Accuracy study of finite difference methods
Perturbation techniques for error analysis of finite difference approximations for linear differential equations
Cyrus, N. J.↗
SEARCH · Engineering Papers
Results for “finite difference”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
An accuracy study of finite difference methods in structural analysis
Accuracy study of finite difference methods for solving boundary value problems in structural analysis
Cyrus, N. J.↗
An analysis of finite-difference techniques applied to equations governing convective transfer
Finite difference analysis of hyperbolic partial differential equations
Lomax, H.↗
Accurate finite difference methods for time-harmonic wave propagation
Finite difference methods for solving problems of time-harmonic acoustics are developed and analyzed. Multidimensional inhomogeneous problems with variable, possibly discontinuous, coefficients are considered, accounting for the effects of employing nonuniform grids. A weighted-average representation is less sensitive to transition in wave resolution (due to variable wave numbers or nonuniform grids) than the standard pointwise representation. Further enhancement in method performance is obtained by basing the stencils on generalizations of Pade approximation, or generalized definitions of the derivative, reducing spurious dispersion, anisotropy and reflection, and by improving the representation of source terms. The resulting schemes have fourth-order accurate local truncation error on uniform grids and third order in the nonuniform case. Guidelines for discretization pertaining to grid orientation and resolution are presented.
Harari, Isaac↗
An inviscid analysis of the plume created by multiple rocket engines and a comparison with available Schlieren data. I - Calculation of multiple rocket engine exhaust plumes by the method of characteristics. II - A finite difference method.
Multiple rocket engine exhaust plumes calculated by method of characteristics and finite difference and compared with schlieren data
ROCKET EXHAUST↗
An exploratory study of finite difference grids for transonic unsteady aerodynamics
A pulse-transfer function technique for calculating unsteady aerodynamic forces for a wide range of reduced frequencies is implemented in a finite difference program solving the complete unsteady transonic small perturbation equation. Forces are calculated for a two-dimensional linear flat plate case utilizing the default grids from several currently used finite difference programs. The forces are compared to exact theoretical values and grid generated boundary and internal reflections are demonstrated. Grids designed to alleviate the reflections are presented and forces for a 6% thick parabolic arc airfoil are calculated to investigate non-linear transonic effects.
Seidel, D. A.↗
Analysis of two-dimensional, unsteady flow in a propellant tank under low gravity by finite difference methods
Two-dimensional unsteady flow in propellant tank under low gravity by finite difference methods - reduction to boundary value problem
BOUNDARY VALUE PROBLEM↗
Coarse Mesh Finite Difference Acceleration for Pebble Tracking Transport in Griffin
We implemented a coarse mesh finite difference (CMFD) for accelerating transport calculations with PTT (pebble tracking transport) in the Griffin code. More specifically, extensions for transport update with the consideration of scattering operator and CMFD projection were implemented for PTT. The implementation was verified with a simplified PBR (pebble bed reactor) benchmark problem and significant performance improvements in CPU time was observed.
97 MATHEMATICS AND COMPUTING↗
Optimum sensitivities obtained without using finite differences.
Optimum sensitivities of control function with respect to vehicle parameter changes and state variables without using finite differences
OPTIMAL CONTROL↗
Finite difference methods for transient signal propagation in stratified dispersive media
Explicit difference equations are presented for the solution of a signal of arbitrary waveform propagating in an ohmic dielectric, a cold plasma, a Debye model dielectric, and a Lorentz model dielectric. These difference equations are derived from the governing time-dependent integro-differential equations for the electric fields by a finite difference method. A special difference equation is derived for the grid point at the boundary of two different media. Employing this difference equation, transient signal propagation in an inhomogeneous media can be solved provided that the medium is approximated in a step-wise fashion. The solutions are generated simply by marching on in time. It is concluded that while the classical transform methods will remain useful in certain cases, with the development of the finite difference methods described, an extensive class of problems of transient signal propagating in stratified dispersive media can be effectively solved by numerical methods.
Lam, D. H.↗
Wideband finite difference time domain implementation of surface impedance boundary conditions for good conductors
Surface impedance boundary conditions are employed to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be utilized to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A 1-D implementation for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique.
Beggs, John H.↗
Wideband finite difference time domain implementation of surface impedance boundary conditions for good conductors
Surface impedance boundary conditions are used to reduce the solution volume during the analysis of scattering from lossy dielectric objects. In a finite difference solution, they also can be used to avoid using small cells, made necessary by shorter wavelengths in conducting media, throughout the solution volume. A one dimensional implementation is presented for a surface impedance boundary condition for good conductors in the Finite Difference Time Domain (FDTD) technique. In order to illustrate the FDTD surface impedance boundary condition, a planar air-lossy dielectric interface is considered.
Beggs, John H.↗
Probability limit theorems and the convergence of finite difference approximations of partial differential equations
Partial differential equations finite difference approximation, applying convergence theorems with probabilistic method
Kushner, H. J.↗
Computation of space shuttle flow fields using noncentered finite-difference schemes.
Second- and third-order, noncentered finite-difference schemes are described for the numerical solution of the hyperbolic equations of fluid dynamics. The advantages of noncentered methods over the more conventional centered schemes are: simpler programming logic, nonhomogeneous terms are easily included, and generalization to multidimensional problems is direct. Second- and third-order methods are compared with regard to dissipative and dispersive errors and shock-capturing ability. These schemes are then used in a shock-capturing technique to determine the inviscid, supersonic flow field surrounding space shuttle vehicles (SSV). Resulting flow fields about typical pointed and blunted, delta-winged SSVs at angle of attack are presented and compared with experiment.
Kutler, P.↗
A fourth order accurate finite difference scheme for the computation of elastic waves
A finite difference for elastic waves is introduced. The model is based on the first order system of equations for the velocities and stresses. The differencing is fourth order accurate on the spatial derivatives and second order accurate in time. The model is tested on a series of examples including the Lamb problem, scattering from plane interf aces and scattering from a fluid-elastic interface. The scheme is shown to be effective for these problems. The accuracy and stability is insensitive to the Poisson ratio. For the class of problems considered here it is found that the fourth order scheme requires for two-thirds to one-half the resolution of a typical second order scheme to give comparable accuracy.
Bayliss, A.↗
Properties of finite difference models of non-linear conservative oscillators
Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.
Mickens, R. E.↗
Exponential Finite-Difference Technique
Report discusses use of explicit exponential finite-difference technique to solve various diffusion-type partial differential equations. Study extends technique to transient-heat-transfer problems in one dimensional cylindrical coordinates and two and three dimensional Cartesian coordinates and to some nonlinear problems in one or two Cartesian coordinates.
Handschuh, Robert F.↗
Finite difference time domain calculations of antenna mutual coupling
The Finite Difference Time Domain (FDTD) technique has been applied to a wide variety of electromagnetic analysis problems, including shielding and scattering. However, the method has not been extensively applied to antennas. In this short paper calculations of self and mutual admittances between wire antennas are made using FDTD and compared with results obtained using the Method of Moments. The agreement is quite good, indicating the possibilities for FDTD application to antenna impedance and coupling.
Luebbers, Raymond J.↗