Computational science & discovery最新文献

{"title":"Improving parallel scalability for edge plasma transport simulations with neutral gas species","authors":"M. McCourt, T. Rognlien, L. McInnes, H. Zhang","doi":"10.1088/1749-4699/5/1/014012","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014012","url":null,"abstract":"Simulating the transport of multi-species plasma and neutral species in the edge region of a tokamak magnetic fusion energy device is computationally intensive and difficult due to coupling among various components, strong nonlinearities and a broad range of temporal scales. In addition to providing boundary conditions for the core plasma, such models aid in the understanding and control of the associated plasma/material–wall interactions, a topic that is essential for the development of a viable fusion power plant. The governing partial differential equations are discretized to form a large nonlinear system that typically must be evolved in time to obtain steady-state solutions. Fully implicit techniques using preconditioned Jacobian-free Newton–Krylov methods with parallel domain-based preconditioners are shown to be robust and efficient for the plasma components. Inclusion of neutral gas components, however, increases the condition number of the system to the point where improved parallel preconditioning is needed. Standard algebraic preconditioners that provide sufficient coupling throughout the global domain to handle the neutrals are not generally scalable. We present a new preconditioner, termed FieldSplit, which exploits the character of the neutral equations to improve the scalability of the combined plasma/neutral system.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014012"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596278","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiple timescale calculations of sawteeth and other global macroscopic dynamics of tokamak plasmas","authors":"S. Jardin, N. Ferraro, J. Breslau, J. Chen","doi":"10.1088/1749-4699/5/1/014002","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014002","url":null,"abstract":"The M3D-C1 (Breslau et al 2009 Phys. Plasmas 16 092503) code is designed for performing three-dimensional nonlinear magnetohydrodynamics (MHD) calculations of a tokamak plasma that span the timescales associated with ideal and resistive stability as well as parallel and perpendicular transport. This requires a scalable fully implicit time advance where the time step is not limited by a Courant condition based on the MHD wave velocities or plasma flow but is chosen instead to accurately and efficiently resolve the physics. In order to accomplish this, we make use of several techniques to improve the effective condition number of the implicit matrix equation that is solved every time step. The split time advance known as the differential approximation (Caramana 1991 J. Comput. Phys. 96 484) reduces the size of the matrix and improves its diagonal structure. A particular choice of velocity variables and annihilation operators approximately splits the large matrix into three sub-matrices, each with a much improved condition number. A final block-Jacobi preconditioner further dramatically improves the condition number of the final matrix, allowing it to converge in a Krylov solver (GMRES) with a small number of iterations. As an example, we have performed transport timescale simulations of a tokamak plasma that periodically undergoes sawtooth oscillations (Von Goeler et al 1974 Phys. Rev. Lett. 33 1201). We specify the transport coefficients and apply a 'current controller' that adjusts the boundary loop-voltage to keep the total plasma current fixed. The short-time plasma response depends on the initial conditions, but the long-time behavior depends only on the transport coefficients and the boundary conditions applied.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014002"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596573","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mapping the 'materials gene' for binary intermetallic compounds—a visualization schema for crystallographic databases","authors":"C. Kong, P. Villars, S. Iwata, K. Rajan","doi":"10.1088/1749-4699/5/1/015004","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/015004","url":null,"abstract":"This paper provides a new approach for mapping the relative stability of intermetallic compounds. We quantitatively assess the collective role of numerous chemical and bonding parameters that govern the stability of these compounds (which we call 'genes') using the principles of information entropy. It is shown that one can establish a quantitative scaling parameter, in terms of Shannon entropy, that permits one to map the relative contributions of these parameters on to a single map. This new 'structure map' provides a means of exploring a multivariate array of attributes associated with structural stability and of discerning the efficacy of classical classification mappings for crystal chemistry. We used a binary AB2 intermetallics database as a platform for developing a classification scheme of phase stability based on the concept of Shannon information entropy. We have integrated a metric of information entropy into a recursive partitioning classifier for projecting high-dimensional data manifolds on to a low-dimensional structure map, hence providing a new visualization scheme of complex and high-dimensional crystallographic data sets.