Showing papers in "Journal of Computational Physics in 1984"

TL;DR: This work recognizes the need for additional dissipation in any higher-order Godunov method of this type, and introduces it in such a way so as not to degrade the quality of the results.

TL;DR: In this paper, a comparison of numerical methods for simulating hydrodynamics with strong shocks in two dimensions is presented and discussed, and three approaches to treating discontinuities in the flow are discussed.

TL;DR: In this article, a spectral element method was proposed for numerical solution of the Navier-Stokes equations, where the computational domain is broken into a series of elements, and the velocity in each element is represented as a highorder Lagrangian interpolant through Chebyshev collocation points.

TL;DR: In numerical modeling of physical phenomena, it is often necessary to solve the advective transport equation for positive definite scalar functions as discussed by the authors, and two main hybrid-type schemes have been developed.

TL;DR: In this paper, various numerical methods are employed in order to approximate the nonlinear Schrodinger equation, namely: (i) the classical explicit method, (ii) hopscotch method, implicit-explicit method, Crank-Nicolson implicit scheme, (v) the Ablowitz-Ladik scheme, split step Fourier method (F. Tappert), and (vii) pseudospectral (Fourier) method.

TL;DR: A variety of two-phase flow models can be derived following a few basic principles, which are here illustrated which no more generality than is essential are illustrated.

TL;DR: Numerical optimization methods based on thermodynamic concepts are extended to the case of continuous multidimensional parameter spaces, and a self-regulatory mechanism for choosing the random step distribution is described.

TL;DR: In this paper, a numerical model used to simulate global convection and magnetic field generation in stars is described, where the velocity, magnetic field, and thermodynamic perturbations are expanded in spherical harmonics to resolve their horizontal structure and in Chebyshev polynomials to resolve the radial structure.

TL;DR: A second-order accurate scheme for the integration in time of the conservation laws of compressible fluid dynamics is presented, and two related versions are proposed, one Lagrangian and the second direct Eulerian.

TL;DR: In this paper, the Ablowitz-Ladik scheme for the nonlinear Schrodinger equation is compared to other known numerical schemes, and generally proved to be faster than all utilized finite difference schemes but somewhat slower than the finite Fourier (pseudospectral) methods.

TL;DR: In this article, the authors examined several methods for determining the eigenvalues of a system of equations in which the parameter appears nonlinearly and the equations are the result of discretization of differential eigenvalue problems using a finite Chebyshev series.

TL;DR: State of the art and recent developments in computational linear algebra, including linear systems, least squares techniques, the singular value decomposition, and eigenvalue problems are reviewed briefly.

TL;DR: In this article, the authors considered the case of two-phase separated planar flow and developed models with real characteristic values for all physically acceptable states (state space) and except for a set of measure zero have a complete set of characteristic vectors in state space.

TL;DR: In this paper, a microscopic model was proposed to represent blood by a suspension of discrete massless platelets in a viscous incompressible fluid, and the platelet forces were calculated implicitly by minimizing a nonlinear energy function.

TL;DR: Two Chebyshev solvers are presented for the linear Helmholtz equation, one a 3-D direct spectral solver based on a diagonalization technique and the other an iterative pseudospectral 2-D calculation with finite difference preconditioning.

TL;DR: In this article, a model of water waves that describes wave propagation over long distances accurately, at low cost, and for a wide variety of physical situations are given, using exact prognostic equations, and a high-order expansion to relate variables at each time step.

TL;DR: In this paper, a finite analytic (FA) numerical solution was developed for unsteady two-dimensional Navier-Stokes equations, which utilizes the analytic solution in a small local element to formulate the algebraic representation of partial differential equations.

TL;DR: In this paper, a numerical scheme is developed which automatically locates the angle at which a shock might be expected to cross the computing grid then constructs separate finite difference formulas for the flux components normal and tangential to this direction.

TL;DR: New difference formulas are derived for solving the biharmonic problem in two dimensions over a rectangular domain using only the nine grid points of a single mesh cell and do not require fictitious points in order to approximate the boundary conditions.

TL;DR: In this paper, a random flight procedure is proposed to replace a large number of local scattering events by a single advance of the coordinates and time of a particle, which can substantially improve the computational efficiency of the implicit Monte Carlo method without affecting its accuracy.

TL;DR: It is shown that it is possible to convert this integral to a surface integral by the appropriate use of the divergence theorem, thus greatly reducing the complexity of the problem.

TL;DR: In this article, two distinctly different numerical methods were developed for solving the conservative initial value problem x = f(x), x(O)= α, dot x (O)= β.

TL;DR: In this paper, a numerical analysis of the Hermite function series is presented, where the authors use Steepest descent and residues to asymptotically evaluate the coefficient integrals.

TL;DR: In this article, the authors present a numerical technique to approximate the solution of a simplified model of turbulent combustion, which is particularly suited for flows at high Reynolds number, using random vortex element techniques coupled to a flame propagation algorithm based on Huyghens' principle.

TL;DR: In this article, a discrete ordinate method is developed for the solution of linear differential equations, which is based on a Gaussian quadrature procedure and is an extension of the discrete ordination method used for the solutions of integral equations.

TL;DR: In this paper, a new and efficient iteration method for obtaining simultaneously several eigensolutions, and even for obtaining only one solution, of a large real-symmetric matrix is presented by modifying the simultaneous expansion method by Davidson and Liu.

TL;DR: In this article, a full implicit continuous Eulerian (FICE) scheme is developed for solving multidimensional transient MHD flow problems, where the boundary conditions are treated by classifying them into physical and computational ones.

TL;DR: In this article, an expansion procedure using the Chebyshev polynomials as base functions is proposed, which yields more accurate results than either of the Galerkin or tau methods as indicated from solving the Orr-Sommerfeld equation for both the Poiseuille flow and the Blasius velocity profile.

TL;DR: In this article, a technique for applying discrete Fourier series to infinite domains is presented, which uses mappings designed to minimize truncation error and can be applied to solve mixed initial boundary value problems among others.

TL;DR: It is shown that these systems can efficiently be treated by a variable stepsize variable formula method (VSVFM) based on the use of predictor-corrector schemes and the main ideas, implemented in the time-integration part, might be applied in many other situations.