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The electric potential is an essential quantity for the confinement process of tokamak plasmas, with important impact on the performances of fusion reactors. Understanding its evolution in the peripheral region – the part of the plasma interacting with the wall of the device – is of crucial importance, since it governs the boundary conditions for the burning core plasma. The aim of the present paper is to study numerically the evolution of the electric potential in this peripheral plasma region. In particular, we are interested in introducing an efficient Asymptotic-Preserving (AP) numerical scheme capable to cope with the strong anisotropy of the problem as well as the non-linear boundary conditions, and this with acceptable computational costs. This work constitutes the numerical follow-up of the more mathematical paper by C. Negulescu, A. Nouri, Ph. Ghendrih, Y. Sarazin, Existence and uniqueness of the electric potential profile in the edge of tokamak plasmas when constrained by the plasma-wall boundary physics . [ABSTRACT FROM AUTHOR]

Abstract Many PDEs can be recast into the general multi-symplectic formulation possessing three local conservation laws. We devote the present paper to some systematic methods, which hold the discrete versions of the local conservation laws respectively, for the general multi-symplectic PDEs. For the original problem subjected to appropriate boundary conditions, the proposed methods are globally conservative. The proposed methods are successfully applied to many one-dimensional and multi-dimensional Hamiltonian PDEs, such as KdV equation, G–P equation, Maxwell's equations and so on. Numerical experiments are carried out to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

The aim of this paper is to describe a Matlab toolbox, called μ -diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in μ -diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized. Some complete numerical examples of applications (direct and inverse scattering) are provided to show that μ -diff is a flexible, efficient and robust toolbox for solving some complex multiple scattering problems. Program summary Program title: μ -diff Catalogue identifier: AEWH_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEWH_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 13,718 No. of bytes in distributed program, including test data, etc.: 1,466,301 Distribution format: tar.gz Programming language: Matlab. Computer: PC, Mac. Operating system: Windows, Mac OS, Linux. Has the code been vectorized or parallelized?: Yes RAM: 2000 Megabytes Classification: 4.6, 10, 18. Nature of problem: Modeling and simulation of two-dimensional multiple wave scattering by large clusters of circular cylinders for any frequency. The program is well-designed to manage highly accurate solutions for deterministic or random media, with various boundary conditions and physics properties of the scatterers. Pre- and post-processing facilities are designed specifically for these problems. Solution method: We use spectral Fourier approximation schemes and direct or iterative Krylov subspace methods. Running time: From a few seconds for simple problems to a few minutes for more complex situations on a medium computer. [ABSTRACT FROM AUTHOR]

This paper introduces a new publicly available numerical library for cosmology, C osmo++. The library has been designed using object-oriented programming techniques, and fully implemented in C++. C osmo++ introduces a unified interface for using most of the frequently used numerical methods in cosmology. Most of the features are implemented in C osmo++ itself, while a part of the functionality is implemented by linking to other publicly available libraries. The most important features of the library are Cosmic Microwave Background anisotropies power spectrum and transfer function calculations, likelihood calculations, parameter space sampling tools, sky map simulations, and mask apodization. C osmo++ also includes a few mathematical tools that are frequently used in numerical research in cosmology and beyond. A few simple examples are included in C osmo++ to help the user understand the key features. The library has been fully tested, and we describe some of the important tests in this paper. C osmo++ is publicly available at http://cosmo.grigoraslanyan.com . [ABSTRACT FROM AUTHOR]

In the paper, gridless particle techniques are presented in order to solve problems involving electrostatic, collisionless plasmas. The method makes use of computational particles having the shape of spherical shells or of rings, and can be used to study cases in which the plasma has spherical or axial symmetry, respectively. As a computational grid is absent, the technique is particularly suitable when the plasma occupies a rapidly changing space region. [ABSTRACT FROM AUTHOR]

