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At least 631 records · Page 35
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NASA NTRS1987

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Glaisner, F.↗
NASA NTRS1986

Application of the method of lines for solution of the Navier-Stokes equations using nonuniform grid distributions

The method of lines is investigated for the numerical solution of the stream function and velocity form of the Navier-Stokes equations on nonuniform grids. Stiffness characteristics of a linear one-dimensional model equation are examined to establish the feasibility of applying the method to the volicity equation in two dimensions. It is observed that the transformed governing equations in computational domain become stiffer with increasing the number of grid points and the differencing technique affects the stiffness characteristics. The results demonstrate that the method of lines under certain circumstances is highly suitable for the numerical solution of physical problems on domains covered with variable grids.

Tiwari, S. N.↗
NASA NTRS1986

On spectral multigrid methods for the time-dependent Navier-Stokes equations

A splitting scheme is proposed for the numerical solution of the time-dependent, incompressible Navier-Stokes equations by spectral methods. A staggered grid is used for the pressure, improved intermediate boundary conditions are employed in the split step for the velocity, and spectral multigrid techniques are used for the solution of the implicit equations.

Zang, T. A.↗
NASA NTRS1987

Incompressible Navier-Stokes solutions for a sharp-edged double-delta wing

An implicit finite-difference scheme is used to compute the incompressible laminar vortical flow around a double-delta wing with an aspect ratio of 2.06. By adding a time derivative of the pressure to the continuity equation, the unsteady incompressible Navier-Stokes equations can be integrated like a conventional parabolic time-dependent system of equations. The flux-difference split scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. The trajectory of the vortical core is well predicted in comparison with experimental data.

Hsu, Chung-Hao↗
NASA NTRS1987

Navier-Stokes calculation of the flow around simplified LOX posts arrays

The steady laminar flow around the Space Shuttle main engine main injector LOX posts is investigated by using a three dimensional incompressible Navier-Stokes flow solver and a multiblock technique to calculate the flow around simplified LOX post arrays. Post flow physics and loads are examined. The effect of multiple posts, shields and a secondary post row is calculated.

Williams, M.↗
NASA NTRS1987

Numerical solutions of Navier-Stokes equations for a Butler wing

The flow field is simulated on the surface of a Butler wing in a uniform stream. Results are presented for Mach number 3.5 and Reynolds number of 2,000,000. The simulation is done by integrating the viscous Navier-Stokes equations. These equations govern the unsteady, viscous, compressible and heat conducting flow of an ideal gas. The equations are written in curvilinear coordinates so that the wing surface is represented accurately. The O-type and H-type grids have been used for this study, and results are compared. The governing equations are solved by the MacCormack time-split method, and the results are compared with other theoretical and experimental results. The codes are written in FORTRAN, vectorized and currently run on the CDC Vector Processing System (VPS-32) computer.

Abolhassani, Jamshid S.↗
NASA NTRS1986

Linearized form of implicit TVD schemes for the multidimensional Euler and Navier-Stokes equations

Linearized alternating direction implicit (ADI) forms of a class of total variation diminishing (TVD) schemes for the Euler and Navier-Stokes equations have been developed. These schemes are based on the second-order-accurate TVD schemes for hyperbolic conservation laws developed by Harten (1983, 1984). They have the property of not generating spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1-2 grid points. These schemes are relatively simple to understand and easy to implement into a new or existing computer code. One can modify a standard three-point central-difference code by simply changing the conventional numerical dissipation term into the one designed for the TVD scheme. For steady-state applications, the only difference in computation is that the current schemes require a more elaborate dissipation term for the explicit operator; no extra computation is required for the implicit operator. Numerical experiments with the proposed algorithms on a variety of steady-state airfoil problems illustrate the versatility of the schemes.