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"015004"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/015004","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60597157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluating the performance of the two-phase flow solver interFoam","authors":"S. S. Deshpande, L. Anumolu, M. Trujillo","doi":"10.1088/1749-4699/5/1/014016","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014016","url":null,"abstract":"The performance of the open source multiphase flow solver, interFoam, is evaluated in this work. The solver is based on a modified volume of fluid (VoF) approach, which incorporates an interfacial compression flux term to mitigate the effects of numerical smearing of the interface. It forms a part of the C + + libraries and utilities of OpenFOAM and is gaining popularity in the multiphase flow research community. However, to the best of our knowledge, the evaluation of this solver is confined to the validation tests of specific interest to the users of the code and the extent of its applicability to a wide range of multiphase flow situations remains to be explored. In this work, we have performed a thorough investigation of the solver performance using a variety of verification and validation test cases, which include (i) verification tests for pure advection (kinematics), (ii) dynamics in the high Weber number limit and (iii) dynamics of surface tension-dominated flows. With respect to (i), the kinematics tests show that the performance of interFoam is generally comparable with the recent algebraic VoF algorithms; however, it is noticeably worse than the geometric reconstruction schemes. For (ii), the simulations of inertia-dominated flows with large density ratios yielded excellent agreement with analytical and experimental results. In regime (iii), where surface tension is important, consistency of pressure–surface tension formulation and accuracy of curvature are important, as established by Francois et al (2006 J. Comput. Phys. 213 141–73). Several verification tests were performed along these lines and the main findings are: (a) the algorithm of interFoam ensures a consistent formulation of pressure and surface tension; (b) the curvatures computed by the solver converge to a value slightly (10%) different from the analytical value and a scope for improvement exists in this respect. To reduce the disruptive effects of spurious currents, we followed the analysis of Galusinski and Vigneaux (2008 J. Comput. Phys. 227 6140–64) and arrived at the following criterion for stable capillary simulations for interFoam: where . Finally, some capillary flows relevant to atomization were simulated, resulting in good agreement with the results from the literature.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014016"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Randomized quasi-Monte Carlo simulation of fast-ion thermalization","authors":"L. J. Höök, T. Johnson, T. Hellsten","doi":"10.1088/1749-4699/5/1/014010","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014010","url":null,"abstract":"This work investigates the applicability of the randomized quasi-Monte Carlo method for simulation of fast-ion thermalization processes in fusion plasmas, e.g. for simulation of neutral beam injection and radio frequency heating. In contrast to the standard Monte Carlo method, the quasi-Monte Carlo method uses deterministic numbers instead of pseudo-random numbers and has a statistical weak convergence close to , where N is the number of markers. We have compared different quasi-Monte Carlo methods for a neutral beam injection scenario, which is solved by many realizations of the associated stochastic differential equation, discretized with the Euler–Maruyama scheme. The statistical convergence of the methods is measured for time steps up to 214.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014010"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unitary qubit lattice simulations of complex vortex structures","authors":"G. Vahala, J. Yepez, L. Vahala, M. Soe","doi":"10.1088/1749-4699/5/1/014013","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014013","url":null,"abstract":"A quantum vortex is a topological singularity with quantized circulation, unlike a classical vortex with its continuous circulation strength. Quantum turbulence, envisaged as strong tangle of quantum vortices, of a Bose–Einstein condensate is examined by developing a unitary qubit lattice algorithm for the solution of the Gross–Pitaevskii equation. Earlier, it was shown that a certain class of initial conditions had a very short Poincare recurrence time for this Hamiltonian system. Here it is shown quantitatively that increasing the internal energy of the initial state leads to a systematic degradation of this class of solutions. Coupled Bose–Einstein condensate systems are investigated for a Hopf link class of initial conditions in which a vortex ring core is threaded by a linear vortex core that then closes toroidal around the vortex ring. These states are known as skyrmions and play a role in particle physics, astrophysics and condensed matter physics.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014013"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014013","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fully implicit Newton?Krylov?Schwarz method for tokamak magnetohydrodynamics: Jacobian construction and preconditioner formulation","authors":"D. Reynolds, R. Samtaney, H. Tiedeman","doi":"10.1088/1749-4699/5/1/014003","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014003","url":null,"abstract":"Single-fluid resistive magnetohydrodynamics (MHD) is a fluid description of fusion plasmas which is often used to investigate macroscopic instabilities in tokamaks. In MHD modeling of tokamaks, it is often desirable to compute MHD phenomena to resistive time scales or a combination of resistive-Alfven time scales, which can render explicit time stepping schemes computationally expensive. We present recent advancements in the development of preconditioners for fully nonlinearly implicit simulations of single- fluid resistive tokamak MHD. Our work focuses on simulations using a structured mesh mapped into a toroidal geometry with a shaped poloidal cross-section, and a finite-volume spatial discretization of the partial differential equation model. We discretize the temporal dimension using a fully implicit or the backwards differentiation formula method, and solve the resulting nonlinear algebraic system using a standard inexact Newton-Krylov approach, provided by the sundials library. The focus of this paper is on the construction and performance of various preconditioning approaches for accelerating the convergence of the iterative solver algorithms. Effective preconditioners require information about the Jacobian entries; however, analytical formulae for these Jacobian entries may be prohibitive to derive/implement without error. We therefore compute these entries using automatic differentiation with OpenAD. We then investigate a variety of preconditioning formulations inspired by standard solution approaches in modern MHD codes, in order to investigate their utility in a preconditioning context. We first describe the code modifications necessary for the use of the OpenAD tool and sundials solver library. We conclude with numerical results for each of our preconditioning approaches in the context of pellet-injection fueling of tokamak plasmas. Of these, our optimal approach results in a speedup of a factor of 3 compared with non-preconditioned implicit tests, with that performance gap rapidly widening with increasing mesh refinement.