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Highly accurate simplified lattice Boltzmann method

PHYSICS OF FLUIDS 2018年第10期30卷 103605-103605页

作者： Chen, Z. Shu, C. Tan, D. Natl Univ Singapore Dept Mech Engn 10 Kent Ridge Crescent Singapore 119260 Singapore

In this paper, we present a highly accurate simplified lattice Boltzmann method (HSLBM) which can achieve the third-order of accuracy in space. By introducing virtual streaming nodes and decoupling the streaming distance from the mesh spacing, HSLBM effectively combines the local second-order simplified and highly stable lattice Boltzmann method (SHSLBM) and the overall high order scheme. The correlation between the streaming distance and the mesh spacing is accomplished by a high-order Lagrange interpolation algorithm. Through a series of tests, it is found that using 5 interpolation points and setting streaming distance as 1/5 of the mesh spacing can give optimal results. In general, HSLBM improves the accuracy of SHSLBM from the second order to the third order, while maintaining its merits like low memory cost, convenient implementation of physical boundary conditions, and good numerical stability. To match the accuracy of the flow solver, a linear extrapolation scheme with the third-order of accuracy is also proposed to determine the boundary values of the non-equilibrium distribution functions. Various benchmark tests are performed to demonstrate the robustness of HSLBM in simulating two- and three-dimensional incompressible viscous flows as well as its flexibility in problems with curved boundaries and on body-fitted meshes. Published by AIP Publishing.

关键词： Viscosity Interpolation Incompressible flow Laminar flows numerical algorithms Lattice Boltzmann methods

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SMART: A program to automatically compute accelerations and variational equations

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ASTRONOMY AND COMPUTING 2022年 40卷

作者： Carpintero, D. D. Maffione, N. P. Gomez, F. A. Univ Nacl La Plata Fac Ciencias Astronom & Geofis La Plata Argentina UNLP Conicet Inst Astrofis La Plata La Plata Argentina Univ Nacl Rio Negro Viedma Rio Negro Argentina Consejo Nacl Invest Cient & Tecn Buenos Aires DF Argentina Univ La Serena Inst Invest Multidisciplinar Ciencia & Tecnol Raul Bitran 1305 La Serena Chile Univ La Serena Dept Astron La Serena Chile

Modern astronomical potentials modelling galaxies or stellar systems can be rather involved, and deriving their first derivatives (accelerations) and second derivatives (variational equations) in order to compute orbits and their chaoticity may be a formidable task. We present here a fully automated routine, dubbed SMART, with which the accelerations and the variational equations of an arbitrary potential that has been written in the FORTRAN (77) language can be computed. Almost any FORTRAN (77) statement is admitted in the potential, and the output are standard FORTRAN (77) routines ready to use. We validate our algorithm with a set of potentials including time-dependent, velocity-dependent and very complex potentials that even involve auxiliary routines. We also describe with some detail a realistic seven-component Galactic potential, MILKYWAYHYDRA, which yields very involved derivatives, thus being a good test bed for SMART. (C) 2022 Published by Elsevier B.V.

关键词： Stellar systems Planetary systems Chaos numerical algorithms

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Constitutive model with memory-surface shrinking rule for cyclic plasticity of structural steel

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JOURNAL OF CONSTRUCTIONAL STEEL RESEARCH 2021年 187卷 106923-106923页

作者： Teranishi, Masaki Kaneko, Kensaku Hirata, Hiroshi Hiyoshi, Noritake Niigata Univ Ctr Transdisciplinary Res Inst Res Promot Nishi Ku 8050Ikarashi 2 No Cho Niigata 9502181 Japan Tokyo Inst Technol Inst Innovat Res Lab Future Interdisciplinary Res Sci & Technol Midori Ku 4259 Nagatsuta Cho Yokohama Kanagawa 2268501 Japan Obayashi Corp Technol Res Inst 4-640 Shimokiyoto Tokyo 2048558 Japan Univ Fukui Div Engn Fac Engn 3-9-1 Bunkyo Fukui 9108507 Japan

A constitutive model is proposed for both the cyclic hardening and softening of structural steel. A shrinking rule is incorporated into the memory surface for cyclic softening. The theoretical formulation of the proposed model is derived under cyclic loading with a gradually decreasing strain amplitude. The material constants are iden-tified by numerically minimising the difference between the theoretical result and a single material test result using a genetic algorithm. The proposed model is validated by comparing numerical and material test results under various cyclic loadings for structural steel, where the model exhibits good ability to qualitatively and quantitatively evaluate the stress amplitude variation. The model is implemented in Abaqus FEA software, and the convergence rate of the consistent tangent operator is evaluated. FEA with the consistent tangent operator yields a quadratic convergence.

