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Results for “Finite Difference Methods”

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.

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At least 397 records · Page 22
All sourcesNASA NTRSDOE OSTI
NASA NTRS1975

Numerical computation of two-dimensional viscous blunt body flows with an impinging shock

Two-dimensional, viscous, blunt body flows with an impinging shock wave are computed using a time-dependent, finite-difference method to solve the complete set of Navier-Stokes equations. The bow shock wave is treated as a discontinuity, while all interior shock layer detail such as shear layers, shock waves, jets, and the wall boundary layer are automatically captured in the solution. Numerical results are presented for cases in which shock waves of different strengths are allowed to impinge on the flow field surrounding a circular cylinder resulting in different shock interference patterns. The two-dimensional results are compared qualitatively with existing three-dimensional experiments.

Tannehil, J. C.↗
NASA NTRS1975

Space processing convection evaluation - G-jitter convection of confined fluids in low gravity

G-jitter convection, caused by time-varying accelerations imparted on a heated container of fluid in low gravity, is investigated analytically. The mathematical model used is constructed from the Navier-Stokes equations which are solved with a finite-difference method on a digital computer. Results are presented for typical space processing configurations and anticipated g-jitter levels, with emphasis on sounding rocket applications. The calculations indicate that g-jitter can cause significant temperature oscillations, increase or decrease local heat transfer and produce oscillatory convective flow patterns. These factors can have significant effects on important processes such as crystal growth (banding, for example) and separation techniques.

Spradley, L. W.↗
NASA NTRS1975

Computation of separated transonic turbulent flows

The two-dimensional Reynolds-averaged compressible Navier-Stokes equations are solved using MacCormack's second-order-accurate explicit finite difference method to simulate the separated transonic turbulent flow field over an airfoil. Four different algebraic eddy viscosity models are tested for viability to achieve turbulence closure for the class of flows considered. These models range from an unmodified boundary-layer mixing-length model to a relaxation model incorporating special considerations for the separation bubble region. Results of this study indicate the necessity for special attention to the separated flow region and suggest limits of applicability of algebraic turbulence models to these separated flow fields.

Deiwert, G. S.↗
NASA NTRS1975

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure has recently been developed for the numerical solution of partial differential equations. In the present paper, this spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a non-uniform mesh and overall fourth-order accuracy for a uniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, will be presented for several model problems.-

Rubin, S. G.↗
NASA NTRS1975

A study of the efficiency of various Navier-Stokes solvers

A comparative study of the efficiency of some finite difference methods for the solution of the Navier-Stokes equations was conducted. The study was restricted to the two-dimensional steady, uniform property vorticity-stream function equations. The comparisons were drawn by recording the CPU time required to obtain a solution as well as the accuracy of this solution using five numerical methods: central differences, first order upwind differences, second order upwind differences, exponential differences, and an ADI solution of the central difference equations. Solutions were obtained for two test cases: a recirculating eddy inside a square cavity with a moving top, and an impinging jet flow. The results show that whenever the central difference method is stable it generates results with a given accuracy for less CPU time than any other method.

Atias, M.↗
NASA NTRS1975

High Reynolds number transonic flow simulation

A code has been developed for simulating high Reynolds number transonic flow fields of arbitrary configuration. An explicit finite-difference method with time splitting is used to solve the time-dependent equations for compressible turbulent flow. A nonorthogonal computational mesh of arbitrary configuration facilitates the description of the flow field. The code is applied to simulate the flow over a two-dimensional 18 percent thick circular-arc biconvex airfoil at zero angle of attack for several different Reynolds numbers and a free-stream Mach number of 0.775.

Deiwert, G. S.↗
NASA NTRS1975

A finite-difference analysis of the nozzle starting process in an expansion tunnel

A suitable finite-difference method for computing the quasi-one-dimensional unsteady flow in an expansion tunnel nozzle was identified. The difference equations are presented along with the appropriate stability limits. A parametric study of the starting process in an expansion tunnel nozzle is made, and acceptable operating conditions were determined.

Weilmuenster, K. J.↗
NASA NTRS1976

Higher-order numerical solutions using cubic splines

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for several model problems.

Rubin, S. G.↗
NASA NTRS1976

On the computation of the transonic perturbation flow field around two- and three-dimensional oscillating wings

A finite difference method for solving the unsteady flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. Solutions are obtained using relaxation procedures. It is determined that there is a limit on reduced frequency, which is a function of Mach number and size of mesh region, above which the relaxation procedures will not converge. It is found that row line relaxation is more efficient than column relaxation and results are presented for a rectangular wing in harmonic pitch.

