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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

A spectral collocation method for the Navier-Stokes equations

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

Malik, M. R.↗
NASA NTRS1983

Finite element methods for the inhomogeneous Navier-Stokes equations

A conforming mixed finite element method for the stationary Navier-Stokes equations with inhomogeneous boundary conditions is considered. Estimates for the error in the velocity and pressure approximations are derived. A computational example is provided to illustrate the implementation of the method.

Peterson, J. S.↗
NASA NTRS1985

A spectral collocation method for the Navier-Stokes equations

A Fourier-Chebyshev spectral method for the incompressible Navier-Stokes equations is described. It is applicable to a variety of problems including some with fluid properties which vary strongly both in the normal direction and in time. In this fully spectral algorithm, a preconditioned iterative technique is used for solving the implicit equations arising from semi-implicit treatment of pressure, mean advection and vertical diffusion terms. The algorithm is tested by applying it to hydrodynamic stability problems in channel flow and in external boundary layers with both constant and variable viscosity.

Malik, M. R.↗
NASA NTRS1985

Calculations of two and three-dimensional transonic cascade flow fields using the Navier-Stokes equations

The multidimensional, ensemble-averaged, compressible, time-dependent Navier-Stokes equations have been used to study the turbulent flow field in two and three-dimensional turbine cascades. The viscous regions of the flow were resolved and non-slip boundary conditions were utilized on solid surfaces. The calculations were performed in a constructive 'O'-type grid which allows representation of the blade rounded trailing edge. Converged solutions were obtained in relatively few time steps (about 80-150) and comparisons for both surface pressure and heat transfer showed good agreement with data. The three-dimensional turbine cascade calculation showed many of the expected flow-field features.

Weinberg, B. C.↗
NASA NTRS1987

Streamline-upwind/Petrov-Galerkin procedures for the vorticity-stream function form of the Navier-Stokes equations

The paper presents procedures for the solution of the Navier-Stokes equations in the vorticity-stream function form. The difficulties involved are related to the convection term in the vorticity transport equation and to the lack of boundary conditions for voritcity at no-slip surfaces. The use of a streamline-upwind/Petrov-Galerkin finite element formulation for the solution of the vorticity transport equation. In the present scheme, the weighting functions are dependent on both spatial and temporal discretizations. A proper numerical treatment of the boundary conditions leading to an implicit treatment of the vorticity at no-slip surfaces is presented. These procedures have successfully been employed to simulate various flows of engineering interest.

Tezduyar, T. E.↗
NASA NTRS1991

Newton's method applied to finite-difference approximations for the steady-state compressible Navier-Stokes equations

Finite-difference approximations for steady-state compressible Navier-Stokes equations, whose two spatial dimensions are written in generalized curvilinear coordinates and strong conservation-law form, are presently solved by means of Newton's method in order to obtain a lifting-airfoil flow field under subsonic and transonnic conditions. In addition to ascertaining the computational requirements of an initial guess ensuring convergence and the degree of computational efficiency obtainable via the approximate Newton method's freezing of the Jacobian matrices, attention is given to the need for auxiliary methods assessing the temporal stability of steady-state solutions. It is demonstrated that nonunique solutions of the finite-difference equations are obtainable by Newton's method in conjunction with a continuation method.

Bailey, Harry E.↗
NASA NTRS1992

Dual-Potential Formulation Of Navier-Stokes Equations

Report discusses research on dual-potential formulation of Navier-Stokes equations. Purpose of study to extend capability of dual-potential method to computation of unsteady flows of viscous, compressible fluids.

Gegg, S. G.↗
NASA NTRS1996

The Multigrid-Mask Numerical Method for Solution of Incompressible Navier-Stokes Equations

A multigrid-mask method for solution of incompressible Navier-Stokes equations in primitive variable form has been developed. The main objective is to apply this method in conjunction with the pseudospectral element method solving flow past multiple objects. There are two key steps involved in calculating flow past multiple objects. The first step utilizes only Cartesian grid points. This homogeneous or mask method step permits flow into the interior rectangular elements contained in objects, but with the restriction that the velocity for those Cartesian elements within and on the surface of an object should be small or zero. This step easily produces an approximate flow field on Cartesian grid points covering the entire flow field. The second or heterogeneous step corrects the approximate flow field to account for the actual shape of the objects by solving the flow field based on the local coordinates surrounding each object and adapted to it. The noise occurring in data communication between the global (low frequency) coordinates and the local (high frequency) coordinates is eliminated by the multigrid method when the Schwarz Alternating Procedure (SAP) is implemented. Two dimensional flow past circular and elliptic cylinders will be presented to demonstrate the versatility of the proposed method. An interesting phenomenon is found that when the second elliptic cylinder is placed in the wake of the first elliptic cylinder a traction force results in a negative drag coefficient.

