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A Runge Kutta Discontinuous Galerkin Method for Lagrangian Compressible Euler Equations in Two-Dimensions

Communications in computational Physics 2014年第4期15卷 1184-1206页

作者： Zhenzhen Li Xijun Yu Jiang Zhu Zupeng Jia School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026P.R.China Graduate School China Academy of Engineering PhysicsBeijing 100088P.R.China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088P.R.China National Laboratory for Scientific Computing LNCC/MCTIAvenida Getúlio Vargas 33325651-075 PetrópolisRJBrazil

This paper presents a new Lagrangian type scheme for solving the Euler equations of compressible gas *** this new scheme the system of equations is discretized by Runge-Kutta Discontinuous Galerkin(RKDG)method,and the mesh moves with the fluid *** scheme is conservative for the mass,momentum and total energy and maintains second-order *** scheme avoids solving the geometrical part and has free *** of some numerical tests are presented to demonstrate the accuracy and the non-oscillatory property of the scheme.

关键词： Lagrangian type scheme compressible Euler equations RKDG method conservative scheme

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Model reduction opportunities in detailed simulations of combustion dynamics 52

Model reduction opportunities in detailed simulations of com...

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52nd AIAA Aerospace Sciences Meeting - AIAA Science and Technology Forum and Exposition, SciTech 2014

作者： Munipalli, Ramakanth Liu, Zhining Zhu, Xueyu Menon, Suresh Hesthaven, Jan S. HyPerComp Inc Westlake Village CA 91361 United States Scientific Computing and Imaging Institute University of Utah United States Department of Aerospace Engineering Georgia Institute of Technology Computational Combustion Laboratory United States Division of Applied Mathematics Brown University United States EPFL-SB-MATHICSE-MCSS Lausanne Switzerland

ISBN: (数字)9781624102561

ISBN: (纸本)9781624102561

Rocket and gas turbine combustion dynamics involves a confluence of diverse physics and interaction across a number of system components. Any comprehensive, self-consistent numerical model is burdened by a very large computational mesh, stiff unsteady processes which limit the permissible time step, and the need to perform tedious, repeated calculations for a broad parametric range. Predictive CFD models rely on very large scale simulations and advanced hardware. Reduced Basis Methods (RBM) have grown in usage during the past decade, as promising new techniques in making large simulations more accessible. These methods create models with far fewer unknown quantities than the original system, by generating "proper" fundamental solutions and their Galerkin projections, while guaranteeing accuracy and computational efficiency. RBMs seek to reproduce full CFD solutions, rather than solutions to a simplified or linearized set of equations. We present here some recent work in this area, focusing on approaches to model large scale combustor systems. The maturation of methods leading to LES-based turbulent combustion modeling is discussed, and model reduction goals and strategies are explored from the perspective of applicability in real life problems in both gas turbine, and rocket engines.

关键词： Rockets

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Rotated block triangular preconditioning based on PMHSS

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Science China mathematics 2013年第12期56卷 2523-2538页

作者： BAI Zhong-Zhi State Key Laboratory of Scientific/Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems ScienceChinese Academy of Sciences

Based on the PMHSS preconditioning matrix, we construct a class of rotated block triangular preconditioners for block two-by-two matrices of real square blocks, and analyze the eigen-properties of the corresponding preconditioned matrices. Numerical experiments show that these rotated block triangular pre- conditioners can be competitive to and even more efficient than the PMHSS preconditioner when they are used to accelerate Krylov subspeme iteration methods for solving block two-by-two linear systems with coefficient matrices possibly of nonsymmetric sub-blocks.

关键词： block two-by-two matrix PMHSS preconditioner block triangular preconditioning product-typepreconditioning eigen-properties

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Non-Darcy behavior of two-phase channel flow

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Physical Review E 2014年第2期90卷 023010-023010页

作者： Xianmin Xu Xiaoping Wang LSEC Institute of Computational Mathematics and Scientific/Engineering Computing NCMIS AMSS Chinese Academy of Sciences Beijing 100190 China Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong China

We study the macroscopic behavior of two-phase flow in porous media from a phase-field model. A dissipation law is first derived from the phase-field model by homogenization. For simple channel geometry in pore scale, the scaling relation of the averaged dissipation rate with the velocity of the two-phase flow can be explicitly obtained from the model which then gives the force-velocity relation. It is shown that, for the homogeneous channel surface, Dacry's law is still valid with a significantly modified permeability including the contribution from the contact line slip. For the chemically patterned surfaces, the dissipation rate has a non-Darcy linear scaling with the velocity, which is related to a depinning force for the patterned surface. Our result offers a theoretical understanding on the prior observation of non-Darcy behavior for the multiphase flow in either simulations or experiments.

关键词： TWO-phase flow ENERGY dissipation HOMOGENIZATION (Differential equations) CHANNEL flow (Fluid dynamics) RESEARCH DARCY'S law POROUS materials

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The efect of ghost forces for a quasicontinuum method in three dimension

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Science China mathematics 2013年第12期56卷 2571-2589页

作者： CUI Long MING PingBing LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

We study the effect of ＂ghost forces＂ for a quasicontinuum method in three dimension with a planar interface. ＂Ghost forces＂ are the inconsistency of the quasicontinuum method across the interface between the atomistic region and the continuum region. Numerical results suggest that ＂ghost forces＂ may lead to a negilible error on the solution, while lead to a finite size error on the gradient of the solution. The error has a layer-like profile, and the interfacial layer width is of O（ε）. The error in certain component of the displacement gradient decays algebraically from O（1） to O（ε） away from the interface. A surrogate model is proposed and analyzed, which suggests the same scenario for the effect of ＂ghost forces＂. Our analysis is based on the explicit solution of the surrogate model.