关键词： Cyclic hardening and softening Finite element analysis numerical algorithms Constitutive model Memory surface

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Data-driven deconvolution for large eddy simulations of Kraichnan turbulence

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PHYSICS OF FLUIDS 2018年第12期30卷 125109-125109页

作者： Maulik, R. San, O. Rasheed, A. Vedula, P. Oklahoma State Univ Sch Mech & Aerosp Engn Stillwater OK 74078 USA SINTEF Digital CSE Grp Math & Cybernet Trondheim Norway Univ Oklahoma Sch Aerosp & Mech Engn Norman OK 73019 USA

In this article, we demonstrate the use of artificial neural networks as optimal maps which are utilized for convolution and deconvolution of coarse-grained fields to account for sub-grid scale turbulence effects. We demonstrate that an effective eddy-viscosity is predicted by our purely data-driven large eddy simulation framework without explicit utilization of phenomenological arguments. In addition, our data-driven framework precludes the knowledge of true sub-grid stress information during the training phase due to its focus on estimating an effective filter and its inverse so that grid-resolved variables may be related to direct numerical simulation data statistically. The proposed predictive framework is also combined with a statistical truncation mechanism for ensuring numerical realizability in an explicit formulation. Through this, we seek to unite structural and functional modeling strategies for modeling non-linear partial differential equations using reduced degrees of freedom. Both a priori and a posteriori results are shown for a two-dimensional decaying turbulence case in addition to a detailed description of validation and testing. A hyperparameter sensitivity study also shows that the proposed dual network framework simplifies learning complexity and is viable with exceedingly simple network architectures. Our findings indicate that the proposed framework approximates a robust and stable sub-grid closure which compares favorably to the Smagorinsky and Leith hypotheses for capturing the theoretical k(-3) scaling in Kraichnan turbulence. Published by AIP Publishing.

关键词： Computational fluid dynamics Partial differential equations Machine learning Turbulence theory and modelling numerical algorithms Artificial neural networks Turbulence simulations

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Algorithm 942: Semi-Stencil

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ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE 2014年第3期40卷 23-23页

作者： De La Cruz, Raul Araya-Polo, Mauricio Barcelona Supercomp Ctr CASE Dept Barcelona Spain Repsol USA The Woodlands TX USA

Finite Difference (FD) is a widely used method to solve Partial Differential Equations (PDE). PDEs are the core of many simulations in different scientific fields, such as geophysics, astrophysics, etc. The typical FD solver performs stencil computations for the entire computational domain, thus solving the differential operators. In general terms, the stencil computation consists of a weighted accumulation of the contribution of neighbor points along the cartesian axis. Therefore, optimizing stencil computations is crucial in reducing the application execution time. Stencil computation performance is bounded by two main factors: the memory access pattern and the inefficient reuse of the accessed data. We propose a novel algorithm, named Semi-stencil, that tackles these two problems. The main idea behind this algorithm is to change the way in which the stencil computation progresses within the computational domain. Instead of accessing all required neighbors and adding all their contributions at once, the Semi-stencil algorithm divides the computation into several updates. Then, each update gathers half of the axis neighbors, partially computing at the same time the stencil in a set of closely located points. As Semi-stencil progresses through the domain, the stencil computations are completed on precomputed points. This computation strategy improves the memory access pattern and efficiently reuses the accessed data. Our initial target architecture was the Cell/B.E., where the Semi-stencil in a SPE was 44% faster than the naive stencil implementation. Since then, we have continued our research on emerging multicore architectures in order to assess and extend this work on homogeneous architectures. The experiments presented combine the Semi-stencil strategy with space-and time-blocking algorithms used in hierarchical memory architectures. Two x86 (Intel Nehalem and AMD Opteron) and two POWER (IBM POWER6 and IBM BG/P) platforms are used as testbeds, where the best imp