Abstract: Focusing on the local geometric properties of the shockpeakon for the Degasperis–Procesi equation, a multi-symplectic method for the quasi-Degasperis–Procesi equation is proposed to reveal the jump discontinuity of the shockpeakon for the Degasperis–Procesi equation numerically in this paper. The main contribution of this paper lies in the following: (1) the uniform multi-symplectic structure of the b-family equation is constructed; (2) the stable jump discontinuity of the shockpeakon for the Degasperis–Procesi equation is reproduced by simulating the peakon–antipeakon collision process of the quasi-Degasperis–Procesi equation. First, the multi-symplectic structure and several local conservation laws are presented for the b-family equation with two exceptions ( and ). And then, the Preissman Box multi-symplectic scheme for the multi-symplectic structure is constructed and the mathematical proofs for the discrete local conservation laws of the multi-symplectic structure are given. Finally, the numerical experiments on the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation are reported to investigate the jump discontinuity of shockpeakon of the Degasperis–Procesi equation. From the numerical results, it can be concluded that the peakon–antipeakon collision of the quasi-Degasperis–Procesi equation can be simulated well by the multi-symplectic method and the simulation results can reveal the jump discontinuity of shockpeakon of the Degasperis–Procesi equation approximately. [Copyright &y& Elsevier]

In electrical engineering and physics, Maxwell's equations play a very important role and have a variety of applications. In this paper, we propose and analyse a novel class of time domain conservative schemes in rectangular coordinate to solve Maxwell's equations with periodic boundary conditions. This class of methods is explicit and easy to implement with low computational cost and memory storage. The error estimates presented in this paper demonstrate that the numerical solutions obtained by this class of conservative schemes can achieve arbitrarily high-order accuracy. The discrete divergences in numerical experiments motivate us to show that the conservative scheme is divergence-free by the rigorous numerical analysis, which is of great importance in the sense of geometric numerical integration. The discrete energy monitors give light to the statement that the conservative scheme can keep the linear relationship among some qualitative features of the underlying Maxwell's equations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a phase-field model for dendritic growth in a two-dimensional cavity flow and propose a computationally efficient numerical method for solving the model. The crystal is fixed in the space and cannot be convected in most of the previous studies, instead the supercooled melt flows around the crystal, which is hard to be realized in the real world experimental setting. Applying advection to the crystal equation, we have problems such as deformation of crystal shape and ambiguity of the crystal orientation for the anisotropy. To resolve these difficulties, we present a phase-field method by using a moving overset grid for the dendritic growth in a cavity flow. Numerical results show that the proposed method can predict the crystal growth under flow. [ABSTRACT FROM AUTHOR]

We consider the relativistic Vlasov–Maxwell (RVM) equations in the limit when the light velocity c goes to infinity. In this regime, the RVM system converges towards the Vlasov–Poisson system and the aim of this paper is to construct asymptotic preserving numerical schemes that are robust with respect to this limit. Our approach relies on a time splitting approach for the RVM system employing an implicit time integrator for Maxwell’s equations in order to damp the higher and higher frequencies present in the numerical solution. A number of numerical simulations are conducted in order to investigate the performances of our numerical scheme both in the relativistic as well as in the classical limit regime. In addition, we derive the dispersion relation of the Weibel instability for the continuous and the discretized problem. [ABSTRACT FROM AUTHOR]

