Showing papers in "Journal of Computational Physics in 1981"
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TL;DR: In this paper, the concept of a fractional volume of fluid (VOF) has been used to approximate free boundaries in finite-difference numerical simulations, which is shown to be more flexible and efficient than other methods for treating complicated free boundary configurations.
11,567 citations
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TL;DR: The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one as mentioned in this paper, which readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum.
2,042 citations
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TL;DR: The modification transforms the coupled system of equations into an uncoupled diagonal form that requires less computational work and has an important effect on the application of implicit finite-difference schemes to vector processors.
1,232 citations
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TL;DR: A survey of methods for imposition of radiation boundary conditions in numerical schemes is presented in this article, where combining of absorbing boundary conditions with damping (in particular, sponge filters) and with wave-speed modification are shown to offer significant improvements over earlier methods.
625 citations
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TL;DR: In this paper, a set of numerical techniques for calculating heat and particle source rates due to neutral beam injection in axisymmetric tokamaks is described, taking into account a number of significant, and normally neglected, effects.
518 citations
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TL;DR: The paper gives decompositions for various types of matrices as they occur in the implicit discretisation of practical problems, including symmetric M -matrices of very regular structure and positive definite matrices.
302 citations
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TL;DR: In this article, a finite-difference method to approximate a Schrodinger equation with a power non-linearity is described, which is used to model the propagation of a laser beam in a plasma.
282 citations
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TL;DR: The MFE method requires a small fraction of the grid nodes which are used in conventional PDE solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate PDE solutions on entire problem domains.
216 citations
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TL;DR: Silliman's analysis of slot coating is extended to accommodate film flows with highly bent menisci, as in slide and curtain coating, by combining polar and Cartesian coordinate parametrizations of meniscus shape as discussed by the authors.
205 citations
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TL;DR: In this article, a new Gaussian quadrature procedure was developed for integrals of the form ∫ 0 ∞ e − y 2 y p ( y ) dy for p = 0, 1 and 2.
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TL;DR: In this paper, a new numerical scheme is proposed for the dispersion-convection equation which combines the utility of a fixed grid in Eulerian coordinates with the computational power of the Lagrangian method.
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TL;DR: The n-element smoothing operator is constructed which consists of IZ basic operators in form (1) with the following essential properties: the smoothing of the longer waves is too strong.
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TL;DR: In this article, it was shown that an implicit E field can be obtained from Poisson's equation with the aid of the lower two fluid moment equations, permitting stable particle simulations.
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TL;DR: In this paper, a new explicit, time splitting algorithm for finite difference modeling of the Navier-Stokes equations of fluid mechanics is presented. But it is not shown that the split operators achieve their maximum allowable time step, i.e., the corresponding Courant number.
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IBM1
TL;DR: A Lanczos procedure is described which allows us to compute either few or many eigenvalues of such matrices in any intervals specified by the user, and can even be used to compute all of the eigen values.
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TL;DR: In this article, a numerical method for analyzing transient eddy currents on thin conductors with arbitrary connections and shapes is presented, described by current functions and discretized in the usual manner of the finite element method.
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TL;DR: In this article, the general problem of finite differencing the diffusion equation on a two-dimensional Lagrangian hydrodynamic mesh is discussed and a set of general criteria is developed.
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TL;DR: In this article, a code is described which transfers an arbitrary initial plasma and field configuration under the constaints of mass and flux conservation into an equilibrium state by minimizing the energy of the system so that, in principle, the equilibrium attained is stable.
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TL;DR: Methods are described for the solution of certain sparse linear systems with a non-symmetric matrix that arises from discretisation of second order partial differential equations with first order derivative terms.
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TL;DR: In this article, a new method to solve the Boltzmann equation is proposed, based on concepts from the kinetic theory of gases. But it is not shown that the method can offer significant advantages over standard finite difference methods for certain problems, such as the Riemann shock-tube problem.
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TL;DR: In this article, Petrov-Galerkin methods based on piecewise linear interpolants for the Korteweg-de Vries and related equations are studied and both accuracy and stability are analyzed for the linearised case.
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TL;DR: In this article, it is demonstrated how the computer, used in a heuristic mode, has greatly augmented our understanding of the mathematics of nonlinear dynamical process, and the role of good graphics in enhancing the discovery and retention of new mathematical properties of equations is illustrated.
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TL;DR: In this paper, the authors used the random choice method to compute the oil-water interface for two dimensional porous media equations and showed that it is a correct numerical procedure for this problem even in the highly fingered case.
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TL;DR: In this article, a nonlinear filtering methodology for numerical solution of the convective terms in the Eulerian form of the hydrodynamic equations was developed for the multidimensional continuity equation and tested on several differencing schemes in both one and two spatial dimensions.
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TL;DR: In this article, the implicit determination of the electric field required in these simulations is achieved by using the continuity and momentum equations in conjunction with the Poisson equation in a manner guaranteeing numerical stability for long wavelengths satisfying the condition k/sub max/v/sub the/..delta..t<<1.
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TL;DR: In this article, the steady state transport of neutral atoms cylindrical plasmas is described, where the physical model used represents atoms emerging from charge exchange collisions by an isotropic source of neutrals with energy equal to 3/2 times the local ion temperature.
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TL;DR: In this paper, a comparison of 11 different methods applied to three different test problems was made and the results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions.
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TL;DR: In this paper, a new technique of moving mesh points in physical space is introduced so as to reduce the error in a computed asymptotic solution relative to that obtained using a fixed mesh.
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TL;DR: In this paper, a comparison of solutions of the continuity equations for the motion of electrons and ions in a strong electric field using the methods of Euler, Runge-Kutta, Lax-Wendroff, characteristics and the flux-corrected transport (FCT) algorithm was made.