Showing papers in "Journal of Computational Physics in 2014"

TL;DR: This paper will review the development of high order accurate multi-block finite difference schemes, point out the main contributions and speculate about the next lines of research in this area.

TL;DR: Flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

TL;DR: The comparison with the corresponding results of finite difference methods by the L1 formula demonstrates that the new L1-2 formula is much more effective and more accurate than the L2 formula when solving time-fractional differential equations numerically.

TL;DR: A procedure for the estimation of the numerical uncertainty of any integral or local flow quantity as a result of a fluid flow computation; the procedure requires solutions on systematically refined grids with least squares fits to power series expansions to handle noisy data.

TL;DR: The Monte Carlo algorithm includes quantum corrections to the photon emission, which it is shown must be included if the pair production rate is to be correctly determined.

TL;DR: A successful case of combining an existing immersed-boundary flow solver with a nonlinear finite-element solid-mechanics solver specifically for three-dimensional FSI simulations is reported, representing a significant enhancement from the similar methods that are previously available.

TL;DR: A novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method.

TL;DR: In this paper, compact finite difference schemes for the modified anomalous fractional sub-diffusion equation and fractional diffusion-wave equation are studied, and based on the idea of weighted and shifted Grunwald difference operator, they establish schemes with temporal and spatial accuracy order equal to two and four respectively.

TL;DR: This study presents the derivation of ordinary state-based perid dynamic heat conduction equation based on the Lagrangian formalism, which paves the way for applying the peridynamic theory to other physical fields such as neutronic diffusion and electrical potential distribution.

TL;DR: The finite difference approximation of Caputo derivative on non-uniform meshes is investigated and a semi-discrete scheme is obtained and the unconditional stability and H^1 norm convergence are proved.

TL;DR: A numerical method for the solution of the elliptic Monge-Ampere Partial Differential Equation, with boundary conditions corresponding to the Optimal Transportation problem, is presented, leading to a fast solver comparable to solving the Laplace equation on the same grid several times.

TL;DR: This paper proposes a method for dealing with the problem of mesh deformation (or mesh evolution) in the context of free and moving boundary problems, in three space dimensions by combining two different numerical parameterizations of domains.

TL;DR: This work modify the standard l1l1-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refers to the resulting algorithm as weighted l1l 1- Minimization.

TL;DR: An equivalence is established between the dissipative terms of GSPH and the signal based SPH artificial viscosity, under the restriction of a class of approximate Riemann solvers, to explain the anomalous “wall heating” experienced by G SPH.

TL;DR: It is shown that an earlier introduced l 2 -regularized pseudolikelihood maximization method called plmDCA can be modified as to be easily parallelizable, as well as inherently faster on a single processor, at negligible difference in accuracy.

TL;DR: A shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier-Stokes equations is developed, which is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free.

TL;DR: Estimates for the error in Reynolds-averaged Navier-Stokes (RANS) simulations based on the Launder-Sharma [email protected] turbulence closure model, for a limited class of flows are obtained.

TL;DR: A generalized framework is presented that extends the classical theory of finite-difference summation-by-parts (SBP) operators to include a wide range of operators, where the main extensions are non-repeating interior point operators, nonuniform nodal distribution in the computational domain, and operators that do not include one or both boundary nodes.

TL;DR: The method developed herein has the potential to significantly expedite simulations of incompressible flows involving outflow or open boundaries, and to enable such simulations at Reynolds numbers significantly higher than the state of the art.

TL;DR: Different methods for fractional ODEs that lead to exponentially fast decay of the error are presented that confirm the exponential/algebraic convergence in p- and h-refinements, for various test cases with integer- and fractional-order solutions.

TL;DR: A parallel version of the MHD and extended magnetohydrodynamic codes is proposed for the high-performance liquid chromatography of Na6(CO3)(SO4)2, where Na2CO3 is the major mineral component of the plasma and Na2SO4 is the gas molecule.

TL;DR: This paper overcomes the adjoint method failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”, which is then linearized in the sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average.

TL;DR: A class of two-dimensional Riesz space fractional diffusion equations is considered, and according to Lax–Milgram theorem, the existence and uniqueness of the solution to the fully discrete scheme are investigated.

TL;DR: An approach is developed to perform explicit time domain finite element simulations of elastodynamic problems on the graphical processing unit, using Nvidia?s CUDA, significantly faster than an equivalent commercial CPU package.

TL;DR: A numerical approach based on the Lattice Boltzmann and Immersed Boundary methods is proposed to tackle the problem of the interaction of moving and/or deformable slender solids with an incompressible fluid flow.

TL;DR: This article presents a new reduced order model based upon proper orthogonal decomposition (POD) for solving the Navier-Stokes equations that is a hybrid of two existing approaches, namely the quadratic expansion method and the Discrete Empirical Interpolation Method (DEIM).

TL;DR: This work devise second-order accurate, unconditionally uniquely solvable and unconditionally energy stable schemes for the nonlocal Cahn-Hilliard and nonlocal Allen-Cahn equations for a large class of interaction kernels and presents numerical evidence that both schemes are convergent.

TL;DR: It is shown that consideration of Galilean invariance in fluid-solid interfacial dynamics can greatly enhance the computational accuracy and robustness in a numerical simulation.

TL;DR: An a-posteriori error indicator is derived for the Generalized Multiscale Finite Element Method (GMsFEM) framework which gives an estimate of the local error over coarse grid regions and is used to develop an adaptive enrichment algorithm for the linear elliptic equation with multiscale high-contrast coefficients.

TL;DR: The Riemann solver is shown to operate well for traditional second order accurate total variation diminishing (TVD) schemes as well as for weighted essentially non-oscillatory (WENO) schemes with ADER time-stepping.