Showing papers in "Journal of Computational Physics in 2011"

TL;DR: A non intrusive method that builds a sparse PC expansion, which may be obtained at a reduced computational cost compared to the classical ''full'' PC approximation.

TL;DR: The method converges in probability as a consequence of sparsity and a concentration of measure phenomenon on the empirical correlation between samples, and it is shown that the method is well suited for truly high-dimensional problems.

TL;DR: This article takes a closer look at Taylor expansions of the Lagrangian polynomials of the WENO substencils and the related inherited symmetries of the classical lower order smootherness indicators to obtain a general formula for the higher order smoothness indicators that allows the extension of theWENO-Z scheme to all (odd) orders of accuracy.

TL;DR: It is shown that MPS-based simulations are prone to become destabilized in presence of attractive interparticle forces, similar to the so-called tensile instability in SPH method, and two new modifications are proposed to resolve this shortcoming.

TL;DR: The proposed cut-cell based approach to reducing spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods is shown to retain all the desirable properties of the original finite-difference based IBM while at the same time, reducing pressure oscillation for moving boundaries by roughly an order of magnitude.

TL;DR: The stability and convergence of the finite difference scheme in maximum norm are proved using the energy method, where a new inner product is introduced for the theoretical analysis.

TL;DR: The extension of the well-established and widely used gyrokinetic code GENE from a radially local to a radial global version is described, including the change from spectral methods to finite difference and interpolation techniques in the radial direction.

TL;DR: A new class of high-order numerical methods for approximating nonlinear conservation laws is described (entropy viscosity method), where a nonlinear viscosities based on the local size of an entropy production is added to the numerical discretization at hand.

TL;DR: The present method can preserve the total mass as the Cahn-Hilliard equation, but the calculation and implementation are much simpler than that and the satisfactions of mass conservations are guaranteed.

TL;DR: An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework and it is demonstrated that the new method is an effectiveMultiscale approach for simulations of realistic multiphases flows in fractured heterogeneous porous media.

TL;DR: This paper presents a convergence study that shows that the convergence rate (in energy norm) is proportional to (H/??)1/2, where ?? is proportionalto the minimum of the eigenvalues that the corresponding eigenvectors are not included in the coarse space.

TL;DR: Numerical results on classical and demanding test cases for advection and Euler system are presented on quadrangular meshes to support the promising potential of the multi-dimensional Optimal Order Detection approach.

TL;DR: An implicit high-order hybridizable discontinuous Galerkin method for the steady-state and time-dependent incompressible Navier-Stokes equations and displays superconvergence properties that allow it to use the above-mentioned optimal convergence properties to define an element-by-element postprocessing scheme to compute a new and better approximate velocity.

TL;DR: A provably unconditionally stable mixed variational methods for phase-field models based on a mixed finite element method for space discretization and a new second-order accurate time integration algorithm that inherits the main characteristics of conserved phase dynamics.

TL;DR: A modified penalty approach is introduced into the flow-structure interaction solver that combines an immersed boundary method (IBM) and a multi-block lattice Boltzmann method (LBM) to model an incompressible flow and elastic boundaries with finite mass.

TL;DR: A novel moment-inversion algorithm, based on 1-D adaptive quadratures of conditional velocity moments, is introduced and shown to always yield realizable distribution functions (i.e. non-negative quadrature weights).

TL;DR: This paper uses higher order piecewise interpolation polynomial to approximate the fractional integral and fractional derivatives, and uses the Simpson method to design a higher order algorithm for the fractionsal differential equations.

TL;DR: Using a fourth order accurate kernel for interpolation between the particles and the mesh, the results of the hybrid vortex method and of the pseudo-spectral method agree well in both flow cases.

TL;DR: A method is presented to solve two-phase problems involving soluble surfactants using a non-linear multigrid method based on the use of a diffuse interface, which allows a simple implementation using standard finite difference or finite element techniques.

TL;DR: The algorithm features a tiling scheme to maximize the reuse of data at the fastest levels of the GPU's memory hierarchy and dynamic load balancing to allow high performance on heterogeneous configurations of GPUs.

TL;DR: The interface jump in the THINC (tangent of hyperbola for INterface capturing) scheme is adaptively scaled to a proper thickness according to the interface orientation to improve the numerical accuracy in computing multi-dimensional moving interfaces.

TL;DR: Numerical experiments are reported, showing that the quasi-Monte Carlo method consistently outperforms the Monte Carlo method, with a smaller error and a noticeably better than O(N^-^1^/^2) convergence rate.

TL;DR: This work develops a method that discretizes the 1+1 Vlasov-Poisson system via a high-order discontinuous Galerkin (DG) method in phase space, and an operator split, semi-Lagrangian method in time, and shows how to resolve all of the Lagrangian dynamics in such a way that mass is exactly conserved, positivity is maintained, and high- order accuracy is achieved.

TL;DR: A charge-conservative scheme to solve two-phase electrohydrodynamic (EHD) problems using the volume-of-fluid (VOF) method using an adaptive VOF method on octree meshes developed by Popinet.

TL;DR: A versatile, high-order accurate immersed boundary method for solving the LPCE in complex domains by combining the ghost-cell approach with a weighted least-squares error method based on a high- order approximating polynomial.

TL;DR: It is shown that the framework to construct positivity-preserving high order schemes in 16,17] can also be applied to Euler equations with a general equation of state and an extension to Eucharist equations with source terms is discussed.

TL;DR: The fully nonlinear and weakly dispersive Green-Naghdi model for shallow water waves of large amplitude is studied and gives a good account of all the processes of wave transformation in coastal areas: shoaling, wave breaking and run-up.

TL;DR: In this article, a fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach is presented. But unlike previous implicit PIC approaches, which are based on a linearized Vlasov-Poisson formulation, ours is based on the nonlinearly converged VA model.

TL;DR: Two new alternating direction implicit schemes based on the L"1 approximation and backward Euler method are considered for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative, and the solvability, unconditional stability and H^1 norm convergence are proved.

TL;DR: This study presents a new filter mechanism, allowing such gains to be realized also for purely convective PDEs that do not naturally feature any stabilizing dissipation.