Showing papers in "Journal of Computational Physics in 2013"

TL;DR: The main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space.

TL;DR: Global state-space error bounds are developed that justify the method's design and highlight its advantages in terms of minimizing components of these error bounds and a 'sample mesh' concept is introduced that enables a distributed, computationally efficient implementation of the GNAT method in finite-volume-based computational-fluid-dynamics (CFD) codes.

TL;DR: A strategy capable of simulating polydisperse flows in complex geometries is employed where the fluid transport equations are solved in an Eulerian framework and the dispersed phase is represented as Lagrangian particles.

TL;DR: This work proposes a general mathematical framework and an algorithmic approach for optimal experimental design with nonlinear simulation-based models, and focuses on finding sets of experiments that provide the most information about targeted sets of parameters.

TL;DR: A comparison technique is used to derive a new Entropy Stable Weighted Essentially Non-Oscillatory (SSWENO) finite difference method, appropriate for simulations of problems with shocks.

TL;DR: It is proved that the eigenvalues of the singular problems are real-valued and the corresponding eigenfunctions are orthogonal, hence completing the whole family of the Jacobi poly-fractonomials.

TL;DR: A drastic redesign of the algorithm, and moving all the major computation parts into GPU, is reached, reaching a speed of 12s per molecular dynamics step for a 512 atom system using 256GPU cards.

TL;DR: A truly boundary-only meshless method is applied to Laplace-transformed inhomogeneous problem, which effectively simulates 3D long time-history fractional diffusion systems and evades costly convolution integral calculation in time fractional derivation approximation.

TL;DR: This paper presents a systematic, high-order approach that works for any singularity (including hypersingular kernels), based only on the assumption that the field induced by the integral operator is locally smooth when restricted to either the interior or the exterior.

TL;DR: The implicit finite difference scheme with the shifted Grunwald formula is employed to discretize fractional diffusion equations and the spectrum of the preconditioned matrix is proven to be clustered around 1 if diffusion coefficients are constant; hence the convergence rate of the proposed iterative algorithm is superlinear.

TL;DR: A block-structured finite volume method with adaptive mesh refinement (AMR) for three dimensional ice sheets, which allows to discretize a narrow region around the grounding line at high resolution and the remainder of the ice sheet at low resolution.

TL;DR: Three schemes are developed that have Mach-proportional dissipation inside the numerical shock wave structure, in contrast to Mach independent dissipation provided by conventional AUSM fluxes, and their desired performances are demonstrated for a wide spectrum of Mach numbers.

TL;DR: A simple method to enforce the positivity-preserving property for general high-order conservative schemes is proposed for solving compressible Euler equations and a number of numerical examples suggest that this method can be used to prevent positivity failure when the flow involves vacuum or near vacuum and very strong discontinuities.

TL;DR: The novelty of this work, is the recognition that the Gaussian process model defines a posterior probability measure on the function space of possible surrogates for the computer code and the derivation of an algorithmic procedure that allows us to sample it efficiently.

TL;DR: A simple limiter using weighted essentially non-oscillatory (WENO) methodology for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving conservation laws, with the goal of obtaining a robust and high order limiting procedure to simultaneously achieve uniform high order accuracy and sharp, non- oscillatory shock transitions.

TL;DR: A spatially coupled formula relating the boundary temperature, boundary normal heat flux, and the distribution functions near the boundary is derived for the Neumann problems on curved boundaries.

TL;DR: The proposed algorithms are simple and efficient especially when including multidimensional MHD terms that maintain in-plane magnetic field dynamics and are able to run with CFL numbers close to unity.

TL;DR: New methods for creating three-dimensional patient-specific models of ventricular biomechanics in the failing heart showed good agreement with measured echocardiographic and global functional parameters such as ejection fraction and peak cavity pressures.

TL;DR: First and second order in time linear schemes based on different ways to approximate the double-well potential term are presented, detailing their advantages over other linear schemes that have been previously introduced in the literature.

TL;DR: A new algorithm is proposed that combines the homogenization of the particle configuration by a background pressure while at the same time reduces artificial numerical dissipation in weakly-compressible SPH method.

TL;DR: An alternative proof of the sufficient condition is derived using special properties of βk, which proves that in fact the optimal order of the WENO-Z scheme can be guaranteed with a much weaker condition e = ?

TL;DR: An accurate moving boundary formulation based on the varying discretization operators yielding a cut-cell method which avoids discontinuities in the hydrodynamic forces exerted on the moving boundary is developed.

TL;DR: The proposed scheme that combines for the first time high order ADER methods with space–time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.

TL;DR: A fourth-order compact and energy conservative difference scheme is proposed for solving the two-dimensional nonlinear Schrodinger equation with periodic boundary condition and initial condition and the optimal convergent rate, without any restriction on the grid ratio, is obtained.

TL;DR: Divergence-conforming B-splines are developed for application to the incompressible Navier-Stokes equations on geometrically mapped domains that enable smooth, pointwise divergence-free solutions and thus satisfy mass conservation in the strongest possible sense.

TL;DR: The necessary formulation for coupling an arbitrary LPN to a finite element Navier-Stokes solver is presented, and implicit, semi-implicit, and explicit quasi-Newton formulations are compared.

TL;DR: A new phase-change model has been developed for a mass-conservative interface tracking method and the accuracy of the model is confirmed to be of second-order in space using a grid refinement study.

TL;DR: The Crank-Nicolson (CN) difference scheme for the coupled nonlinear Schrodinger equations with the Riesz space fractional derivative is studied and the existence of this difference solution is proved by the Brouwer fixed point theorem.

TL;DR: In this article, the Lax-Wendroff theorem states that conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts spatial operator yield discrete operators that are conservative.

TL;DR: In this paper, the authors describe computational techniques to predict free molecular collision cross sections for fixed structural models of gas phase entities where inelastic and non-specular gas molecule reemission rules can be invoked, and the long range ion-induced dipole (polarization) potential between gas molecules and a charged entity can be considered.