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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

An implicit factored scheme for the compressible Navier-Stokes equations. II - The numerical ODE connection

An attempt is made to establish a connection between linear multistep methods for applications to ordinary differential equations and their extension (by approximate factorization) to alternating direction implicit methods for partial differential equations. An earlier implicit factored scheme for the compressible Navier-Stokes equations is generalized by innovations that (1) increase the class of temporal difference schemes to include all linear multistep methods, (2) optimize the class of unconditionally stable factored schemes by a new choice of unknown variable, and (3) improve the computational efficiency by the introduction of quasi-one-leg methods.

Beam, R. M.↗
NASA NTRS1979

Boundary conditions for implicit solutions to the compressible Navier-Stokes equations in finite computational domains

The admissible boundary conditions for the unsteady Navier-Stokes equations are insufficient to determine completely the flow variables at grid points on the boundaries of a finite computational domain. A general method is presented in which the boundary conditions are supplemented by conservatively differenced forms of the flow equations. For implicit algorithms, the method provides a fully implicit coupling between boundary and interior points. Implicit boundary-point computation schemes are given for most types of flow boundary encountered in internal and external flow problems. Convergence to steady state is generally faster than with locally explicit boundary-point schemes.

Thomas, P. D.↗
NASA NTRS1979

Application of a velocity-split Navier-Stokes solution technique to external flow problems

A method for solving the Navier-Stokes equations based on splitting the velocity vector into its rotational and irrotational parts has recently been applied successfully to internal flow computations. In this paper, the applicability of the method to external flows is examined by studying two model problems; laminar incompressible flow over semiinfinite and finite flat plates. For these problems the procedure accurately reproduces the known solutions and is computationally very efficient even at high Reynolds numbers. Computational aspects of the method are discussed along with the possibility of using the procedure to retrofit a viscous capability into existing transonic potential flow codes.

Dwoyer, D. L.↗
NASA NTRS1980

Velocity-split Navier-Stokes solution procedure for incompressible high Reynolds number external flows

A method for solving the Navier-Stokes equations based on splitting the velocity vector into its rotational and irrotational parts was sucessfully applied to internal flow computations. The applicability of the method to external flows is examined by studying several model problems. The model problems are those of laminar and turbulent incompressible flow past a semi-infinite flat plate and laminar incompressible flow past a finite flat plate. For these problems, the procedure accurately reproduces the known solutions and is computationally very efficient even at high Reynolds numbers. Computational aspects of the method are discussed along with the possibility of using the procedure to retrofit a viscous capability into existing potential flow codes.

Dwoyer, D. L.↗
NASA NTRS1980

A Navier-Stokes fast solver for turbulence modeling applications

A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Murphy, J. D.↗
NASA NTRS1980

An approximate factorization solution of the Navier-Stokes equations for transonic flow using body-fitted coordinates with application to NACA 64A010 airfoils

The implementation of the approximate factorization algorithm and its ability to efficiently and accurately describe transonic flow about an NACA 64A010 airfoil section is examined. The approximate factorization algorithm is developed from the nondimensional, conservative, vectorized Navier-Stokes equations expressed in curvilinear coordinates. Equations of state and transport coefficient relations appropriate to atmospheric air are appended to close the system of partial differential equations. An algebraic turbulence model is also incorporated into the equation set. This algorithm was verified by investigating the flow about an NACA 64A010 airfoil at 0, 2, and 3.5 deg angle of attack for free-stream conditions of 2,000,000 Reynolds number and 0.8 Mach number. Overall results were in good qualitative agreement with wind tunnel data sets. However, while nondimensional times of six were attained, numerical difficulties prevented any case from reaching a true steady state.

Copper, G. K.↗
NASA NTRS1980

A rapid implicit-explicit solution to the two-dimensional time dependent incompressible Navier-Stokes equations

A second-order time-accurate and spatially factored algorithm was used in a finite difference scheme for the numerical solution of the time-dependent, incompressible, two dimensional Navier-Stokes equations in conservation-law form using vorticity and stream function variables. The systems of equations are solved at each time step by an iterative technique. Numerical results were obtained for a circular cylinder at a Reynolds number of 15, and an NACA 0012 airfoil at zero angle of attack at Reynolds numbers of 10 to the third and 10 to the fourth powers. The results are in agreement with another numerical technique, and the computing time required to obtain the steady state solution at the Reynolds number of 10 to the 4th power was 49.7 sec on CDC 7600 computer using a 65 x 84 computational grind.

Davis, J. E.↗
NASA NTRS1979

The solution of the three-dimensional viscous-compressible Navier-Stokes equations on a vector computer

The development of a vectorized computer code for the solution of the three-dimensional viscous-compressible Navier-Stokes equations is described. The code is applied on the CDC STAR-100 vector computer which is capable of achieving high result rates when a high degree of parallelism is present in the computations. The computational technique is an explicit time-split MacCormack predictor-corrector algorithm. Since a large volume of data is processed and virtual memory utilized, a data management scheme based on interleaving is used. The program has been applied to obtain the solution of the laminar supersonic flow about a family of three-dimensional corners. The equations of motion are expressed in a generalized form relative to a uniform rectangular computational domain. The metric coefficient and boundary conditions must be supplied for the corresponding physical domain. For calculations with 30,000 grid points, a computational rate of 0.00015 seconds per grid point per time step is observed.