关键词： algorithms Experimentation Measurement Performance Stencil computation Semi-stencil blocking time skewing cache oblivious HPC code optimization numerical algorithms performance model

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An inverse averaging finite element method for solving three-dimensional Poisson-Nernst-Planck equations in nanopore system simulations

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JOURNAL OF CHEMICAL PHYSICS 2021年第19期155卷 194106-194106页

作者： Zhang, Qianru Wang, Qin Zhang, Linbo Lu, Benzhuo Chinese Acad Sci Acad Math & Syst Sci NCMIS CEMSLSEC Beijing Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

The Poisson-Nernst-Planck (PNP) model plays an important role in simulating nanopore systems. In nanopore simulations, the large-size nanopore system and convection-domination Nernst-Planck (NP) equations will bring convergence difficulties and numerical instability problems. Therefore, we propose an improved finite element method (FEM) with an inverse averaging technique to solve the three-dimensional PNP model, named inverse averaging FEM (IAFEM). At first, the Slotboom variables are introduced aiming at transforming non-symmetric NP equations into self-adjoint second-order elliptic equations with exponentially behaved coefficients. Then, these exponential coefficients are approximated with their harmonic averages, which are calculated with an inverse averaging technique on every edge of each tetrahedral element in the grid. Our scheme shows good convergence when simulating single or porous nanopore systems. In addition, it is still stable when the NP equations are convection domination. Our method can also guarantee the conservation of computed currents well, which is the advantage that many stabilization schemes do not possess. Our numerical experiments on benchmark problems verify the accuracy and robustness of our scheme. The numerical results also show that the method performs better than the standard FEM when dealing with convection-domination problems. A successful simulation combined with realistic chemical experiments is also presented to illustrate that the IAFEM is still effective for three-dimensional interconnected nanopore systems.

关键词： Topics: Semiconductor devices Electrolytes Mass diffusivity Electrostatics Nanomaterials Finite-element analysis numerical algorithms Partial differential equations Matrix methods

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Exascale applications: skin in the game

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PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES 2020年第2166期378卷 20190056-20190056页

作者： Alexander, Francis Almgren, Ann Bell, John Bhattacharjee, Amitava Chen, Jacqueline Colella, Phil Daniel, David DeSlippe, Jack Diachin, Lori Draeger, Erik Dubey, Anshu Dunning, Thom Evans, Thomas Foster, Ian Francois, Marianne Germann, Tim Gordon, Mark Habib, Salman Halappanavar, Mahantesh Hamilton, Steven Hart, William Huang, Zhenyu (Henry) Hungerford, Aimee Kasen, Daniel Kent, Paul R. C. Kolev, Tzanio Kothe, Douglas B. Kronfeld, Andreas Luo, Ye Mackenzie, Paul McCallen, David Messer, Bronson Mniszewski, Sue Oehmen, Chris Perazzo, Amedeo Perez, Danny Richards, David Rider, William J. Rieben, Rob Roche, Kenneth Siegel, Andrew Sprague, Michael Steefel, Carl Stevens, Rick Syamlal, Madhava Taylor, Mark Turner, John Vay, Jean-Luc Voter, Artur F. Windus, Theresa L. Yelick, Katherine Brookhaven Natl Lab Upton NY 11973 USA Lawrence Berkeley Natl Lab Berkeley CA USA Princeton Plasma Phys Lab POB 451 Princeton NJ 08543 USA Sandia Natl Labs POB 5800 Albuquerque NM 87185 USA Los Alamos Natl Lab Los Alamos NM USA Lawrence Livermore Natl Lab Livermore CA 94550 USA Argonne Natl Lab 9700 S Cass Ave Argonne IL 60439 USA Pacific Northwest Natl Lab Richland WA 99352 USA Oak Ridge Natl Lab Oak Ridge TN 37830 USA Ames Lab Ames IA USA Fermilab Natl Accelerator Lab POB 500 Batavia IL 60510 USA SLAC Natl Accelerator Lab Menlo Pk CA USA Natl Renewable Energy Lab Golden CO USA Natl Energy Technol Lab Morgantown WV USA

