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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

Second-order explicit finite-difference methods for transient-flow analysis

Three second-order accurate numerical methods - MacCormack's method, Lambda scheme and Gabutti scheme - are introduced to solve the quasi-linear, hyperbolic partial differential equations describing transient flows in closed conduits. The details of these methods and the treatment of boundary conditions are presented and the results computed by using these methods for a typical piping system are compared. It is shown that for the same accuracy, second-order methods require considerably lesser number of computational nodes and computer time as compared to those required by the first-order methods.

Chaudhry, M. H.↗
NASA NTRS1985

Implicit finite-difference methods for the Euler equations

The present paper is concerned with two-dimensional Euler equations and with schemes which are in use of the time of this writing. Most of the development presented carries over directly to three dimensions. The characteristics of the two-dimensional Euler equations in Cartesian coordinates are considered along with generalized curvilinear coordinate transformations, metric relations, invariants of the transformation, flux Jacobian matrices and eigensystems, numerical algorithms, flux split algorithms, implicit and explicit nonlinear control (smoothing), upwind differencing in supersonic regions, unsteady and steady-state computation, the diagonal form of implicit algorithm, metric differencing and invariants, boundary conditions, geometry and mesh generation, and sample solutions.

Pulliam, T. H.↗
NASA NTRS1984

Finite difference simulation of unsteady interactive flows

The development of time-dependent numerical simulations of unsteady interactive flows of an aerodynamic nature is reviewed with emphasis on compressible flows at flight Reynolds numbers and noniterative schemes based on Navier-Stokes equations. The importance of writing the equations in strong conservation-law form for a generalized body-oriented coordinate system is pointed out. The discussion covers time and length scales and numerical methods currently in use. Some computed results are presented and compared with experimental data.

Deiwert, G. S.↗
NASA NTRS1985

Finite difference operators on unstructured triangular meshes

A new form of the Laplace operator is derived which is shown to be second-order accurate when calculated at mesh triangle nodes if the cells corresponding to the nodes have a high degree of symmetry. It is demonstrated that the Laplace operator directly derived from Stokes' integral theorem is only zeroth-order accurate on these same cells. The construction of gradient and Laplace operators on unstructured triangular grids are discussed from the variational point of view. Two discrete representations of the Laplacian are compared to each other, and conclusions are drawn regarding their accuracy on a pointwise basis. Finally, geometric relations valid on arbitrary polygons are given for completeness in an appendix.

Erlebacher, G.↗
NASA NTRS1987

Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow

An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

Braun, M. J.↗
NASA NTRS1987

Adaptive finite difference methods in fluid dynamics

An adaptive method to solve partial differential equations in fluid mechanics is presented. The approach requires internal boundary conditions that must be conservative, data structures for keeping track of several layers of fine grid patches, error estimation, and heuristics for automatic grid generation. In practical calculations gains in computer efficiency up to 10 over nonadaptive methods are observed. The whole procedure takes 3000 lines of FORTRAN code.

Berger, Marsha J.↗
NASA NTRS1989

Personal computer study of finite-difference methods for the transonic small disturbance equation

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment of the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Bland, Samuel R.↗
NASA NTRS1990

Comparison of several finite-difference methods

The present numerical study establishes that, with the MacCormack and 'two-four' methods, the solution accuracy obtainable in problems involving wave propagation, shock-wave and contact discontinuities, and viscous effects, will be strongly dependent on Courant number. The application of flux correction to the MacCormack and two-four methods is noted to significantly attenuate dispersion errors; the ensuing solutions capture the discontinuities in the shock-tube problem with improved accuracy and resolution, and are free of dispersion errors for the viscous Burgers' equation.

Biringen, S.↗
NASA NTRS1990

Comparison between analytical models and finite-difference simulations in transmission-line tap resistors and L-type cross-Kelvin resistors

Approximate analytical models of the transmission-line tap resistor and the cross-Kelvin resistor are compared with computer-simulated pseudo-three-dimensional resistor network models. The analytical formulas are in good agreement with the simulations over a useful range of parameters and are readily applied to the extraction of the contact resistivity and the sheet resistances of the semiconducting layer under and outside the contacts. The extraction procedure, which is easily implemented on a personal computer, is carried out for the case of alloyed AuGeNi/GaAs contacts, illustrating the importance of (1) distinguishing between layer sheet resistance under and outside the contacts and (2) considering two-dimensional current flow in the semiconducting layer.

Scorzoni, Andrea↗
NASA NTRS1990

Personal computer study of finite-difference methods for the transonic small disturbance equation

Calculation of unsteady flow phenomena requires careful attention to the numerical treatment to the governing partial differential equations. The personal computer provides a convenient and useful tool for the development of meshes, algorithms, and boundary conditions needed to provide time accurate solution of these equations. The one-dimensional equation considered provides a suitable model for the study of wave propagation in the equations of transonic small disturbance potential flow. Numerical results for effects of mesh size, extent, and stretching, time step size, and choice of far-field boundary conditions are presented. Analysis of the discretized model problem supports these numerical results. Guidelines for suitable mesh and time step choices are given.

Bland, Samuel R.↗
NASA NTRS1991

A finite-difference, frequency-domain numerical scheme for the solution of the linearized unsteady Euler equations

A numerical method is developed for solving periodic, three-dimensional, vortical flows around lifting airfoils in subsonic flow. The first-order method, that is presented, fully accounts for the distortion effects of the nonuniform mean flow on the convected upstream vortical disturbances. The unsteady velocity is split into a vortical component which is a known function of the upstream flow conditions and the Lagrangian coordinates of the mean flow, and an irrotational field whose potential satisfies a nonconstant-coefficient, inhomogeneous, convective wave equation. Using an elliptic coordinate transformation, the unsteady boundary value problem is solved in the frequency domain on grids which are determined as a function of the Mach number and reduced frequency. Extensive comparisons are made with known solutions to unsteady vortical flow problems, and it is seen that the agreement is generally very good for reduced frequencies ranging from 0 up to 4.

Scott, James R.↗
NASA NTRS1990

Matrix-based, finite-difference algorithms for computational acoustics

A compact numerical algorithm is introduced for simulating multidimensional acoustic waves. The algorithm is expressed in terms of a set of matrix coefficients on a three-point spatial grid that approximates the acoustic wave equation with a discretization error of O(h exp 5). The method is based on tracking a local phase variable and its implementation suggests a convenient coordinate splitting along with natural intermediate boundary conditions. Results are presented for oblique plane waves and compared with other procedures. Preliminary computations of acoustic diffraction are also considered.

Davis, Sanford↗
NASA NTRS1991

Time-accurate finite difference solutions to the incompressible Navier-Stokes/energy equations

Two new algorithms for solving coupled Navier-Stokes and energy equations are presented. The algorithms are compared with available Navier-Stokes solutions for the model problem of a driven-cavity-flow over a range of Reynolds numbers. It is noted that the algorithms represent two different implementations of the fractional step approach to the solution of the coupled Navier-Stokes and energy equations using the Boussinesq approximation.

Mirfakhraee, Ali↗