Calculating strong-field, momentum-resolved photoelectron spectra (PES) from numerical solutions of the time-dependent Schrödinger equation (TDSE) is a very demanding task due to the large spatial excursions and drifts of electrons in intense laser fields. The time-dependent surface flux (t-SURFF) method for the calculation of PES [Tao and Scrinzi (2012)] allows to keep the numerical grid much smaller than the space over which the wavefunction would be spread at the end of the laser pulse. We present an implementation of the t-SURFF method in the well established TDSE-solver Qprop [Bauer and Koval (2006)]. Qprop efficiently propagates wavefunctions for single-active electron systems with spherically symmetric binding potentials in classical, linearly (along z ) or elliptically (in the x y -plane) polarized laser fields in dipole approximation. Its combination with t-SURFF makes the simulation of PES feasible in cases where it is just too expensive to keep the entire wavefunction on the numerical grid, e.g., in the long-wavelength or long-pulse regime. Program summary Program title: Qprop Catalogue identifier: ADXB_v2_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/ADXB_v2_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 12458 No. of bytes in distributed program, including test data, etc.: 86258 Distribution format: at.gz Programming language: C++. Computer: x86_64. Operating system: Linux. RAM: The memory requirements for calculating PES are determined by the maximum ℓ in the spherical harmonics expansion of the wave function and the number of momentum (or energy) values for which the PES are to be calculated. The example with the largest memory demand ( large-clubs ) uses approximately 6GB of RAM. The size of the numerical representation of a wavefunction during propagation is modest for the examples included (53 MB for the large-club example). Number of processors used: The evaluation of the PES can be distributed over up to N k MPI processes ( N k is the number of momentum values). Catalogue identifier of previous version: ADXB_v1_0 Journal reference of previous version: Comput. Phys. Comm. 174(2006)396 Classification: 2.5. External routines: GNU Scientific Library, Open MPI (optional), BOOST (optional) Does the new version supersede the previous version?: For TDDFT calculations the previous version should be used. Nature of problem: When atoms are ionized by intense laser fields electrons may escape with large momenta (especially when rescattering is involved). This translates to a rapidly spreading wavefunction in numerical simulations of these systems thus rendering the calculation of PES very costly for increasing wave lengths and peak intensities. Solution method: The TDSE is solved by propagating the wavefunction using a Crank–Nicolson propagator. The wavefunction is represented by an expansion in spherical harmonics. In order to reduce the requirements with respect to the grid size the t-SURFF method is used to calculate PES. Reasons for new version: Using the window operator method to calculate PES is increasingly costly with increasing ponderomotive energies and pulse durations. The new version of Qprop provides an implementation of the t-SURFF method which allows the use of much smaller numerical grids. Summary of revisions: An implementation of the t-SURFF method and examples for calculating PES are provided in the new release. Restrictions: The dipole approximation for the laser interaction has to be applicable. t-SURFF is only implemented for velocity gauge. Furthermore a finite cutoff for long range binding potentials has to be used in the implemented t-SURFF method. Additional comments: For additional information see www.qprop.de Running time: Depends strongly on the laser interaction studied. The examples given in this paper have run times from a few minutes to 12.5 hours. [ABSTRACT FROM AUTHOR]

Mitigation of soot emissions from combustion devices is a global concern. For example, recent EURO 6 regulations for vehicles have placed stringent limits on soot emissions. In order to allow design engineers to achieve the goal of reduced soot emissions, they must have the tools to so. Due to the complex nature of soot formation, which includes growth and oxidation, detailed numerical models are required to gain fundamental insights into the mechanisms of soot formation. A detailed description of the CoFlame FORTRAN code which models sooting laminar coflow diffusion flames is given. The code solves axial and radial velocity, temperature, species conservation, and soot aggregate and primary particle number density equations. The sectional particle dynamics model includes nucleation, PAH condensation and HACA surface growth, surface oxidation, coagulation, fragmentation, particle diffusion, and thermophoresis. The code utilizes a distributed memory parallelization scheme with strip-domain decomposition. The public release of the CoFlame code, which has been refined in terms of coding structure, to the research community accompanies this paper. CoFlame is validated against experimental data for reattachment length in an axi-symmetric pipe with a sudden expansion, and ethylene–air and methane–air diffusion flames for multiple soot morphological parameters and gas-phase species. Finally, the parallel performance and computational costs of the code is investigated. Program summary Program title: CoFlame Catalogue identifier: AFAU_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AFAU_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 94964 No. of bytes in distributed program, including test data, etc.: 6242986 Distribution format: tar.gz Programming language: Fortran 90, MPI. (Requires an Intel compiler). Computer: Workstations. Operating system: Linux. RAM: From 16 GB to over 1000 GB depending on size of system being simulated Classification: 22. Nature of problem: Soot formation in laminar diffusion flames with detailed description of thermodynamics, kinetic, and transport data Solution method: Finite volume method utilizing the pseudo-transient SIMPLE algorithm and locally coupled chemistry solver Additional comments: The code was specifically developed for modeling soot formation in laminar diffusion flames Running time: From hours to a month depending on the complexity of the chemical mechanism and the disparity between the initial guess and the final solution. [ABSTRACT FROM AUTHOR]

