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Showing papers in "Journal of Computational Physics in 2002"


Journal ArticleDOI
Michele Benzi1
TL;DR: This article surveys preconditioning techniques for the iterative solution of large linear systems, with a focus on algebraic methods suitable for general sparse matrices, including progress in incomplete factorization methods, sparse approximate inverses, reorderings, parallelization issues, and block and multilevel extensions.

1,219 citations


Journal ArticleDOI
TL;DR: A new approach to the stabilization of numerical schemes in magnetohydrodynamic processes in which the divergence errors are transported to the domain boundaries with the maximal admissible speed and are damped at the same time is developed.

1,194 citations


Journal ArticleDOI
TL;DR: A class of numerical methods for stiff systems, based on the method of exponential time differencing, is developed, with schemes with second- and higher-order accuracy, and new Runge?Kutta versions of these schemes are introduced.

1,189 citations


Journal ArticleDOI
TL;DR: A new numerical method for improving the mass conservation properties of the level set method when the interface is passively advected in a flow field that compares favorably with volume of fluid methods in the conservation of mass and purely Lagrangian schemes for interface resolution.

1,120 citations


Journal ArticleDOI
TL;DR: A simple technique is adopted which ensures metric cancellation and thus ensures freestream preservation even on highly distorted curvilinear meshes, and metric cancellation is guaranteed regardless of the manner in which grid speeds are defined.

950 citations


Journal ArticleDOI
Walter Dehnen1
TL;DR: A novel code for the approximate computation of long-range forces between N mutually interacting bodies based on a hierarchical tree of cubic cells and features mutual cell–cell interactions which are calculated via a Cartesian Taylor expansion in a symmetric way, such that total momentum is conserved.

769 citations


Journal ArticleDOI
TL;DR: A convergent high-order accurate scheme for the solution of linear conservation laws in geometrically complex domains and demonstrates the versatility, flexibility, and robustness when solving two- and three-dimensional benchmark problems in computational electromagnetics.

763 citations


Journal ArticleDOI
TL;DR: In this article, the authors developed an accurate representation of the body force due to surface tension, which effectively eliminates spurious currents, and called this algorithm PROST: parabolic reconstruction of surface tension.

544 citations


Journal ArticleDOI
TL;DR: In this article, the spectral volume (SV) method was proposed to achieve high-order accuracy in an efficient manner similar to spectral element and multidomain spectral methods.

498 citations


Journal ArticleDOI
TL;DR: In this article, the variable coefficient Poisson equation with Dirichlet boundary conditions on an irregular domain is considered and a symmetric implicit time discretization matrix is proposed to obtain second-order accuracy.

478 citations


Journal ArticleDOI
TL;DR: In this article, a diffuse-interface method is proposed for the simulation of interfaces between compressible fluids with general equations of state, including tabulated laws, and the interface is allowed to diffuse on a small number of computational cells.

Journal ArticleDOI
TL;DR: In this paper, an uncertainty quantification scheme was developed for the simulation of stochastic thermofluid processes, which relies on spectral representation of uncertainty using the polynomial chaos (PC) system.

Journal ArticleDOI
TL;DR: In this paper, the simulation of a flapping flexible filament in a flowing soap film using the immersed boundary method is described. But the simulation is restricted to the case of a single filament.

Journal ArticleDOI
TL;DR: In this paper, an efficient hybrid compact-WENO scheme is proposed to obtain high resolution in shock-turbulence interaction problems, which is based on a fifth-order compact upwind algorithm in conservation form to solve for the smooth part of the flow field.

Journal ArticleDOI
TL;DR: An approach for the design of adaptive discontinuous Galerkin finite element methods is applied to physically relevant problems arising in inviscid compressible fluid flows governed by the Euler equations of gas dynamics, providing reliable and efficient error estimation.

Journal ArticleDOI
TL;DR: In this paper, a time-splitting spectral approximation for the Schrodinger equation in the semiclassical regime is proposed. But the authors consider the case where the Planck constant e is small and require the spatial mesh size h = O(e) and the time step k = o(e).

Journal ArticleDOI
TL;DR: In this paper, attention is limited to two-dimensional inviscid flows using a standard finite volume discretization, although the procedure may be readily applied to other types of multidimensional problems and discretizations.

Journal ArticleDOI
TL;DR: This paper presents and analyze a new approach for high-order-accurate finite-volume discretization for diffusive fluxes that is based on the gradients computed during solution reconstruction, and introduces a technique for constraining the least-squares reconstruction in boundary control volumes.

Journal ArticleDOI
TL;DR: The new level contour reconstruction technique presented here enables front tracking methods to naturally, automatically, and robustly model the merging and breakup of interfaces in three-dimensional flows using a simplified method of tracking and reconstructing the phase interface.

Journal ArticleDOI
TL;DR: Simulations show that using the data at the superconvergence points, the accuracy of the numerical discretization is O(h5/2) in space for smooth subsonic flows, both on structured and on locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numeric method.

Journal ArticleDOI
TL;DR: It is shown that for a relatively small additional computational cost nonlinear neural networks provide us with improved reconstruction and prediction capabilities for the near wall velocity fields.

Journal ArticleDOI
TL;DR: The framework for constructing a high-order, conservative spectral (finite) volume (SV) method is presented for two-dimensional scalar hyperbolic conservation laws on unstructured triangular grids and the convergence of the SV method is shown to depend on how a SV is partitioned.

Journal ArticleDOI
TL;DR: In this article, a monotonically integrated large eddy simulation (MILES) approach is introduced for closure of the low-pass filtered Navier-Strokes equations (NSE) using high-resolution monotone algorithms.

Journal ArticleDOI
TL;DR: It is shown that the full Navier?Stokes solver is between first- and second-order accurate and reproduces results from well-studied benchmark problems in viscous fluid flow and the robustness of the code on flow in a complex domain is demonstrated.

Journal ArticleDOI
TL;DR: The ghost fluid method is used to create accurate discretizations across the Eulerian/Lagrangian interface and is presented in both one and two spatial dimensions; three-dimensional extensions (to the interface coupling method) are straightforward.

Journal ArticleDOI
TL;DR: The shock entropy wave interaction problem is used to demonstrate the advantage of using higher order WENO schemes when both shocks and complex solution features coexist, and the decomposition increases the computational cost.

Journal ArticleDOI
TL;DR: In this paper, a pressure-based algorithm is presented for turbulent cavitating flow computations, where single-fluid Navier-Stokes equations cast in their conservative form, along with a volume fraction transport equation, are employed.

Journal ArticleDOI
TL;DR: In this paper, a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere is presented, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface.

Journal ArticleDOI
TL;DR: Techniques for estimating modeling errors in such quantities of interest are developed and applications to solid and fluid mechanics are presented.

Journal ArticleDOI
TL;DR: In this article, a 3D spatially unsplit implementation of the piecewise parabolic (PPM) method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions.