Showing papers in "Journal of Computational Physics in 1997"

TL;DR: In this article, it is shown that these features can be obtained by constructing a matrix with a certain property U, i.e., property U is a property of the solution of the Riemann problem.

TL;DR: In this article, a numerical method for solving incompressible viscous flow problems is introduced, which uses the velocities and the pressure as variables and is equally applicable to problems in two and three space dimensions.

TL;DR: In this article, a new numerical technique is presented that has many advantages for obtaining solutions to a wide variety of time-dependent multidimensional fluid dynamics problems, including stability, accuracy, and zoning.

TL;DR: In this article, a quasi-Newton method is used to simultaneously relax the internal coordinates and lattice parameters of crystals under pressure, and the symmetry of the crystal structure is preserved during the relaxation.

TL;DR: In this article, a second-order extension of the Lagrangean method is proposed to integrate the equations of ideal compressible flow, which is based on the integral conservation laws and is dissipative, so that it can be used across shocks.

TL;DR: This paper studies a multiscale finite element method for solving a class of elliptic problems arising from composite materials and flows in porous media, which contain many spatial scales and proposes an oversampling technique to remove the resonance effect.

TL;DR: This paper extends a discontinuous finite element discretization originally considered for hyperbolic systems such as the Euler equations to the case of the Navier?Stokes equations by treating the viscous terms with a mixed formulation, and finds the method is ideally suited to compute high-order accurate solution of theNavier?

TL;DR: In this article, the smoothed particle hydrodynamics (SPH) method is extended to model incompressible flows of low Reynolds number, and the results show that the SPH results exhibit small pressure fluctuations near curved boundaries.

TL;DR: In this article, it was shown that the derived form of the finite difference Jacobian can prevent nonlinear computational instability and thereby permit long-term numerical integrations, which is not the case in finite difference analogues of the equation of motion for two-dimensional incompressible flow.

TL;DR: In this paper, a model for studying ocean circulation problems taking into account the complicated outline and bottom topography of the World Ocean is presented, and the model is designed to be as consistent as possible with the continuous equations with respect to energy.

TL;DR: This paper focuses its attention on two-dimensional steady-state problems and presents higher order accurate discontinuous finite element solutions on unstructured grids of triangles and shows that, in the presence of curved boundaries, a meaningful high-order accurate solution can be obtained only if a corresponding high- order approximation of the geometry is employed.

TL;DR: In this paper, it was shown that discrepancies between the results of dealiased spectral and standard nondialiased finite-difference methods are due to both aliasing and truncation errors with the latter being the leading source of differences.

TL;DR: In this paper, a simple level set method for solving the Stefan problem is presented, which can handle topology changes and complicated interfacial shapes and can numerically simulate many of the physical features of dendritic solidification.

TL;DR: A class of high resolution multidimensional wave-propagation algorithms is described for general time-dependent hyperbolic systems based on solving Riemann problems and applying limiter functions to the resulting waves, which are then propagated in a multiddimensional manner.

TL;DR: In this paper, the authors present a numerical method for computing solutions of the incompressible Euler or Navier?Stokes equations when a principal feature of the flow is the presence of an interface between two fluids with different fluid properties.

TL;DR: A new class of high-order monotonicity-preserving schemes for the numerical solution of conservation laws is presented, designed to preserve accuracy near extrema and to work well with Runge?Kutta time stepping.

TL;DR: In this paper, a finite-difference method using a nonuniform triangle mesh is described for the numerical solution of the nonlinear two-dimensional Poisson equation, where  is a function of � or its derivatives,Sis a function for position, and  or its normal derivative is specified on the boundary.

TL;DR: A class of explicit, Eulerian finite-difference algorithms for solving the continuity equation which are built around a technique called “flux correction,” which are of indeterminate order but yield realistic, accurate results.

TL;DR: A finite element-based additive Schwarz preconditioner using overlapping subdomains plus a coarse grid projection operator which is applied directly to the pressure on the interior Gauss points can yield as much as a fivefold reduction in simulation time over previously employed methods based upon deflation.

TL;DR: In this paper, the authors introduced the idea of time-varying coefficients which fits more naturally with a particle formulation, which is a Lagrangian particle method for fluid dynamics which simulates shocks by using an artificial viscosity.

TL;DR: In this paper, a specific energy equation instead of the thermal energy equation is used to handle shocks in smooth particle hydrodynamics (SPH) and the resulting equations are very similar to the equations constructed for Riemann solutions of compressible gas dynamics.

TL;DR: In the context of generic rigidity percolation, it is shown how to calculate the number of internal degrees of freedom, identify all rigid clusters, and locate the overconstrained regions.

TL;DR: An hierarchy of uniformly high-order accurate schemes is presented which generalizes Godunov's scheme and its second- order accurate MUSCL extension to an arbitrary order of accuracy.

TL;DR: In this article, a contour dynamics algorithm for the Euler equations of fluid dynamics in two dimensions is presented, which is applied to regions of piecewise-constant vorticity within finite-area-vortex regions (FAVRs).

TL;DR: Several new implicit schemes for the solution of the compressible Navier?Stokes equations are presented, with attention on the development of a new implicit scheme using a positivity-preserving version of Toroet al.'s HLLC scheme, which is the simplest average-state solver capable of exactly preserving isolated shock, contact, and shear waves.

TL;DR: In this article, the lattice Boltzmann method is extended to apply to general curvilinear coordinate systems, and numerical simulations are carried out for impulsive initial conditions with Reynolds numbers up to 104.

TL;DR: In this paper, the spectral element method is implemented for the shallow water equations in spherical geometry and its performance is compared with other models, and the potential advantages and disadvantages of spectral elements over more conventional models used for climate studies are discussed.

TL;DR: This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems and is applied to Hele?Shaw flow, an unstable flow involving two fluids with very different viscosity.

TL;DR: In this paper, a detailed mathematical analysis of the Berenger PML method for the electromagnetic equations is carried out on the PDE level, as well as for the semidiscrete and fully discrete formulations.