Showing papers in "Journal of Computational Physics in 2006"

TL;DR: The theoretical development for the low Mach number limit is focused on, and asymptotic analysis is employed to formally derive proper scalings for the numerical fluxes in the limit of small Mach number.

TL;DR: It is demonstrated that a flow algorithm designed to legislate force balance retains an exact balance between surface tension forces and the resulting pressure gradients for both continuous and sharp representations of interfacial surface tension.

TL;DR: A multi-phase smoothed particle hydrodynamics (SPH) method for both macroscopic and mesoscopic flows is proposed, and a new simple algorithm capable for three or more immiscible phases is developed.

TL;DR: It is shown that the fractional Crank-Nicholson method based on the shifted Grunwald formula is unconditionally stable and compared with the exact analytical solution for its order of convergence.

TL;DR: A non-boundary-conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed Cartesian grids is proposed and the concept of field-extension is also introduced to treat the points emerging from a moving solid body to the fluid.

TL;DR: A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed, which is much simpler than the discontinuous Galerkin and spectral volume methods for un Structured grids.

TL;DR: Two new formulations of a symmetric WENO method for the direct numerical simulation of compressible turbulence are presented, designed to maximize order of accuracy and bandwidth, while minimizing dissipation.

TL;DR: A new validation metric is developed that is based on the statistical concept of confidence intervals and constructed two specific metrics: one that requires interpolation of experimental data andOne that requires regression (curve fitting) of experimentalData.

TL;DR: All the numerical experiments show that the present approach can be used to model multiphase flows with large density ratios and its efficiency could be greatly improved, especially in 3D applications.

TL;DR: In this article, a practical alternating directions implicit method to solve a class of two-dimensional initial-boundary value fractional partial differential equations with variable coefficients on a finite domain is discussed.

TL;DR: The approach involves Galerkin approximation of the KL eigenvalue problem by discontinuous finite elements of degree p ≥ 0 on a quasiuniform, possibly unstructured mesh of width h in D, plus a generalized fast multipole accelerated Krylov-Eigensolver.

TL;DR: A novel numerical algorithm for simulating interfacial dynamics of non-Newtonian fluids using an efficient adaptive meshing scheme governed by the phase-field variable that easily accommodates complex flow geometry and makes it possible to simulate large-scale two-phase systems of complex fluids.

TL;DR: This study involves a spatially varying resolution, based on the so-called variable smoothing length technique, for which a new formulation of the equations is proposed, aiming at an accurate numerical simulation of solid-fluid coupling in a free surface flow context.

TL;DR: This paper shows that a finite volume formulation where the appropriately averaged primitive variables are reconstructed leads to the oscillation-free advection of an isolated interface and numerical experiments show no spurious oscillations for problems where shockwaves and interfaces interact.

TL;DR: This paper introduces a novel high order interface scheme, the matched interface and boundary (MIB) method, for solving elliptic equations with discontinuous coefficients and singular sources on Cartesian grids by appropriate use of auxiliary line and/or fictitious points.

TL;DR: A class of finite difference methods for solving fractional diffusion equations is considered, an extension of the weighted average methods for ordinary (non-fractional) diffusion equations, and a simple and accurate stability criterion valid for different discretization schemes of the fractional derivative, arbitrary weight factor, and arbitrary order is found.

TL;DR: The generalization of compact FD formulas that are proposed for scattered nodes and radial basis functions (RBFs) achieves the goal of still keeping the number of stencil nodes small without a similar reduction in accuracy.

TL;DR: The results show that the immersed interface method implemented here has second-order accuracy in the infinity norm for both the velocity and the pressure, and the method is equally effective in computing flow subject to boundaries with prescribed force or boundaries withcribed motion.

TL;DR: This paper generalizes high order finite volume WENO schemes and Runge-Kutta discontinuous Galerkin (RKDG) finite element methods to the same class of hyperbolic systems to maintain a well-balanced property.

TL;DR: A class of schemes of any desired order of accuracy which preserve the lake at rest perfectly are presented, which should have an impact for studying important classes of lake and ocean flows.

TL;DR: This work proposes an evolution equation for the level-set function based on a generalization of the concept of topological gradient, which results in a new algorithm allowing for all kinds of topology changes.

TL;DR: A wideband version of the Fast Multipole Method for the Helmholtz equation in three dimensions is described, which is accurate and efficient for any frequency, having a CPU time of O(N) if low-frequency computations dominate, or O( NlogN)if high-frequency Computations dominate.

TL;DR: It is concluded that the simplified spherical harmonics methods can accurately model light propagation in small tissue geometries at visible and near-infrared wavelengths, yielding transport-like solutions with only a fraction of the computational cost of the transport calculation.

TL;DR: A new three-dimensional model that couples Navier-Stokes equations with cell interactions to investigate RBC aggregation and its effect on blood rheology is introduced and shows that cell-cell interaction and cell deformability have significant effects on bloodRheology in capillaries.

TL;DR: An implementation of the fast marching algorithm for solving Eikonal equations that in practice reduces the original run-time from O(NlogN) to linear, while keeping an error bound of the same order of magnitude as the original algorithm.

TL;DR: This paper studies the three-dimensional deformation of a vesicle membrane under the elastic bending energy, with prescribed bulk volume and surface area, with a newly developed energetic variational formulation.

TL;DR: In this article, the adaptive local deconvolution method (ALDM) is proposed as a new nonlinear discretization scheme designed for implicit large-eddy simulation (ILES) of turbulent flows.

TL;DR: A modified multiscale finite element method for two-phase flow simulations in heterogeneous porous media to use the global fine-scale solution at initial time to determine the boundary conditions of the basis functions to capture the long-range effect in channelized media.

TL;DR: It is found that the rate of convergence of the actual solution to the target solution, with an appropriate norm, is inversely proportional to the sponge strength, and a detailed analysis for acoustic wave propagation in one-dimension verifies the convergence rate given by the general theory.

TL;DR: A conservative interface method is presented, in which the standard finite volume scheme on Cartesian grids is modified by considering computational cells being cut by interface, which treats the topological changes naturally by combining interface description and geometric operations with a level set technique.