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Showing papers on "Finite difference method published in 1980"


Book
01 Feb 1980
TL;DR: The authors created Reference Record created on 2005-11-18, modified on 2016-08-08, and used it to build a reference record for mathematical calculiques and differentielles.
Abstract: Keywords: elements : finis ; equations : differentielles ; methodes de : calcul ; mathematiques Reference Record created on 2005-11-18, modified on 2016-08-08

1,003 citations


Journal ArticleDOI
TL;DR: The FIDAM code as discussed by the authors is a system of computer programs designed for the solution of two-dimensional, linear and nonlinear, elliptic problems and three-dimensional parabolic problems.

670 citations


Journal ArticleDOI
TL;DR: In this article, a numerical procedure is described that simplifies the analysis of the EMP response of structures with dielectric or poorly conducting segments, which is similar to the one described in this paper.
Abstract: A numerical procedure is described that will simplify the analysis of the EMP response of structures with dielectric or poorly conducting segments.

261 citations


Journal ArticleDOI
TL;DR: In this article, a numerical simulation of a laboratory experiment involving coupled heat and mass transfer in a horizontal porous medium column with one end subjected to a temperature below 0°C has been carried out.
Abstract: A numerical simulation of a laboratory experiment involving coupled heat and mass transfer in a horizontal porous medium column with one end subjected to a temperature below 0°C has been carried out. The model is essentially that of Harlan (1973) and is solved numerically by the finite difference method using the Crank-Nicholson scheme. The solution yields temperature, liquid water content, and ice content profiles along the column as a function of time. Comparison of the experimental results and the simulation analysis results shows that Harlan's model, with some modification in the hydraulic conductivity of the frozen medium, can be used successfully to simulate numerically the coupled heat and mass transfer processes when ice lensing does not occur.

209 citations


Journal ArticleDOI
TL;DR: In this article, a general numerical method to solve two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically is presented.
Abstract: A study of two-point seismic-ray tracing problems in a heterogeneous isotropic medium and how to solve them numerically will be presented in a series of papers. In this Part 1, it is shown how a variety of two-point seismic-ray tracing problems can be formulated mathematically as systems of first-order nonlinear ordinary differential equations subject to nonlinear boundary conditions. A general numerical method to solve such systems in general is presented and a computer program based upon it is described. High accuracy and efficiency are achieved by using variable order finite difference methods on nonuniform meshes which are selected automatically by the program as the computation proceeds. The variable mesh technique adapts itself to the particular problem at hand, producing more detailed computations where they are needed, as in tracing highly curved seismic rays. A complete package of programs has been produced which use this method to solve two- and three-dimensional ray-tracing problems for continuous or piecewise continuous media, with the velocity of propagation given either analytically or only at a finite number of points. These programs are all based on the same core program, PASVA3, and therefore provide a compact and flexible tool for attacking ray-tracing problems in seismology. In Part 2 of this work, the numerical method is applied to two- and three-dimensional velocity models, including models with jump discontinuities across interfaces.

128 citations


Journal ArticleDOI
TL;DR: In this article, numerical perturbation calculations on Be and C2+ were performed starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s 22p2.
Abstract: We report here numerical perturbation calculations on Be and C2+ starting from a model space consisting of the two strongly interacting configurations 1s22s2 and 1s22p2. We use numerically represented radial pair functions which are solutions of a system of coupled differential equations obtained by a finite difference method. By iterating the system of pair equations the most important correlation effects are included to all orders. This is demonstrated for C2+, where excitation energies for the 2p2 levels are obtained with an accuracy better than 1% or 0.2 eV. For Be only second-order results are reported. Here the iterative scheme does not converge, probably due to the presence of intruder states of the type 2sns 1S, which lie between the two 1S states originating from the model space. The second-order calculation with the two-configurational model space and orbitals generated in the 1s2 Hertree-Fock core yields 93.6% of the correlation energy, compared to 80.9% for a similar calculation using a model space with only the ground-state configuration 1s22s2 and orbitals generated in the Hartree-Fock potential of that configuration.

116 citations


Journal ArticleDOI
TL;DR: In this paper, a nonlinear analysis is carried out for the motion of the inviscid, incompressible fluid in a two-dimensional, rigid, open container which is subjected to forced sinusoidal pitching oscillation.
Abstract: A nonlinear analysis is carried out for the motion of the inviscid, incompressible fluid in a two-dimensional, rigid, open container which is subjected to forced sinusoidal pitching oscillation. Firstly, the problem is defined as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions. Next, the problem is formulated in the form of a pseudo-variational principle, which provides a basis for our discretization. The finite element method and finite difference method are used spacewise and timewise, respectively. Due to the strong nonlinearity of the problem, an incremental method is used for the numerical analysis. Numerical results obtained by the present method are compared with solutions of the linear theory and experimental data. The difference between linear and nonlinear analysis has been clearly indicated.

101 citations


Journal ArticleDOI
TL;DR: Computational methods for fluid-structure analysis are surveyed, and emphasis is placed on semi-discretization methods, such as finite element and finite difference methods.

98 citations


DissertationDOI
01 Jan 1980
TL;DR: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented in this paper, which is a new method based on the mathematical theory of characteristics.
Abstract: The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

95 citations


Journal ArticleDOI
TL;DR: In this article, the authors give convergence criteria for general difference schemes for boundary value problems in Lipschitzian regions, and prove convergence for the multi-grid algorithm with Gauss-Seidel's iteration as smoothing procedure.
Abstract: Convergence proofs for the multi-grid iteration are known for the case of finite element equations and for the case of some difference schemes discretizing boundary value problems in a rectangular region. In the present paper we give criteria of convergence that apply to general difference schemes for boundary value problems in Lipschitzian regions. Furthermore, convergence is proved for the multi-grid algorithm with Gauss-Seidel's iteration as smoothing procedure.

93 citations



Journal ArticleDOI
TL;DR: A finite difference method has been developed to study the inviscid stability of swirling flows to small non-axisymmetric disturbances as mentioned in this paper, which appears to be more efficient and simpler to implement for this class of problem, than previously reported methods.
Abstract: A finite difference method has been developed to study the inviscid stability of swirling flows to small non-axisymmetric disturbances. We apply the method to Batchelor's trailing line vortex solution [3]. The method appears to be more efficient, and simpler to implement for this class of problem, than previously reported methods.

Journal ArticleDOI
TL;DR: In this paper, a numerical method for solving the equations governing the steady motion of a viscous fluid through a slightly curved tube of circular cross-section is described, which is also applicable to the solution of any problem governed by the steady two-dimensional Navier-Stokes equations in the plane polar co-ordinate system.
Abstract: A numerical method is described which is suitable for solving the equations governing the steady motion of a viscous fluid through a slightly curved tube of circular cross-section but which is also applicable to the solution of any problem governed by the steady two-dimensional Navier–Stokes equations in the plane polar co-ordinate system. The governing equations are approximated by a scheme which yields finite-difference equations which are of second-order accuracy with respect to the grid sizes but which have associated matrices which are diagonally dominant. This makes them generally more amenable to solution by iterative techniques than the approximations obtained using standard central differences, while preserving the same order of accuracy.The main object of the investigation is to obtain numerical results for the problem of steady flow through a curved tube which corroborate previous numerical work on this problem in view of a recent paper (Van Dyke 1978) which tends to cast doubt on the accuracy of previous calculations at moderately high values of the Dean number; this is the appropriate Reynolds-number parameter in this problem. The present calculations tend to verify the accuracy of previous results for Dean numbers up to 5000, beyond which it is difficult to obtain accurate results. Calculated properties of the flow are compared with those obtained in previous numerical work, with the predictions of boundary-layer theory for large Dean numbers and with the predictions of Van Dyke (1978).


Journal ArticleDOI
TL;DR: In this paper, a nonlinear, time-dependent, hydromagnetic model is developed, based on the eight partial differential equations of resistive magnetohydrodynamics (MHD), which are expressed as a set of conservation laws in general, orthogonal, curvilinear coordinates in two space dimensions.

Journal ArticleDOI
TL;DR: A unified framework is presented for analyzing the accuracy of finite difference, finite element, and spectral methods in approximating evolutionary problems and demonstrates the importance of the interpretation given to the discrete data generated in any computation.

Journal ArticleDOI
TL;DR: In this paper, the issue of numerical precision as affected by the use of different routing schemes was investigated, based on the observation that in an application of the Kalinin-Miljukov method, accuracy improved when a more refined difference scheme was used in place of the conventional one.
Abstract: This note will center on the issue of numerical precision as affected by the use of different routing schemes. The investigation is prompted by the observation that in an application of the Kalinin-Miljukov method, accuracy improved when a more refined difference scheme was used in place of the conventional one.

Journal ArticleDOI
01 Sep 1980
TL;DR: In this article, the combined approach of linearisation and finite difference method was used to solve the improved Boussinesq equation and a three-level iterative scheme having second order accuracy and constant coefficients matrix was devised and used in discussing the dynamics of waves having various initial wave packets.
Abstract: The combined approach of linearisation and finite difference method is used to solve the improved Boussinesq equation. A three-level iterative scheme having second order accuracy and constant coefficients matrix is devised and used in discussing the dynamics of waves having various initial wave packets. The results are in good agreement with the available results.

Journal ArticleDOI
TL;DR: In this paper, the buckling loads for tapered and stepped columns have been determined by a finite difference method using a matrix iteration solution technique (a BASIC program for which is appended).

Journal ArticleDOI
TL;DR: In this paper, a detailed study of the error growth associated with explicit difference schemes for a conduction-convection problem is made, and it is shown that the error can become arbitrarily large after a finite number of time steps even though it ultimately decays to zero.
Abstract: A detailed study is made of the error growth associated with explicit difference schemes for a conduction-convection problem. It is shown that the error can become arbitrarily large after a finite number of time steps even though it ultimately decays to zero. Certain ambiguities reported in the literature can thereby be resolved.