This paper describes the functionality and usage of bal , a C/C++ library with a Python front-end for the brute-force analysis of continuous-time dynamical systems described by ordinary differential equations (ODEs). bal provides an easy-to-use wrapper for the efficient numerical integration of ODEs and, by detecting intersections of the trajectory with appropriate Poincaré sections, allows to classify the asymptotic trajectory of a dynamical system for bifurcation analysis. Some examples of application are discussed, concerning two-dimensional bifurcation diagrams, Lyapunov exponents and finite-time Lyapunov exponents, basins of attraction, simulation of switching ODE systems, and integration with AUTO, a software package for continuation analysis. Program summary Program title: BAL (Library) Catalogue identifier: AEYY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEYY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 65256 No. of bytes in distributed program, including test data, etc.: 438133 Distribution format: tar.gz Programming language: C/C++, Python. Computer: PCs and Workstations. Operating system: Any Unix based system such as Linux and Mac OSX. RAM: Variable, depending on the number of dimensions of the dynamical system and duration of the simulation. Classification: 4.3, 4.12. External routines: CVODE, Boost, HDF5 Nature of problem: The numerical analysis of continuous-time nonlinear dynamical systems often requires the computation of a large number of solutions of the system, for varying parameter sets, and the subsequent classification of the steady state solution. Solution method: This library provides a convenient interface to the library CVODE for the integration of sets of differential equations and at the same time implements all the machinery required for integrating and classifying the behaviour of the system for varying parameter sets and initial conditions. A high-level Python interface makes the usage of the library amenable also to users who are not familiar with the C/C++ programming languages. [ABSTRACT FROM AUTHOR]

In this paper, an improved weakly compressible smoothed particle hydrodynamics (SPH) method is proposed to simulate transient free surface flows of viscous and viscoelastic fluids. The improved SPH algorithm includes the implementation of (i) the mixed symmetric correction of kernel gradient to improve the accuracy and stability of traditional SPH method and (ii) the Rusanov flux in the continuity equation for improving the computation of pressure distributions in the dynamics of liquids. To assess the effectiveness of the improved SPH algorithm, a number of numerical examples including the stretching of an initially circular water drop, dam breaking flow against a vertical wall, the impact of viscous and viscoelastic fluid drop with a rigid wall, and the extrudate swell of viscoelastic fluid have been presented and compared with available numerical and experimental data in literature. The convergent behavior of the improved SPH algorithm has also been studied by using different number of particles. All numerical results demonstrate that the improved SPH algorithm proposed here is capable of modeling free surface flows of viscous and viscoelastic fluids accurately and stably, and even more important, also computing an accurate and little oscillatory pressure field. [ABSTRACT FROM AUTHOR]

Numerical kinetic models of plasma turbulence require careful treatment of conserved quantities. In the collisionless limit, numerical dissipation can impact entropy in a non-controlled manner. In this paper, the impact of the error in entropy conservation is investigated. In a simulation of ion-acoustic turbulence, a large error ( 15 % ) in entropy conservation is found. Surprisingly, this error is independent of the numerical method, scheme, or number of grid points. Adding a collision operator resolves this issue, but only if the collision frequency is large enough that it modifies the qualitative time evolution of observables, such as electric field amplitude, anomalous resistivity, or phase-space structures. [ABSTRACT FROM AUTHOR]

In this paper we present a novel Lattice Boltzmann model for immiscible fluids with soluble surfactants adsorbing at the interface with improved numerical and extended physical properties. The numerical improvements are based on the use of an analytical representation of a regularized delta-function in the surface free energy functional for the surfactant. Furthermore, the physics of the system have been extended to differential solubility of the surfactant combined with the use of Frumkin sorption behaviour. This enables the scheme to approach more realistic systems like foams and emulsions. This novel scheme is much superior in numerical stability than our previous scheme, based on a squared gradient approximation. Furthermore, we have observed the phenomenon of interface broadening under certain conditions. This phenomenon limits the surface pressure to about 30% of the capillary pressure of a bare droplet. It remains to be investigated whether this interface broadening reflects some physical effect, as has been observed for proteins. [ABSTRACT FROM AUTHOR]

