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Results for “Finite difference scheme”

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 289 records · Page 16
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Explicit finite difference predictor and convex corrector with applications to hyperbolic partial differential equations

An explicit finite difference scheme consisting of a predictor and a corrector has been developed and applied to solve some hyperbolic partial differential equations (PDEs). The corrector is a convex-type function which is applied at each time level and at each mesh point. It consists of a parameter which may be estimated such that for larger time steps the algorithm should remain stable and generate a fast speed of convergence to the steady-state solution. Some examples have been given.

Dey, C.↗
NASA NTRS1983

Nonparametric solution of the Euler equations for steady flow

A theory is presented for formulating well-posed boundary value problems for the Euler equations for steady rotational flow. It is shown that the Euler equations of motion are equivalent to a variational principle, which is used to define a finite difference scheme for numerically solving the Euler equations. The principle is extended to MHD problems in terms of a potential energy of a perfectly conducting plasma having a minimum number of stable configurations. The flow around a cylinder is considered, noting that time-independent solutions of the Euler equations can be used to provide limits to solutions of the Navier-Stokes equations. A sample is worked out in terms of the motion of vortices inside a circle.

Garabedian, P. R.↗
NASA NTRS1983

Computation of potential flows with embedded vortex rings and applications to helicopter rotor wakes

A finite difference scheme for solving the motion of a number of vortex rings is developed. The method is an adaptation of the 'cloud-in-cell' technique to axisymmetric flows, and is thus a combined Eulerian-Lagrangian technique. A straightforward adaptation of the cloud-in-cell scheme to an axisymmetric flow field is shown to introduce a grid dependent self-induced velocity to each vortex ring. To correct this behavior the potential is considered to consist of two parts, a local and a global field. An improved difference formula is derived, allowing the accurate calculation of the potential at points near vortex locations. The local potential is then subtracted before calculating the velocity, leaving only the influences of the remaining vortices. The correct self-induced velocity is then explicitly added to the vortex velocity. Calculations of the motion of one and two vortex rings are performed, demonstrating the ability of the new method to eliminate the grid dependence of the self-induced velocity. The application of the method to the calculation of helicopter rotor flows in hover is attempted.

Roberts, T. W.↗
NASA NTRS1984

Navier-Stokes calculations for the vortex of a rotor in hover

An efficient finite-difference scheme for the solution of the incompressible Navier-Stokes equation is used to study the vortex wake of a rotor in hover. The solution Procedure uses a vorticity-stream function formulation and incorporates an asymptotic far-field boundary condition enabling the size of the computational domain to be reduced in comparison to other methods. The results from the present method are compared with experimental data obtained by smoke flow visualization and hot-wire measurements for several rotor blade configurations.

Liu, C. H.↗
NASA NTRS1984

An investigation of the transient thermal analysis of spur gears

A finite element computer program is developed for evaluating the transient behavior of surface temperature in high performance spur gears. The time dimension is implemented using two and three point finite difference schemes. The different schemes are provided for the purpose of numerical stability and convergence studies. A detailed explanation of the gear cooling process leading to the establishment of a modified Blok model is also included. Other conventional models for approximating the heat transfer coefficients are available for comparison. Preliminary results are given showing snap shots of gear temperature contours at the initial stages of tooth engagement.

El-Bayoumy, L. E.↗
NASA NTRS1983

Quasiconformal mappings and grid generation

A finite difference scheme is developed for constructing quasiconformal mappings for arbitrary simply and doubly connected regions. Computational grids are generated to reduce elliptic equations to canonical form. Examples of conformal mappings on surfaces are also included.

Mastin, C. W.↗
NASA NTRS1983

A numerical model of acoustic choking. I - Shock free solutions

The phenomenon of acoustic choking in near sonic flows is investigated using the one-dimensional gasdynamic equations for an ideal gas. It is pointed out that this approach eliminates the need to make the classical small disturbance assumption. A finite difference scheme is elaborated to approximate these equations. Boundary conditions that correctly model the physics of the acoustics problems are chosen. The use of a fast Fourier transform routine allows the results to be compared with those obtained by using the conventional harmonic assumptions. Only solutions in which shocks have not fully developed are reported. Continuous solutions are sought, and these are compared with the Fubini solution and with certain results of Myers and Callegari (1977, 1978, 1979).

Walkington, N. J.↗
NASA NTRS1984

Numerical solution of a coupled pair of elliptic equations from solid state electronics

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem. Previously announced in STAR as N83-30109

Phillips, T. N.↗
NASA NTRS1983

On numerical simulation of viscous flows

Numerical simulation methods for viscous incompressible laminar flows are reviewed, with a focus on finite-difference schemes. The approaches to high/moderate-Reynolds-number flows (strong-viscous-interaction model or single sets of equations) and the factors affecting the versatility, reliability, and accuracy of the analysis algorithms are considered; approximate-factorization implicit solution techniques for low-Reynolds-number flows are discussed; and the procedures used in a number of specific problems are indicated.