Journal ArticleDOI
TL;DR: In this article, methods of order two and four are developed for the continuous approximation of the solution of a two-point boundary value problem associated with a certain fourth order linear differential equation via quintic and sextic spline functions.
Abstract: Methods of order two and four are developed for the continuous approximation of the solution of a two-point boundary value problem associated with a certain fourth order linear differential equation via quintic and sextic spline functions. Numerical results are summarized for some typical numerical examples and compared with some known finite difference methods of the same order.

Journal ArticleDOI
TL;DR: In this paper, a method for solving the linear hydrodynamic equations for the sea, using an expansion of the horizontal component of current in terms of depth-varying functions (the basis functions) with coefficients that vary with time and horizontal position, is presented.

Journal ArticleDOI
J. Gazdag1
TL;DR: In this article, an alternative method, termed ASD (for Accurate Space Derivative), and its application to the wave equation migration problem is described. But this method cannot accommodate media with vertical as well as horizontal velocity variations.
Abstract: A stacked seismic section represents a wave-field recorded at regularly spaced points on the surface. The seismic migration process transforms this recorded data into a reflectivity display. In recent years, Jon F. Claerbout and his co-workers developed migration techniques based on the numerical approximation of the wave equation by finite difference methods. This paper describes an alternative method, termed ASD (for Accurate Space Derivative), and its application to the wave equation migration problem. In this approach to the numerical solution of partial differential equations, partial derivatives are computed by finite Fourier transform methods. This migration method can accommodate media with vertical as well as horizontal velocity variations.

Journal ArticleDOI
TL;DR: In this paper, a new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain, which is more restrictive than one based only on the nodal values.
Abstract: Convection–diffusion equations are difficult to solve when the convection term dominates because most solution methods give solutions which oscillate in space. Previous criteria based on the one-dimensional convection–diffusion equation have shown that finite difference and Galerkin (linear or quadratic basis functions) will not give oscillatory solutions provided the Peclet number times the mesh size (Pe Δx) is below a critical value. These criteria are based on the solution at the nodes, and ensure that the nodal values are monotone. Similar criteria are developed here for other methods: quadratic Galerkin with upwind weighting, cubic Galerkin, orthogonal collocation on finite elements with quadratic, cubic or quartic polynomials using Lagrangian interpolation, cubic or quartic polynominals using Hermite interpolation, and the method of moments. The nodal values do not oscillate for collocation or moments methods with Hermite cubic polynomials regardless of the value of Pe Δx. A new criterion is developed for all methods based on the monotonicity of the solutions throughout the domain. This criterion is more restrictive than one based only on the nodal values. All methods that are second order (Δx2) or better in truncation error give oscillatory solutions (based on the entire domain) unless Pe Δx is below a critical value. This value ranges from 2 for finite difference methods to 4·6 for Hermite, quartic, collocation methods.

Journal ArticleDOI
TL;DR: In this article, the authors investigated several factors affecting the accuracy and efficiency of numerical determination of the bound state energy eigenvalues of the one dimensional Schrodinger equation, and concluded that the Numerov-Cooley method is the most efficient method for most complex potentials.

Journal ArticleDOI
TL;DR: In this article, the authors studied the effect of the density inversion on the cooling process of a 2D laminar natural convection of water, enclosed in rectangular cavities with wall temperature maintained at 0°C.


Journal ArticleDOI
TL;DR: A new method of formulating the discrete equations suggests itself and is presented, that appears to hold considerable promise for future development.
Abstract: Finite-difference and finite-element methods are widely used to solve problems described by sets of partial differential equations. However, the connections between the approximations made in the discretization process and the final solution errors, for a given grid, are often not clearly understood, especially when convection is a dominant factor. These connections are clarified in the present paper and, from the insight gained, a new method of formulating the discrete equations suggests itself. The results of applying two different schemes, that are both based on this method, to an example problem are presented. These are compared with results obtained using two finite-difference schemes. The new approach appears to hold considerable promise for future development.

Journal ArticleDOI
TL;DR: In this paper, a new approach to the solution of two-dimensional boundary value problems is described, which eliminates the disadvantages and combines the advantages of both conformal transformations and numerical methods, and is applied to the calculation of the even and odd mode capacitances of cylindrical rods between plane parallel ground planes.
Abstract: This paper describes a new approach to the solution of two-dimensional boundary value problems which eliminates the disadvantages and combines the advantages of both conformal transformations and numerical methods. The conformal transformations are used to remove potential gradient singularities, and numerical (e.g., finite difference) methods may then be applied to the resulting almost-regular field problems. Boundary value problems previously regarded as very difficult become tractable, and considerable savings in computer time and storage requirements are achieved. The method is applied to the calculation of the even and odd mode capacitances of cylindrical rods between plane parallel ground planes. Excellent agreement with resuIts obtained previously is demonstrated.

Journal ArticleDOI
TL;DR: In this paper, an implicit scheme for solving Maxwell's equations is proposed, in which space discretization is obtained by the finite element method, while Newmark's scheme provides the time discretisation.