Weatherill, W. H.↗
NASA NTRS1976

Comparison of a two-dimensional shock impingement computation with experiment

Results of computations of two-dimensional viscous blunt-body flowfields with an impinging shock wave, with a time-dependent finite-difference method employed to solve the complete set of Navier-Stokes equations, are compared with experimental results. The experimental results were obtained in a 20-inch hypersonic tunnel with a planar shock impinging on the cylindrical leading edge of a fin, hence with the shock parallel to the centerline of the leading edge, so that type III and type IV interference patterns were generated. Close agreement is found. The overall effects of smoothing and grid size on the calculations are determined. A 31 x 51 mesh is adequate for wall pressure values (except in peaked regions).

Tannehill, J. C.↗
NASA NTRS1976

A note on the leap-frog scheme in two and three dimensions

The paper considers the leap-frog finite-difference method (Kreiss and Oliger, 1973) for systems of partial differential equations of the form du/dt = dF/dx + dG/dy + dH/dz, where d denotes partial derivative, u is a q-component vector and a function of x, y, z, and t, and the vectors F, G, and H are functions of u only. The original leap-frog algorithm is shown to admit a modification that improves on the stability conditions for two and three dimensions by factors of 2 and 2.8, respectively, thereby permitting larger time steps. The scheme for three dimensions is considered optimal in the sense that it combines simple averaging and large time steps.

Abarbanel, S.↗
NASA NTRS1976

High-latitude truncation errors of box-type primitive equation models

The 'box-type' finite-difference method includes a weighted average of the pressure gradient with weights proportional to the surface of the grid walls. It is shown that this averaging introduces first-order truncation errors near the poles. An example is shown in which the relative error is of zero order and the scheme produces large distortions in the solution at high latitudes.

Kalnay-Rivas, E.↗
NASA NTRS1977

Timing formulas for dissection algorithms on vector computers

The use of the finite element and finite difference methods often leads to the problem of solving large, sparse, positive definite systems of linear equations. MACSYMA plays a major role in the generation of formulas representing the time required for execution of the dissection algorithms. The use of MACSYMA in the generation of those formulas is described.

Poole, W. G., Jr.↗
NASA NTRS1977

Liquid jet impingement normal to a disk in zero gravity

The free surface shapes of circular liquid jets impinging normal to sharp-edged disks in zero gravity are determined. Zero gravity drop tower experiments yielded three distinct flow patterns that were classified in terms of the relative effects of surface tension and inertial forces. An order of magnitude analysis was conducted that indicated regions where viscous forces were not significant in the computation of free surface shapes. The free surface analysis was simplified by transforming the governing potential flow equations and boundary conditions into the inverse plane, where the stream function and velocity potential became the coordinates. The resulting nonlinear equations were solved by standard finite difference methods, and comparisons were made with the experimental data for the inertia dominated regime.

Labus, T. L.↗
NASA NTRS1977

Study of effects of injector geometry on fuel-air mixing and combustion

An implicit finite-difference method has been developed for computing the flow in the near field of a fuel injector as part of a broader study of the effects of fuel injector geometry on fuel-air mixing and combustion. Detailed numerical results have been obtained for cases of laminar and turbulent flow without base injection, corresponding to the supersonic base flow problem. These numerical results indicated that the method is stable and convergent, and that significant savings in computer time can be achieved, compared with explicit methods.

Bangert, L. H.↗
NASA NTRS1977

Numerical solution of the viscous hypersonic flow past blunted cones at angle of attack

Hypersonic viscous flow over spherically blunted cones of large half angle is computed at small angles of attack in the plane of symmetry of the flow field. Time-dependent viscous shock-layer equations in body-oriented coordinates are used to describe the flow field. The shock wave is treated as a discontinuity, across which the Rankine-Hugoniot relations are used to compute the flow conditions behind the shock. A time-marching second-order finite-difference method is used to solve the equations for a perfect gas. The local CFL (Courant-Friedrich-Lewy) time increment is used to advance the solution in time at each grid point. A fourth-order damping is used to damp the oscillations in the flow quantities. The numerical results of the present analysis for quantities such as shock standoff distance, surface-pressure distribution, and heating rates compare well with the existing theoretical and experimental results.

Kumar, A.↗
NASA NTRS1977

Heat transfer in cooled guide vanes

A numerical study to determine the temperature distribution in the guide vanes of a radial inflow turbine is presented. A computer program has been developed to calculate the temperature distribution when the vanes are cooled internally using a combination of impingement and film cooling techniques. The study is based on the use of the finite difference method in a two dimensional heat conduction problem. The results are then compared to determine the best cooling configuration for a certain coolant to primary mass flow ratio.

Tabakoff, W.↗