Ghia, K. N.↗
NASA NTRS1984

A compact finite element method for elastic bodies

A nonconforming finite method is described for treating linear equilibrium problems, and a convergence proof showing second order accuracy is given. The close relationship to a related compact finite difference scheme due to Phillips and Rose is examined. A condensation technique is shown to preserve the compactness property and suggests an approach to a certain type of homogenization.

Rose, M. E.↗
NASA NTRS1985

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗
NASA NTRS1985

Error Reduction Program

The details of a study to select, incorporate and evaluate the best available finite difference scheme to reduce numerical error in combustor performance evaluation codes are described. The combustor performance computer programs chosen were the two dimensional and three dimensional versions of Pratt & Whitney's TEACH code. The criteria used to select schemes required that the difference equations mirror the properties of the governing differential equation, be more accurate than the current hybrid difference scheme, be stable and economical, be compatible with TEACH codes, use only modest amounts of additional storage, and be relatively simple. The methods of assessment used in the selection process consisted of examination of the difference equation, evaluation of the properties of the coefficient matrix, Taylor series analysis, and performance on model problems. Five schemes from the literature and three schemes developed during the course of the study were evaluated. This effort resulted in the incorporation of a scheme in 3D-TEACH which is usuallly more accurate than the hybrid differencing method and never less accurate.

Syed, S. A.↗
NASA NTRS1985

A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field

A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modelled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.

Macaraeg, M. G.↗
NASA NTRS1984

A numerical study of the steady scalar convective diffusion equation for small viscosity

A time-independent convection diffusin equation is studied by means of a compact finite difference scheme and numerical solutions are compared to the analytic inviscid solutions. The correct internal and external boundary layer behavior is observed, due to an inherent feature of the scheme which automatically produces upwind differencing in inviscid regions and the correct viscous behavior in viscous regions.

Giles, M. B.↗
NASA NTRS1985

Multigrid techniques for the solution of the passive scalar advection-diffusion equation

The solution of elliptic passive scalar advection-diffusion equations is required in the analysis of many turbulent flow and convective heat transfer problems. The accuracy of the solution may be affected by the presence of regions containing large gradients of the dependent variables. The multigrid concept of local grid refinement is a method for improving the accuracy of the calculations in these problems. In combination with the multilevel acceleration techniques, an accurate and efficient computational procedure is developed. In addition, a robust implementation of the QUICK finite-difference scheme is described. Calculations of a test problem are presented to quantitatively demonstrate the advantages of the multilevel-multigrid method.

Phillips, R. E.↗
NASA NTRS1985

A mixed pseudospectral/finite difference method for a thermally driven fluid in a nonuniform gravitational field

A numerical study of the steady, axisymmetric flow in a heated, rotating spherical shell is conducted to model the Atmospheric General Circulation Experiment (AGCE) proposed to run aboard a later Shuttle mission. The AGCE will consist of concentric rotating spheres confining a dielectric fluid. By imposing a dielectric field across the fluid a radial body force will be created. The numerical solution technique is based on the incompressible Navier-Stokes equations. In the method a pseudospectral technique is used in the latitudinal direction, and a second-order accurate finite difference scheme discretizes time and radial derivatives. This paper discusses the development and performance of this numerical scheme for the AGCE which has been modeled in the past only by pure FD formulations. In addition, previous models have not investigated the effect of using a dielectric force to simulate terrestrial gravity. The effect of this dielectric force on the flow field is investigated as well as a parameter study of varying rotation rates and boundary temperatures. Among the effects noted are the production of larger velocities and enhanced reversals of radial temperature gradients for a body force generated by the electric field.

Macaraeg, M. G.↗
NASA NTRS1985

Computation of transonic vortex flows past delta wings Integral equation approach

The steady full-potential equation is written in the form of Poisson's equation, and the solution of the velocity field is expressed in terms of an integral equation. The solution consists of a surface integral of vorticity distribution on the wing and its free-vortex sheets and a volume integral of source distribution within a volume around the wing and its free-vortex sheets. The solution is obtained through successive iteration cycles. The source distribution is computed by using a mixed finite-difference scheme of the Murman-Cole type. The method is applied to delta wings. Numerical examples show that a conical shock is captured on the suction side of the wing. It is attached to the lower surface of the leading-edge vortex but does not necessarily reach to the wing surface.

Kandil, O. A.↗
NASA NTRS1986

Theoretical and experimental investigation of the destruction of graphites in a flow of dissociated air

A method is presented for calculating the heating and erosion of blunt bodies made of graphite in a high-enthalpy flow of dissociated air, assuming chemical equilibrium on the surface and taking account of the thermal effects of combustion and sublimation of graphite. The analysis involves the use of a finite difference scheme to solve an equation of unsteady heat conduction. Attention is given to the equilibrium vaporization of C, C2 and C3 molecules. The calculations agree well with experimental data for a wide range of temperatures and stagnation pressures.

Bovina, T. A.↗