Smith, R. E.↗
NASA NTRS1980

A nonreflecting outflow boundary condition for subsonic Navier-Stokes calculations

A nonreflecting boundary condition is presented for the numerical solution of the time-dependent compressible Navier-Stokes equations when these equations are used to obtain a steady state. This boundary condition is shown to be effective in reducing reflections at a subsonic outflow boundary. Numerical calculations using a model problem were made to compare this boundary condition with other outflow boundary conditions. The nonreflecting boundary condition contains a parameter whose optimal value is estimated using the analysis of a simplified set of equations.

Rudy, D. H.↗
NASA NTRS1980

Computation of three-dimensional viscous flows with the Navier-Stokes equations

The paper presents computations of three-dimensional viscous flows generated with the General Interpolation Method/STAR code based on the time-averaged Navier-Stokes equations. Calculations are presented for three viscous flow problems, and a two dimensional nozzle-exhaust shear flow case is solved and compared to an inviscid slip-line code. This nozzle-exhaust flow case is then extended to three dimensions and the steady solution displayed at pressure contours in the cross planes. The third problem consists of a simulated two-dimensional aircraft inlet flow which includes calculation of the 'spillage' flow and a shock wave/boundary layer interaction in the nozzle.

Spradley, L. W.↗
NASA NTRS1980

On the solution of the unsteady Navier-Stokes equations for hypersonic flow about axially-symmetric blunt bodies

A formulation of the complete Navier-Stokes problem for a viscous hypersonic flow in general curvilinear coordinates is presented. This formulation is applicable to both the axially symmetric and three dimensional flows past bodies of revolution. The equations for the case of zero angle of attack were solved past a circular cylinder with hemispherical caps by point SOR finite difference approximation. The free stream Mach number and the Reynolds number for the test case are respectively 22.04 and 168883. The whole algorithm is presented in detail along with the preliminary results for pressure, temperature, density and velocity distributions along the stagnation line.

Warsi, Z. U. A.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

The unaveraged Navier-Stokes equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗
NASA NTRS1980

Numerical solutions of the Navier-Stokes equations for transonic afterbody flows

The time dependent Navier-Stokes equations in mass averaged variables are solved for transonic flow over axisymmetric boattail plume simulator configurations. Numerical solution of these equations is accomplished with the unsplit explict finite difference algorithm of MacCormack. A grid subcycling procedure and computer code vectorization are used to improve computational efficiency. The two layer algebraic turbulence models of Cebeci-Smith and Baldwin-Lomax are employed for investigating turbulence closure. Two relaxation models based on these baseline models are also considered. Results in the form of surface pressure distribution for three different circular arc boattails at two free stream Mach numbers are compared with experimental data. The pressures in the recirculating flow region for all separated cases are poorly predicted with the baseline turbulence models. Significant improvements in the predictions are usually obtained by using the relaxation models.

Swanson, R. C., Jr.↗
NASA NTRS1981

Analysis of turbulent flow about an isolated airfoil using a time dependent Navier-Stokes procedure

The procedure solves the Navier-Stokes equations by the consistently split linearized block implicit method of Briley and McDonald in a body fitted coordinate system. The procedure is described and results are presented for flow about an airfoil whose incidence changes from 6 degrees to 19 degrees at a Reynolds number of one million and Mach number of 0.2. In addition, the unsteady flow about an airfoil held at a constant 19 degree incidence is examined and compared to data.

Shamroth, S. J.↗
NASA NTRS1981

Reduction of the two dimensional stationary Navier-Stokes problem to a sequence of Fredholm integral equations of the second kind

Present approaches to solving the stationary Navier-Stokes equations are of limited value; however, there does exist an equivalent representation of the problem that has significant potential in solving such problems. This is due to the fact that the equivalent representation consists of a sequence of Fredholm integral equations of the second kind, and the solving of this type of problem is very well developed. For the problem in this form, there is an excellent chance to also determine explicit error estimates, since bounded, rather than unbounded, linear operators are dealt with.

Gabrielsen, R. E.↗
NASA NTRS1981

Implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows

A fully implicit set of boundary conditions is developed for the solution of the parabolized Navier-Stokes equations for supersonic flow in two dimensions. Shock fitting is employed at the shock and the body has no-slip and specified temperature conditions. A specified heat transfer condition at the wall can be handled in a similar manner. In addition, the shock location is advanced in space in a fully implicit manner by utilizing the Rankine-Hugoniot conditions along with global conservation of mass.

Barnett, M.↗
NASA NTRS1981

Multigrid solution of the Navier-Stokes equations on nonuniform grids

The numerical solution of the Navier-Stokes equations in general two dimensional domains is considered. A proper finite difference approximation to the governing equations, on nonstaggered grids, in a transformed plane is formulated. Several aspects of a multigrid method for the solution of the finite difference equations are described. The efficiency of some relaxation schemes and the transfer among the grids which are nonuniform in the physical plane are emphasized.

Fuchs, L.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier-Stokes equations are solved numerically. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean-square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small-scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