Functionally-fitted methods generalize collocation techniques to integrate exactly a chosen set of linearly independent functions. In this paper, we propose a new type of functionally-fitted block methods for initial value problems of second order ordinary differential equations. The basic theory for the proposed methods is established. First, we present a sufficient condition for the existence of the functionally-fitted block methods. We then obtain some basic characteristics of the methods by Taylor series expansions, and show that the r -point functionally-fitted block method is convergent of order at least r for second order ordinary differential equations. Numerical experiments are conducted to demonstrate the validity and efficiency of the functionally-fitted block methods by comparison with some existing numerical methods. [ABSTRACT FROM AUTHOR]

In its most widespread, classical formulation, the Nernst–Planck–Poisson system for ion transport in electrolytes fails to take into account finite ion sizes. As a consequence, it predicts unphysically high ion concentrations near electrode surfaces. Historical and recent approaches to an appropriate modification of the model are able to fix this problem. Several appropriate formulations are compared in this paper. The resulting equations are reformulated using absolute activities as basic variables describing the species amounts. This reformulation allows to introduce a straightforward generalisation of the Scharfetter–Gummel finite volume discretisation scheme for drift–diffusion equations. It is shown that it is thermodynamically consistent in the sense that the solution of the corresponding discretised generalised Poisson–Boltzmann system describing the thermodynamical equilibrium is a stationary state of the discretised time-dependent generalised Nernst–Planck system. Numerical examples demonstrate the improved physical correctness of the generalised models and the feasibility of the numerical approach. [ABSTRACT FROM AUTHOR]

This paper analyzes the convergence of the numerical solution of a set of equations which contains Poisson and current continuity equations required to simulate organic solar cells under illumination and bias applied. Due to the strong nonlinearity, choosing appropriate initial guesses is a key parameter in obtaining the convergence. To establish such initial guesses, we analyzed the behavior of electrostatic potential, and electron and hole concentration profiles along the active layer as a function of generation rate of photo-induced e–h pairs, charge mobility and thickness. Based on these results, we propose simple functions to obtain the starting values for reaching the solution in an optimized number of iterations. By using this approach, the convergence can be successfully achieved for a wide range of physical parameters such as generation rate of photo-induced e–h pairs, charge mobility, and thickness. For an organic solar cell with an active layer thickness of around 120 nm, the results show that the solution at equilibrium condition, under illumination without bias applied, and under illumination with bias applied requires around 7, 9 and 5 iterations, respectively. Although the analysis was carried out using physical parameters of one of the most studied material pair: P3HT and PCBM, our proposal can be used for arbitrary organic semiconductor. [ABSTRACT FROM AUTHOR]

The spatial volume occupied by an atom depends on its electronic density. Although this density can only be evaluated exactly for hydrogen-like atoms, there are many excellent algorithms and packages to calculate it numerically for other materials. Three-dimensional visualization of charge density is challenging, especially when several molecular/atomic levels are intertwined in space. In this paper, we explore several approaches to this, including the extension of an anaglyphic stereo visualization application based on the AViz package for hydrogen atoms and simple molecules to larger structures such as nanotubes. We will describe motivations and potential applications of these tools for answering interesting physical questions about nanotube properties. [ABSTRACT FROM AUTHOR]

The commonly used second order Finite-Difference Time-Domain (FDTD) scheme for electromagnetic solvers in Particle-In-Cell codes produces fast solvers that scale well in parallel, but suffers from anomalous numerical effects resulting from discretization, such as numerical dispersion. High order schemes are therefore seen as the remedy for reducing the discretization errors. In the modeling of various applications, an open boundary is necessary for simulating vacuum extending beyond the computational box, for which algorithms based on–or derived from–Bérenger’s Perfectly Matched Layers (PML) have demonstrated high efficiency over a wide range of wavelength and angle of incidence. The amount of numerical reflection of PMLs has been studied numerically and analytically for low order stencils but not systematically at higher order, nor for the pseudo-spectral scheme. In this paper, we extend the theoretical and numerical analysis of the coefficient of reflection of PML layers to solvers of any order of accuracy. Results show that the PML efficiency is preserved at any order, including at the infinite order limit that is attained by the pseudo-spectral formulation. [ABSTRACT FROM AUTHOR]

