Showing papers in "Journal of Computational Physics in 2009"

TL;DR: The method is shown to recover exact equilibrium (to machine accuracy) between surface-tension and pressure gradient in the case of a stationary droplet, irrespective of viscosity and spatial resolution.

TL;DR: A new divergence-free ISPH approach is proposed here which maintains accuracy and stability while remaining mesh free without increasing computational cost by slightly shifting particles away from streamlines, although the necessary interpolation of hydrodynamic characteristics means the formulation ceases to be strictly conservative.

TL;DR: An adaptive sparse grid collocation strategy using piecewise multi-linear hierarchical basis functions and Hierarchical surplus is used as an error indicator to automatically detect the discontinuity region in the stochastic space and adaptively refine the collocation points in this region.

TL;DR: It is shown that a conceptually simple top-down grid partitioning scheme achieves essentially the same efficiency as the more rigorous bottom-up approaches.

TL;DR: This article describes and derives the techniques used to achieve and surpass 200gigaflops/s of net application-level floating point work and presents comprehensive data on the accuracy and runtime behavior of the method.

TL;DR: It is proved that the compact finite difference scheme converges with the spatial accuracy of fourth order using matrix analysis and the stability is discussed using the Fourier method.

TL;DR: A version of immersed boundary-lattice Boltzmann method (IB-LBM) based on the lattice BoltZmann equation with external forcing term is proposed, which shows that there is no any penetration of streamlines to the solid body in the present results.

TL;DR: In an attempt to extend the high-order formulation for 1D conservation laws to other element types such as triangular, tetrahedral or prismatic elements, the idea of ''flux reconstruction'' is generalized into a ''lifting collocation penalty'' approach.

TL;DR: A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of various types of fractional diffusion equation.

TL;DR: A single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms is developed that fulfills the equation of state and energy conservation on both sides of interfaces and guarantees correct transmission of shocks across them.

TL;DR: This work considers a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a spatial or temporal field, endowed with a hierarchical Gaussian process prior, and introduces truncated Karhunen-Loeve expansions, based on the prior distribution, to efficiently parameterize the unknown field.

TL;DR: It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones, which can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.

TL;DR: It is shown that for the pressure treatment, an accurate Fourier representation can be used for more flexible boundary conditions than periodicity or free-slip, and this compromise fits particularly well for very high-resolution simulations of turbulent flows with relatively complex geometries without requiring heavy numerical developments.

TL;DR: The critical temperature of the 2D and 3D Ising model is calculated using finite size scaling techniques and an implementation of the checkerboard algorithm on a GPU is able to generate results up to 35 times faster than on a current CPU core.

TL;DR: A shock-capturing methodology is developed for non-linear computations using low-dissipation schemes and centered finite differences that allows in particular to distinguish shocks from linear waves, and from vortices when it is performed from dilatation rather than from pressure.

TL;DR: A modified ROM is proposed that directly incorporates the pressure term in the model and an improvement of the POD solution subspace is performed thanks to an hybrid method that couples direct numerical simulations and reduced order model simulations.

TL;DR: An entropy-consistent flux is developed that is completely stable which will provide as a candidate to combat multidimensional shock instability, particularly the carbuncle phenomenon.

TL;DR: A new SPH model for simulating interface and free surface flows is presented, an extension of the one discussed in Colagrossi and Landrini (2003) and related to the one proposed by Hu and Adams (2006) to study multi-fluid flows.

TL;DR: The model equations appearing in H2008, Section 2.1 (taken from an earlier article, Haidvogel et al. (2000) [3]) are not entirely consistent with the actual equations solved in the ROMS code, resulting in contradictions within H2008 itself.

TL;DR: In this paper, the authors present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection-diffusion equations, which are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variables and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary.

TL;DR: A robust, implicit, low-dissipation method suitable for LES/DNS of compressible turbulent flows is discussed, which is stable without the addition of any explicit dissipation terms at very high Reynolds numbers for flows without shocks.

TL;DR: It is found that the lattice Boltzmann method is less dissipative than high order schemes and less dispersive than a second order scheme in space with a 3-step Runge-Kutta scheme in time.

TL;DR: This paper presents and compares two unconditionally energy stable finite-difference schemes for the phase field crystal equation and considers a new, fully second-order two-step algorithm that solves the nonlinear equations using an efficient nonlinear multigrid method.

TL;DR: A new high-resolution code for the direct simulation of incompressible boundary layers over a flat plate is described, and it is shown that the overall resolution is controlled by the higher-order advection step.

TL;DR: A new O(N) fast multipole formulation is proposed for non-oscillatory kernels which are only known numerically, that is their numerical value can be obtained for any (x,y), and uses the minimal number of coefficients to represent the far-field.

TL;DR: A method is presented that allows an arbitrary deformation to be represented to within a desired tolerance by using a significantly reduced set of surface points intelligently identified in a fashion that minimises the error in the interpolated surface.

TL;DR: Results for compressible gas-water systems show that the new method can simulate interface dynamics accurately, including the effect of surface tension, and can be used for simulations of fluid interface with large density differences.

TL;DR: A class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form is introduced and it is shown that the increasing computational complexity with increasing order is handily offset by the increased accuracy of the scheme.

TL;DR: In this article, a mesh-dependent dynamic contact angle model is presented, which is based on fundamental hydrodynamics and serves as a more appropriate boundary condition at a moving contact line.

TL;DR: A robust multigrid method based on Gauss-Seidel smoothing is found to require special treatment of the boundary conditions along solid boundaries, and in particular on the sea bottom, and it is shown to provide convergent solutions over the full physical and discrete parameter space of interest.