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014003"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014003","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An iterated, multipoint differential transform method for numerically evolving partial differential equation initial-value problems","authors":"H. Finkel","doi":"10.1088/1749-4699/5/1/014001","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014001","url":null,"abstract":"Traditional numerical techniques for solving time-dependent partial differential equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and a certain number of their time derivatives at each time step. Although redundant in the dx → 0 limit, what if spatial derivatives were also stored? This paper presents an iterated, multipoint differential transform method (IMDTM) for numerically evolving PDE IVPs. Using this scheme, we demonstrate that stored spatial derivatives can be propagated in an efficient and self-consistent manner and can effectively contribute to the evolution procedure in a way that can confer several advantages, including aiding in solution verification. Lastly, in order to efficiently implement the IMDTM scheme, a generalized finite-difference stencil formula is derived that can take advantage of multiple higher-order spatial derivatives when computing even-higher-order derivatives. As demonstrated here, the performance of these techniques compares favorably to other explicit evolution schemes in terms of speed, memory footprint and accuracy.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014001"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directional artificial bulk viscosity for shock capturing on high aspect ratio grids","authors":"B. Olson, S. Lele","doi":"10.1088/1749-4699/5/1/014008","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014008","url":null,"abstract":"An improved shock-capturing method for high-order finite-difference schemes, which alleviates numerical stiffness on anisotropic grids, is proposed. This method is an extension of the artificial bulk viscosity (ABV) scheme, developed to capture shock waves with a minimal dissipation of the physical oscillations present in the flow, such as those associated with turbulence. This modified scheme generalizes the ABV treatment to situations where there are strong spatial inhomogeneities that often require anisotropic grids. To accomplish this, ABV is independently computed and applied along each computational grid direction, therefore taking a multi-valued, directional form rather than a scalar form. Scalar dissipation on high aspect ratio (AR) grids with explicit time-stepping schemes can cause the stable time step to be reduced by a factor of 1/AR. The proposed method removes this constraint and can allow for substantial speedups on high AR grids with shock waves. A two-dimensional test case illustrates the added numerical stability of the method and its ability to capture shock waves more sharply. Brief results from a large-eddy simulation of an over-expanded planar nozzle are given which demonstrate the method's robustness in practical applications.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"88 1","pages":"014008"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ion acceleration and plasma jet formation in the interaction of an intense laser beam normally incident on an overdense plasma: a Vlasov code simulation","authors":"M. Shoucri","doi":"10.1088/1749-4699/5/1/014005","DOIUrl":"https://doi.org/10.1088/1749-4699/5/1/014005","url":null,"abstract":"We use an Eulerian Vlasov code for the numerical solution of the one-dimensional relativistic Vlasov?Maxwell set of equations to study the acceleration of ions during the interaction of a high-intensity circularly polarized laser beam normally incident on an overdense plasma target. Both electrons and ions are treated with a kinetic equation. We consider the case when the laser free space wavelength ? 0 is greater than the scale length of the jump in the plasma density at the target plasma edge Ledge (? 0 Ledge). The laser beam intensity is a Gaussian-shaped pulse. We consider a density such that n/ncr=25 (ncr is the critical density). The ponderomotive pressure due to the incident high-intensity laser radiation pushes the electrons at the target plasma surface, producing a sharp density gradient, which gives rise to a charge separation. The resulting electric field accelerates the ions. Two cases are considered, namely the case of a relatively thin target (about five skin depth) and the case of a much larger target. The evolution of the charge separation, the associated electric field and the formation of a neutral plasma jet ejected toward the rear side of the target differ in the two cases considered. In the case of a thin target, we observe the ion population accelerated to higher velocities. The absence of noise in the Eulerian Vlasov code allows a detailed representation of the phase-space structures of the distribution functions associated with the two cases considered, which shows substantial differences to be discussed in this paper.","PeriodicalId":89345,"journal":{"name":"Computational science & discovery","volume":"5 1","pages":"014005"},"PeriodicalIF":0.0,"publicationDate":"2012-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1088/1749-4699/5/1/014005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60596661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}