OpenSMOKE++ is a general framework for numerical simulations of reacting systems with detailed kinetic mechanisms, including thousands of chemical species and reactions. The framework is entirely written in object-oriented C++ and can be easily extended and customized by the user for specific systems, without having to modify the core functionality of the program. The OpenSMOKE++ framework can handle simulations of ideal chemical reactors (plug-flow, batch, and jet stirred reactors), shock-tubes, rapid compression machines, and can be easily incorporated into multi-dimensional CFD codes for the modeling of reacting flows. OpenSMOKE++ provides useful numerical tools such as the sensitivity and rate of production analyses, needed to recognize the main chemical paths and to interpret the numerical results from a kinetic point of view. Since simulations involving large kinetic mechanisms are very time consuming, OpenSMOKE++ adopts advanced numerical techniques able to reduce the computational cost, without sacrificing the accuracy and the robustness of the calculations. In the present paper we give a detailed description of the framework features, the numerical models available, and the implementation of the code. The possibility of coupling the OpenSMOKE++ functionality with existing numerical codes is discussed. The computational performances of the framework are presented, and the capabilities of OpenSMOKE++ in terms of integration of stiff ODE systems are discussed and analyzed with special emphasis. Some examples demonstrating the ability of the OpenSMOKE++ framework to successfully manage large kinetic mechanisms are eventually presented. Program summary Program title: OpenSMOKE++ Catalogue identifier: AEVY_v1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEVY_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 3 No. of lines in distributed program, including test data, etc.: 146353 No. of bytes in distributed program, including test data, etc.: 4890534 Distribution format: tar.gz Programming language: C++. Computer: Any computer that can run a C++ Compiler. Operating system: Tested on Microsoft Windows 7, Ubuntu 14.4. RAM: From a few Mb to several Gb depending on the size of the system being simulated. Classification: 22. External routines: Eigen, Boost C++ Libraries, RapidXML Nature of problem: Evolution of reacting gas mixtures with detailed description of thermodynamic, kinetic and transport data. Solution method: Stiff systems of Ordinary differential Equations, whose solution is obtained using methods based on the Backward Differentiation Formulas (BDF) (LU factorization of dense matrices is required). Additional comments: The code was specifically conceived for managing homogeneous, reacting mixtures including thousands of species and reactions. Running time: Problem-dependent, from seconds (small kinetics) to hours [ABSTRACT FROM AUTHOR]

In this paper the numerical integration of non conservative perturbations of differential systems that possess a first integral, as for example slowly dissipative Hamiltonian systems, is considered. Numerical methods that are able to reproduce appropriately the evolution of the first integral are proposed. These algorithms are based on a combination of standard numerical integration methods and certain projection techniques. Some conditions under which known conservative methods reproduce that desirable evolution in the invariant are analysed. Finally, some numerical experiments in which we compare the behaviour of the new proposed methods, the averaged vector field method AVF proposed by Quispel and McLaren and standard RK methods of orders 3 and 5 are presented. The results confirm the theory and show a good qualitative and quantitative performance of the new projection methods. [ABSTRACT FROM AUTHOR]

We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low’s Lagrangian or on a Hamiltonian with a non-canonical Poisson bracket. The useful property of this variational principle is that it allows independent transformations of particle coordinates and velocities, i.e., transformations in particle phase space. With such transformations, a finite degree-of-freedom drift-kinetic action is obtained through time-averaging of the finite degree-of-freedom fully-kinetic action. Variation of the drift-kinetic Lagrangian density leads to a self-consistent, macro-particles and fields numerical model. Since the computational particles utilize only guiding center coordinates and velocities, there is a large computational advantage in the time integration part of the algorithm. Numerical comparison between the time-averaged fully-kinetic and drift-kinetic charge and current, deposited on a computational grid, offers insight into the range of validity of the model. Being based on a variational principle, the algorithm respects the energy conserving property of the underlying continuous system. The development in this paper serves to further emphasize the advantages of using variational approaches in plasma particle simulations. [ABSTRACT FROM AUTHOR]