As noted in Wikipedia, skin in the game refers to having 'incurred risk by being involved in achieving a goal', where 'skin is a synecdoche for the person involved, and game is the metaphor for actions on the field of play under discussion'. For exascale applications under development in the US Department of Energy Exascale Computing Project, nothing could be more apt, with the skin being exascale applications and the game being delivering comprehensive science-based computational applications that effectively exploit exascale high-performance computing technologies to provide breakthrough modelling and simulation and data science solutions. These solutions will yield high-confidence insights and answers to the most critical problems and challenges for the USA in scientific discovery, national security, energy assurance, economic competitiveness and advanced healthcare. This article is part of a discussion meeting issue 'numerical algorithms for high-performance computational science'.

关键词： exascale high-performance computing computational science applications numerical algorithms machine learning modelling and simulation

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NONLINEAR DYNAMIC-RESPONSE OF IMPULSIVELY LOADED STRUCTURES - A REDUCED BASIS APPROACH

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AIAA JOURNAL 1991年第4期29卷 613-618页

作者： CHANG, C ENGBLOM, JJ Texas A&M University 77843 College Station Texas

This paper deals with predicting the nonlinear dynamic response of a structure under impulsive loading by means of reduction methods. Techniques for reducing the number of equations to be solved, e.g., when such equations come from a finite element model, are referred to as reduction methods. The order of a dynamical system is reduced by a Rayleigh-Ritz technique using selective basis vectors. numerical results are obtained using Ritz vectors and their derivatives as basis vectors. Both use of such derivatives and use of updating basis vectors provide excellent results. The proposed reduction technique is enhanced by updating the stiffness matrix with a reasonable reassembly frequency.

关键词： Finite Element Modeling Dynamic Response Poisson's Ratio Structural System Structural Vibration Plane Stress numerical algorithms Transient Response Cantilever Beam

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CHEMICAL KINETIC MODELING OF HIGHER HYDROCARBON FLUIDS

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AIAA JOURNAL 1986年第12期24卷 2002-2009页

作者： WESTBROOK, CK Lawrence Livermore National Laboratory Livermore California

This paper discusses current efforts directed toward extension of numerical modeling of chemical kinetics to hydrocarbon fuel molecules that are much larger than those treated in the past. The techniques needed are described and illustrated, including the identification of specific product distributions for decompositions of fuel and alkyl radicals, estimation of site-specific H atom abstraction reaction rates, and coupling between the large molecule reactions and those of the H₂-O₂-CO basis reaction mechanism. © 1986 American Institute of Aeronautics and Astronautics, Inc., All rights reserved.

关键词： Hydrocarbon Fuels numerical Modeling Chemical Kinetics Thermal Decomposition Shock Tube Internal Combustion Engines Combustion Kinetics Fuel Consumption Pyrolysis numerical algorithms

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Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

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JOURNAL OF CHEMICAL PHYSICS 2020年第21期153卷 211101页

作者： Choi, Seonghoon Vanicek, Jiri Ecole Polytech Fed Lausanne EPFL Lab Theoret Phys Chem Inst Sci & Ingn Chim CH-1015 Lausanne Switzerland

Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings in the exact quasidiabatic Hamiltonian. A rigorous numerical comparison of the four different representations is difficult because of the exceptional nature of systems where the four representations can be defined exactly and the necessity of an exceedingly accurate numerical algorithm that avoids mixing numerical errors with errors due to the different forms of the Hamiltonian. Using the quadratic Jahn-Teller model and high-order geometric integrators, we are able to perform this comparison and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results to the benchmark results of the strictly diabatic Hamiltonian, which is not available in general. In this Jahn-Teller model and with the same Fourier grid, the commonly employed approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.

关键词： Communications Topics Diabatic states Quantum chemical dynamics Time-dependent Schrodinger equation Potential energy surfaces Geometric phases Geometrical methods Jahn-Teller distortion Non-adiabatic molecular dynamics numerical algorithms Molecular Hamiltonian

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