Yee, H. C.↗
NASA NTRS1986

Picosecond coherent anti-Stokes Raman scattering (CARS) study of vibrational dephasing of carbon disulfide and benzene in solution

The vibrational dephasing of the 656/cm mode (nu1, a1g) of CS2 and the 991/cm mode (nu2, a1g) of benzene have been studied as a function of concentration in mixtures with a number of solvents using a ps time-resolved CARS technique. This technique employs two tunable synchronously-pumped mode-locked dye lasers in a stimulated Raman pump, coherent anti-Stokes Raman probe time-resolved experiment. Results are obtained for CS2 in carbon tetrachloride, benzene, nitrobenzene, and ethanol and for benzene nu2 in CS2. The dephasing rates of CS2 nu1 increase on dilution with the polar solvents and decrease or remain constant on dilution with the nonpolar solvents. The CS2/benzene solutions show a contrasting behavior, with the CS2 nu1 dephasing rate being nearly independent of concentration whereas the benzene nu2 dephasing rate decreases on dilution. These results are compared to theoretical models for vibrational dephasing of polyatomic molecules in solution.

Perry, Joseph W.↗
NASA NTRS1986

Two-dimensional nonsteady viscous flow simulation on the Navier-Stokes computer miniNode

The needs of large-scale scientific computation are outpacing the growth in performance of mainframe supercomputers. In particular, problems in fluid mechanics involving complex flow simulations require far more speed and capacity than that provided by current and proposed Class VI supercomputers. To address this concern, the Navier-Stokes Computer (NSC) was developed. The NSC is a parallel-processing machine, comprised of individual Nodes, each comparable in performance to current supercomputers. The global architecture is that of a hypercube, and a 128-Node NSC has been designed. New architectural features, such as a reconfigurable many-function ALU pipeline and a multifunction memory-ALU switch, have provided the capability to efficiently implement a wide range of algorithms. Efficient algorithms typically involve numerically intensive tasks, which often include conditional operations. These operations may be efficiently implemented on the NSC without, in general, sacrificing vector-processing speed. To illustrate the architecture, programming, and several of the capabilities of the NSC, the simulation of two-dimensional, nonsteady viscous flows on a prototype Node, called the miniNode, is presented.

Nosenchuck, Daniel M.↗
NASA NTRS1986

A relaxation technique for the parabolized Navier-Stokes (PNS) equations

A rapidly converging relaxation technique for the parabolized Navier-Stokes equations has been devised. The scheme is applicable in both supersonic and subsonic flows, but it is discussed here in the context of supersonic flows. The upstream propagating acoustic influence in the subsonic part of the flow is introduced semi-implicitly through the streamwise momentum equation applied on the body, and through a forward-differencing on the streamwise pressure gradient term in the interior. This procedure yields a new boundary condition on the energy in the total energy equation. The pressure-velocity system in the subsonic layer is coupled, but the positive time-like marching characteristic of the governing equations is still maintained. The relaxation technique is demontrated to work for a three-dimensional flow over a cone-flare in supersonic flight.

Kaul, Upender K.↗
NASA NTRS1986

A coupled marching procedure for the partially parabolized Navier-Stokes equations

A coupled finite-difference formulation is described for solving a reduced form of the compressible Navier-Stokes equations by a multiple space marching procedure. The properties of the equations are discussed and the solution algorithm presented. The scheme is used to compute incompressible flows by taking the incompressible limit (M about 0.1) of the compressible formulation. A separate Poisson equation is not required for the pressure. Results are compared with experimental data and other numerical predictions for low Reynolds number channel inlet flow, flow over a rearward-facing step in a channel, and flow near the trailing edge of a flat plate.

Liu, Xuezong↗
NASA NTRS1987

An LU-SSOR scheme for the Euler and Navier-Stokes equations

A new multigrid relaxation scheme, lower-upper symmetric successive overrelaxation (LU-SSOR) is developed for the steady-state solution of the Euler and Navier-Stokes equations. The scheme, which is based on central differences, does not require flux splitting for approximate Newton iteration. Application to transonic flow shows that the new method is efficient and robust. The vectorizable LU-SSOR scheme needs only scalar diagonal inversions.