This paper studies a periodic one-dimensional exclusion process constituted by multiple diffusive channels and a common driven part. We have performed mean field analysis for the phase diagram, the density profiles, and the currents, which is in good agreement with the Monte Carlo simulations. In particular, in the special case that the diffusive channels are identical, the phase boundaries have been derived explicitly. It is shown that, in the driven part, the low density–high density region and the low density region shrink and will finally vanish with the increase of the number of diffusive channels. On the other hand, the high density region and the low density–high density region vanish if the total number of particles keeps constant. Numerical examples indicate that these features might be extended to a general case in which the diffusive channels are not identical. [ABSTRACT FROM AUTHOR]

In this paper, a new linearized high-order compact difference method is presented for numerical simulation of three dimensional (3D) Allen-Cahn equation with three kinds of boundary conditions. The method, which is based on the Crank-Nicholson/Adams-Bashforth scheme combined with the Douglas-Gunn ADI method, is second order accurate in time and fourth order accurate in space and energy degradation. The main advantages of this method is that the nonlinear penalty term f(u)f(u) is linear and an extra stabilizing term is added to alleviate the stability constraint while maintaining accuracy and simplicity. Numerical experiments are given to demonstrate the validity and applicability of the new method. [ABSTRACT FROM AUTHOR]

The approach used for computation of the convecting face fluxes and the cell face velocities results in different underlying numerical algorithms in finite volume collocated grid solvers for the incompressible Navier–Stokes equations. In this study, the effect of the following five numerical algorithms on the numerical dissipation rate and on the temporal consistency of a selection of Runge–Kutta schemes is analysed: (1) the original algorithm of Rhie and Chow (1983), (2) the standard OpenFOAM method, (3) the algorithm used by Vuorinen et al. (2014), (4) the Kazemi-Kamyab et al. (2015) method, and (5) the D'Alessandro et al. (2018) approach. The last three algorithms refer to recent implementations of low dissipative numerical methods in OpenFOAM®. No new computational methods are presented in this paper. Instead, the main scientific contributions of this paper are: (1) the systematic assessment of the effect of the considered five numerical approaches on the numerical dissipation rate and on the temporal consistency of the selected Runge–Kutta schemes within one unified framework which we have implemented in OpenFOAM, and (2) the application of the method of Komen et al. (2017) in order to quantify the numerical dissipation rate introduced by three of the five numerical methods in quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow. In addition, we explain the effects of the introduced numerical dissipation on the observed trends in the corresponding numerical results. As one of the major conclusions, we found that the pressure error, which is introduced due to the application of a compact stencil in the pressure Poisson equation, causes a reduction of the order of accuracy of the temporal schemes for the test cases in this study. Consequently, application of higher order temporal schemes is not useful from an accuracy point of view, and the application of a second order temporal scheme appears to be sufficient. [ABSTRACT FROM AUTHOR]

