral scheme. The effects of grid density, ranging from 32 cubed to 192 cubed, on the computations are also examined. The fifth-order WENO-based scheme is found to be too dissipative, especially on the coarser grids. However, with the seventh-order and ninth-order WENO-based schemes we observe a significant improvement in accuracy relative to the lower order LES schemes, as revealed by the computed peak in the energy dissipation and by the energy spectrum.

Swanson, R. C.↗

NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗

NASA NTRS2008

Overview of CFD Validation Experiments for Circulation Control Applications at NASA

Circulation control is a viable active flow control approach that can be used to meet the NASA Subsonic Fixed Wing project s Cruise Efficient Short Take Off and Landing goals. Currently, circulation control systems are primarily designed using empirical methods. However, large uncertainty in our ability to predict circulation control performance has led to the development of advanced CFD methods. This paper provides an overview of a systematic approach to developing CFD tools for basic and advanced circulation control applications. This four-step approach includes "Unit", "Benchmar", "Subsystem", and "Complete System" experiments. The paper emphasizes the ongoing and planned 2-D and 3-D physics orientated experiments with corresponding CFD efforts. Sample data are used to highlight the challenges involved in conducting circulation control computations and experiments.

Jones, G. S.↗

NASA NTRS2006

Convergence Acceleration for Multistage Time-Stepping Schemes

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Swanson, R. C.↗

NASA NTRS2005

Aspects of Numerical Simulation of Circulation Control Airfoils

The mass-averaged compressible Navier-Stokes equations are solved for circulation control airfoils. Numerical solutions are computed with a multigrid method that uses an implicit approximate factorization smoother. The effects of flow conditions (e.g., free-stream Mach number, angle of attack, momentum coefficient) and mesh on the prediction of circulation control airfoil flows are considered. In addition, the impact of turbulence modeling, including curvature effects and modifications to reduce eddy viscosity levels in the wall jet (i.e., Coanda flow), is discussed. Computed pressure distributions are compared with available experimental data.

Swanson, R. C.↗

NASA NTRS2005

Progress Towards Computational Method for Circulation Control Airfoils

The compressible Reynolds-averaged Navier-Stokes equations are solved for circulation control airfoil flows. Numerical solutions are computed with both structured and unstructured grid solvers. Several turbulence models are considered, including the Spalart-Allmaras model with and without curvature corrections, the shear stress transport model of Menter, and the k-enstrophy model. Circulation control flows with jet momentum coefficients of 0.03, 0.10, and 0.226 are considered. Comparisons are made between computed and experimental pressure distributions, velocity profiles, Reynolds stress profiles, and streamline patterns. Including curvature effects yields the closest agreement with the measured data.

Swanson, R. C.↗

NASA NTRS2005

A Study of Multigrid Preconditioners Using Eigensystem Analysis

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

Roberts, Thomas W.↗

NASA NTRS2004

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Swanson, R. C.↗

NASA NTRS2004

Textbook Multigrid Efficiency for the Steady Euler Equations

A fast multigrid solver for the steady incompressible Euler equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Solvers for both unstructured triangular grids and structured quadrilateral grids have been written. Computations for channel flow and flow over a nonlifting airfoil have computed. Using Gauss-Seidel relaxation ordered in the flow direction, textbook multigrid convergence rates of nearly one order-of-magnitude residual reduction per multigrid cycle are achieved, independent of the grid spacing. This approach also may be applied to the compressible Euler equations and the incompressible Navier-Stokes equations.

Roberts, Thomas W.↗

NASA NTRS2001

Towards Optimal Multigrid Efficiency for the Navier-Stokes Equations

A fast multigrid solver for the steady incompressible Navier-Stokes equations is presented. Unlike time-marching schemes, this approach uses relaxation of the steady equations. Application of this method results in a discretization that correctly distinguishes between the advection and elliptic parts of the operator, allowing efficient smoothers to be constructed. Numerical solutions are shown for flow over a flat plate and a Karman-Trefftz airfoil. Using collective Gauss-Seidel line relaxation in both the vertical and horizontal directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of a Runge-Kutta based multigrid method.

Swanson, R. C.↗

NASA NTRS1998

On Some Numerical Dissipation Schemes

Several schemes for introducing an artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar dissipation and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical solutions are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme. The coarse-grid accuracy for the original CUSP scheme is improved by modifying the limiter function used with the scheme, giving comparable accuracy to that obtained with the MATD scheme. The modifications reduce the background dissipation and provide control over the regions where the scheme can become first order.