Yoon, Seokkwan↗
NASA NTRS1987

On the accuracy of the pseudocompressibility method in solving the incompressible Navier-Stokes equations

The method of pseudocompressibility is tested for its accuracy in solving the incompressible Navier-Stokes equations. An implicit, finite difference computer code is used to solve the equations in a three-dimensional, curvilinear coordinate system. The code employs artificial compressibiity for solving the pressure field, coupled with an implicit, approximate factorization scheme. This coupling is known as the pseudocompressibility method and introduces pressure waves of finite speed into the fluid medium that would otherwise have an infinite sound speed. The waves die out as the solution converges, and the steady state solution approaches a divergence-free condition. These waves, however, limit the time accuracy of the computations. The effects of these waves are analysed and criteria are set for choosing the pseudocompressibility parameter that governs the pressure wave speed; test cases are presented that verify these criteria. The code is tested by computing laminar flow over a two-dimensional, backward-facing step and over a two-dimensional, impulsively started circular cylinder.

Rogers, S. E.↗
NASA NTRS1986

A Petrov-Galerkin finite element method for the compressible Euler and Navier-Stokes equations

An overview of a new finite element method for the compressible Euler and Navier-Stokes equations is presented. The discretization is based on entropy variables. The method is developed within the framework of a Petrov-Galerkin formulation. Two perturbations are added to the weighting function; one is a generalization of the SUPG operator and the other is designed to enhance shock capturing capability. The treatment of boundary conditions and the consistent calculation of boundary fluxes are addressed. Results of numerical tests are presented which confirm the robustness and wide applicability of the method.

Franca, L. P.↗
NASA NTRS1987

Time-marching solution of incompressible Navier-Stokes equations for internal flow

Primitive variables with central differencing on a staggered grid are used in the present, factored ADI finite-difference scheme for artificial compressibility method solution of the incompressible Navier-Stokes equations, leading to a close coupling between velocity and pressure that both enhances stability and eliminates the need for artificial damping. Computational efficiency is enhanced through the use of a spatially variable, fixed Courant number-based time-step. The numerical results obtained for a driven cavity at Re of 10,000, with local cell Re as high as 100, exhibits no flow variable spatial oscillations on a 40 x 40 stretched grid solution.

Soh, W. Y.↗
NASA NTRS1985

The Stokes force on a droplet in an unbounded fluid medium due to capillary effects

The Stokes force on a fluid droplet is obtained when the droplet is placed in an unbounded fluid medium and motion ensues due to an arbitrary interfacial-tension gradient on the droplet surface. The force, derived here for a spherical droplet, is proportional to the integral of the interfacial-tension gradient over the droplet surface. When the interfacial-tension gradients are caused by temperature or concentration variations, the result for the force may be further specialized when convective transport effects are negligible. In this case, it is possible to express the force in terms of the gradient of the undisturbed temperature (or concentration) field evaluated at the location of the droplet center in a form analogous to Faxen's force law.

Subramanian, R. Shankar↗
NASA NTRS1986

The Navier-Stokes computer

The Navier-Stokes computer (NSC) has been developed for solving problems in fluid mechanics involving complex flow simulations that require more speed and capacity than provided by current and proposed Class VI supercomputers. The machine is a parallel processing supercomputer with several new architectural elements which can be programmed to address a wide range of problems meeting the following criteria: (1) the problem is numerically intensive, and (2) the code makes use of long vectors. A simulation of two-dimensional nonsteady viscous flows is presented to illustrate the architecture, programming, and some of the capabilities of the NSC.

Nosenchuck, D. M.↗
NASA NTRS1987

Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations

An artificial dissipation model, including boundary treatment, that is employed in many central difference schemes for solving the Euler and Navier-Stokes equations is discussed. Modifications of this model such as the eigenvalue scaling suggested by upwind differencing are examined.Multistage time stepping schemes with and without a multigrid method are used to investigate the effects of changes in the dissipation model on accuracy and convergence. Improved accuracy for inviscid and viscous airfoil flows is obtained with the modified eigenvalue scaling. Slower convergence rates are experienced with the multigrid method using such scaling. The rate of convergence is improved by applying a dissipation scaling function that depends on mesh cell aspect ratio.

Swanson, R. C.↗