The goal of this paper is to present a new major release of the program FIESTA (Feynman Integral Evaluation by a Sector decomposiTion Approach). This version presents features like cluster-parallelization, new asymptotic expansion algorithms, calculations in physical regions, new sector-decomposition strategies, as well as multiple speed, memory, and stability improvements. Program summary: Program title: FIESTA 3 Catalogue identifier: AECP_v3_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AECP_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: GNU General Public License, version 2 No. of lines in distributed program, including test data, etc.: 109631 No. of bytes in distributed program, including test data, etc.: 6777017 Distribution format: tar.gz Programming language: Wolfram Mathematica 7.0 or higher, C++. Computer: From a desktop PC to a supercomputer. Operating system: Unix, Linux, Mac OS X. Has the code been vectorized or parallelized?: Yes. Number of processors used: from 1 processor up to loading a supercomputer (tests were performed up to 1024 cores) RAM: Depends on the complexity of the problem Catalogue identifier of previous version: AECP_v2_0 Journal reference of previous version: Comput. Phys. Comm. 182 (2011) 790 Classification: 4.4, 4.12, 5, 6.5. External routines: Wolfram Mathematica [1], KyotoCabinet [2], Cuba [3], QHull [4] Does the new version supercede the previous version?: Yes. Some obsolete options were removed as being superseded by better approaches. Nature of problem: The sector decomposition approach to evaluating Feynman integrals falls apart into the sector decomposition itself, where one has to minimize the number of sectors; the pole resolution and epsilon expansion; and the numerical integration of the resulting expression. Moreover, in cases where the integrand is complex, one has to perform a contour deformation. Solution method: The program has a number of sector decomposition strategies. One of the most important features is the ability to perform a contour deformation, as well as the so-called pre-resolution in the case of integrals at the threshold. Everything except the integration is performed in Wolfram Mathematica [1] (required version is 7.0 or higher). This part of the calculation is parallelizable with the use of shared memory. The database is stored on hard disk with the use of the KyotoCabinet [2] database engine. The integration part of the algorithm, which can be performed on a cluster, is written in c++ and does not need Wolfram Mathematica. For integration we use the Cuba library package [3]. Reasons for new version: Application of FIESTA to physical values (complex integration) as well as the cluster-parallelization. Summary of revisions: FIESTA 3 is an absolutely new version with multiple new features such as [•] integration in physical regions [•] new asymptotic expansion methods [•] MPI-parallelization [•] multiple speed and memory improvements [•] total reconstruction: the integrator is completely separated and can be used by other programs Restrictions: The complexity of the problem is mostly restricted by the CPU time required to perform the integration and obtain a proper precision. Running time: Depends on the complexity of the problem. References: [[1]] http://www.wolfram.com/mathematica/, commercial algebraic software; [[2]] http://fallabs.com/kyotocabinet/, open source; [[3]] http://www.feynarts.de/cuba/, open source; [[4]] http://www.qhull.org, open source. [ABSTRACT FROM AUTHOR]

Abstract: Based on B-series theory, the order conditions of the multidimensional ARKN methods are presented for the general multi-frequency and multidimensional oscillatory second-order initial value problems by Wu et al. (2009). These multidimensional ARKN methods exactly integrate the multi-frequency and multidimensional unperturbed oscillators. In this paper, we pay attention to the analysis of the concrete multidimensional ARKN methods for the general multi-frequency oscillatory second-order initial value problems whose right-hand side functions depend on both and (the class of physical problems which fall within its scope is broader). Numerical experiments are carried out to show that the new multidimensional ARKN methods are more efficient compared with some well-known methods for dealing with the oscillatory problems in the scientific literature. [Copyright &y& Elsevier]

Every computer model depends on numerical input parameters that are chosen according to mostly conservative but rigorous numerical or empirical estimates. These parameters could for example be the step size for time integrators, a seed for pseudo-random number generators, a threshold or the number of grid points to discretize a computational domain. In case a numerical model is enhanced with new algorithms and modelling techniques the numerical influence on the quantities of interest, the running time as well as the accuracy is often initially unknown. Usually parameters are chosen on a trial-and-error basis neglecting the computational cost versus accuracy aspects. As a consequence the cost per simulation might be unnecessarily high which wastes computing resources. Hence, it is essential to identify the most critical numerical parameters and to analyse systematically their effect on the result in order to minimize the time-to-solution without losing significantly on accuracy. Relevant parameters are identified by global sensitivity studies where Sobol' indices are common measures. These sensitivities are obtained by surrogate models based on polynomial chaos expansion. In this paper, we first introduce the general methods for uncertainty quantification. We then demonstrate their use on numerical solver parameters to reduce the computational costs and discuss further model improvements based on the sensitivity analysis. The sensitivities are evaluated for neighbouring bunch simulations of the existing PSI Injector II and PSI Ring as well as the proposed DAE δ ALUS Injector cyclotron and simulations of the rf electron gun of the Argonne Wakefield Accelerator. [ABSTRACT FROM AUTHOR]