Ku, Hwar-Ching↗
NASA NTRS1996

Solutions to Three-Dimensional Thin-Layer Navier-Stokes Equations in Rotating Coordinates for Flow Through Turbomachinery

The viscous, Navier-Stokes solver for turbomachinery applications, MSUTC has been modified to include the rotating frame formulation. The three-dimensional thin-layer Navier-Stokes equations have been cast in a rotating Cartesian frame enabling the freezing of grid motion. This also allows the flow-field associated with an isolated rotor to be viewed as a steady-state problem. Consequently, local time stepping can be used to accelerate convergence. The formulation is validated by running NASA's Rotor 67 as the test case. results are compared between the rotating frame code and the absolute frame code. The use of the rotating frame approach greatly enhances the performance of the code with respect to savings in computing time, without degradation of the solution.

Ghosh, Amrit Raj↗
NASA NTRS1984

Calculation of steady and oscillating airfoil flow fields via the Navier Stokes equations

A Navier-Stokes calculation procedure is applied to high Reynolds number flow about steady and unsteady airfoils. The procedure solves the ensemble averaged governing equations via a linearized block implicit (LBI) technique which in general converges to a nominal steady flow within 120 time steps. The grid used in the computation is highly stretched thus resolving the turbulent boundary layers. Calculations have been compared with data for both NACA 4412 airfoil at high incidence and an NACA 0012 airfoil oscillating in dynamic stall. In both cases, good agreement is noted between measured and calculated surface pressure distributions.

Shamroth, S. J.↗
NASA NTRS1986

Hypersonic low-density solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip

Solutions of the Navier-Stokes equations with chemical nonequilibrium and multicomponent surface slip are presented along the stagnation streamline under low-density hypersonic flight conditions. The conditions analyzed are those encountered by the nose region of the Space Shuttle Orbiter during reentry. A detailed comparison of the Navier-Stokes (NS) results is made with the viscous shock-layer (VSL) and Direct Simulation Monte Carlo (DSMC) predictions. With the inclusion of surface-slip boundary conditions in NS calculations, the surface heat transfer and other flow field quantities adjacent to the surface are predicted favorably with the DSMC calculations from 75 km to 115 km in altitude. Therefore, the practical range for the applicability of Navier-Stokes solutions is much wider than previously thought. This is appealing because the continuum (NS and VSL) methods are commonly used to solve the fluid flow problems and are less demanding in terms of computer resource requirements than the noncontinuum (DSMC) methods. The NS solutions agree well with the VSL results for altitudes less than 92 km. An assessment is made of the frozen flow approximation employed in the VSL calculations.

Gupta, R. N.↗
NASA NTRS1993

Extension of state-vector splitting to the Navier-Stokes equations

A multi-dimensional upwind scheme for solving the Euler equations has been extended to solve the Navier-Stokes equations. These methods share the property of not requiring body-fitted computational grids. A time advance scheme which is second-order accurate in time and space has been developed for use in conjunction with state-vector splitting to accurately resolve regions with significant gradients in flow quantities. The scheme has been tested on several simple viscous flow problems for which analytic solutions are known; the agreement of computation with theory is excellent.

Gooch, Carl F.↗
NASA NTRS1987

Numerical solution of the Navier-Stokes equations about three-dimensional configurations: A survey

The numerical solution of the Navier-Stokes equations about three-dimensional configurations is reviewed. Formulational and computational requirements for the various Navier-Stokes approaches are examined for typical problems including the viscous flow field solution about a complete aerospace vehicle. Recent computed results, with experimental comparisons when available, are presented to highlight the presentation. The future of Navier-Stokes applications in three-dimensions is seen to be rapidly expanding across a broad front including internal and external flows, and flows across the entire speed regime from incompressible to hypersonic applications. Prospects for the future are described and recommendations for areas of concentrated research are indicated.

Holst, Terry L.↗
NASA NTRS1983

Implicit upwind methods for the compressible Navier-Stokes equations

A class of implicit upwind differencing methods for the compressible Navier-Stokes equations is described and applied. The methods are based on the use of local eigenvalues or wave speeds to control spatial differencing of inviscid terms and are aimed at increasing the level of accuracy and stability achievable in computation. Techniques for accelerating the rate of convergence to a steady state solution are also used. Applications to inviscid and viscous transonic flows are discussed and compared with other methods and experimental measurements. It is shown that accurate and efficient transonic airfoil calculations can be made on the Cray-l computer in less than 2 min.

Coakley, T. J.↗
NASA NTRS1989

An efficient cell-vertex multigrid scheme for the three-dimensional Navier-Stokes equations

A cell-vertex scheme for the three-dimensional Navier-Stokes equations, which is based on central difference approximations and Runge-Kutta time stepping, is described. Using local time stepping, implicit residual smoothing with locally varying coefficients, a multigrid method and carefully controlled dissipative terms, very good convergence rates are obtained for two- and three-dimensional flows. Details of the acceleration techniques, which are important for convergence on meshes with high aspect-ratio cells, are discussed. Emphasis is put on the analysis of the stability properties of the implicit smoothing of the explicit residuals with coefficients, which depend on cell aspect ratios.

Radespiel, R.↗
NASA NTRS1991

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

Obayashi, Shigeru↗