Swanson, R. C.↗

NASA NTRS1997

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Swanson, R. C.↗

NASA NTRS1997

Comparison of Several Dissipation Algorithms for Central Difference Schemes

Several algorithms for introducing artificial dissipation into a central difference approximation to the Euler and Navier Stokes equations are considered. The focus of the paper is on the convective upwind and split pressure (CUSP) scheme, which is designed to support single interior point discrete shock waves. This scheme is analyzed and compared in detail with scalar and matrix dissipation (MATD) schemes. Resolution capability is determined by solving subsonic, transonic, and hypersonic flow problems. A finite-volume discretization and a multistage time-stepping scheme with multigrid are used to compute solutions to the flow equations. Numerical results are also compared with either theoretical solutions or experimental data. For transonic airfoil flows the best accuracy on coarse meshes for aerodynamic coefficients is obtained with a simple MATD scheme.

Swanson, R. C.↗

NASA NTRS1997

Relaxation Revisited: A Fresh Look at Multigrid for Steady Flows

The year 1971 saw the publication of one of the landmark papers in computational aerodynamics, that of Murman and Cole. As with many seminal works, its significance lies not so much in the specific problem that it addressed| small disturbance, plane transonic flow - but in the identification of a general approach to the solution of a technically important and theoretically difficult problem. The key features of Murman and Cole's work were the use of type- dependent differencing to correctly account for the proper domain of dependence of a mixed elliptic/hyperbolic equation, and the introduction of line relaxation to solve the steady flow equation. All subsequent work in transonic potential flows was based on these concepts. Jameson extended Murman and Cole's ideas to the full potential equation with two important contributions. First, he introduced the rotated difference stencil, which generalized the Murman and Cole type-dependent difference operator to general coordinates. Second, he used the interpretation, introduced by Garabedian, of relaxation as an iteration in artificial time to construct stable relaxation schemes, generalizing the original line relaxation method of Reference. The decade of the 1970s saw an explosion of activity in the solution of transonic potential flows, which has been summarized in the review article of Caughey.

Roberts, Thomas W.↗

NASA NTRS1993

Multigrid schemes for viscous hypersonic flows

Several multigrid schemes are considered for the numerical computation of viscous hypersonic flows. For each scheme, the basic solution algorithm employs upwind spatial discretization with explicit multistage time stepping. Two-level versions of the various multigrid algorithms are applied to the two-dimensional advection equation, and Fourier analysis is used to determine their damping properties. The capabilities of the multigrid methods are assessed by solving two different hypersonic flow problems. Some new multigrid schemes, based on semicoarsening strategies, are shown to be quite effective in relieving the stiffness caused by the high-aspect-ratio cells required to resolve high Reynolds number flows. These schemes exhibit good convergence rates for Reynolds numbers up to 200 x 10(exp 6).

Swanson, R. C.↗

NASA NTRS1993

Aspects of a high-resolution scheme for the Navier-Stokes equations

In this paper we emphasize the importance of the form of the numerical dissipation model in computing accurate viscous flow solutions. A high-resolution scheme for viscous flows based on three-point central differencing and a matrix dissipation is considered. The various components of this scheme, including 'entropy fix', limiter function, and boundary-point dissipation are discussed. By analyzing boundary-point dissipation stencils, we confirm that with the matrix dissipation model the normal numerical dissipation terms in the streamwise momentum equation are independent of the Reynolds number. Such independence is not achieved with a scalar dissipation form. The accuracy of the central-difference scheme, with and without matrix dissipation, and the flux-difference split scheme of Roe, which is classified as a high-resolution scheme, is compared. For this comparison, three high Reynolds number laminar flows are considered. Solutions of the Navier-Stokes equations are obtained for low-speed flow over a flat plate, transonic flow over an airfoil with transition near the leading edge, and hypersonic flow over a compression ramp. The emphasis of the comparison is primarily on the details of the viscous flows. The necessity of the high-resolution property is revealed.

Swanson, R. C.↗

NASA NTRS1993

A Navier-Stokes solver for turbomachinery applications

A computer code for solving the Reynolds-averaged full Navier-Stokes equations has been developed and applied using H- and C-type grids. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. The integration in time is based on an explicit four-stage Runge-Kutta scheme. Local time stepping, variable coefficient implicit residual smoothing, and a full multigrid method have been implemented to accelerate steady-state calculations. A grid independence analysis is presented for a transonic rotor blade. Comparisons with experimental data show that the code is an accurate viscous solver and can give very good blade-to-blade predictions for engineering applications.

Arnone, A.↗