关键词： quasicontinuum method atomistic-to-continuum ghost force

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A Source Transfer Domain Decomposition Method For Helmholtz Equations in Unbounded Domain Part II: Extensions

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Numerical mathematics(Theory,Methods and Applications) 2013年第3期6卷 538-555页

作者： Zhiming Chen Xueshuang Xiang LSEC Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China

In this paper we extend the source transfer domain decomposition method(STDDM)introduced by the authors to solve the Helmholtz problems in two-layered media,the Helmholtz scattering problems with bounded scatterer,and Helmholtz problems in 3D unbounded *** STDDM is based on the decomposition of the domain into non-overlapping layers and the idea of source transfer which transfers the sources equivalently layer by layer so that the solution in the final layer can be solved using a PML method defined locally outside the last two *** details of STDDM is given for each *** results are presented to demonstrate the efficiency of STDDM as a preconditioner for solving the discretization problem of the Helmholtz problems considered in the paper.

关键词： Helmholtz equation high frequency waves PML source transfer

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Feasible Barzilai-Borwein-like methods for extreme symmetric eigenvalue problems

Feasible Barzilai-Borwein-like methods for extreme symmetric...

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作者： Jiang, Bo Dai, Yu-Hong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences Beijing 100190 China

This paper aims to study feasible Barzilai-Borwein (BB)-like methods for extreme symmetric eigenvalue problems. For the two-dimensional case, we establish the local superlinear convergence result of FLBB, FSBB, FABB, and FADBB algorithms. A counter-example is also given, showing that the algorithms may cycle or stop at a non-stationary point. In order to circumvent the difficulty, we propose a safeguard in choosing the stepsize. We also adopt an adaptive non-monotone line search with an improved line search to ensure the global convergence of AFBB-like methods. Numerical experiments on a set of test problems from UF Sparse Matrix Collection demonstrate that, comparing several available codes including eigs, irbleigs and jdcg, AFBB-like methods are very useful for large-scale sparse extreme symmetric eigenvalue problems. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Eigenvalues and eigenfunctions

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A New Analysis on the Barzilai-Borwein Gradient Method

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Journal of the Operations Research Society of China 2013年第2期1卷 187-198页

作者： Yu-Hong Dai State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190P.R.China

Due to its simplicity and efficiency,the Barzilai and Borwein(BB)gradi-ent method has received various attentions in different *** paper presents a new analysis of the BB method for two-dimensional strictly convex quadratic *** analysis begins with the assumption that the gradient norms at the first two iterations are *** show that there is a superlinear convergence step in at most three consecutive ***,we provide a better convergence relation for the BB *** influence of the starting point and the condition number to the convergence rate is comprehensively addressed.

关键词： Unconstrained optimization Barzilai and Borwein gradient method Quadratic function R-superlinear convergence Condition number

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11th German Conference on Chemoinformatics (GCC 2015) Abstracts

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JOURNAL OF CHEMINFORMATICS 2016年第SUPPL 1期8卷 1-27页

作者： [Anonymous] GDCh-CIC Division Associated Board Member Beilstein-Institut zur Förderung der Chemischen Wissenschaften Trakehner Str. 7-9 60487 Frankfurt Germany. ufechner@beilstein-institut.de. Division Medicinal Chemistry Amsterdam Institute for Molecules Medicines and Systems (AIMMS) VU University Amsterdam The Netherlands. Centre for Bioinformatics Uni Hamburg Bundesstr. 43 20146 Hamburg Germany. Sanofi-Aventis Deutschland GmbH 65926 Frankfurt am Main Germany. stefan.guessregen@***. Sanofi-Aventis Deutschland GmbH 65926 Frankfurt am Main Germany. GlaxoSmithKline Stevenage SG1 2NY UK. nicola.j.richmond@***. Discngine Paris 75011 France. Organisch-Chemisches Institut Westfälische Wilhelms-Universität Münster Germany. marwin.segler@wwu.de. Organisch-Chemisches Institut Westfälische Wilhelms-Universität Münster Germany. Bundeskriminalamt Wiesbaden Central Analytics II 65173 Wiesbaden Germany. Department of Chemistry and Biochemistry University of California Santa Barbara CA 93111 USA. shea@chem.ucsb.edu. Department of Chemistry and Biochemistry University of California Santa Barbara CA 93111 USA. Chemistry Department Ludwig-Maximilians-Universität München Butenandtstr. 7 81377 Munich Germany. Inorganic Chemistry and Center for Nanointegration University of Duisburg-Essen Essen Germany. CAM-D Technologies Essen Germany. Institute for Bioinformatics and Chemoinformatics Westphalian University of Applied Sciences Recklinghausen Germany. Institute for Bioinformatics and Chemoinformatics Westphalian University of Applied Sciences Recklinghausen Germany. achim.zielesny@w-hs.de. Leiden University Leiden Netherlands. j.fraaije@chem.leidenuniv.nl. Culgi BV Berlin Germany. Physikalische Chemie III TU Dortmund 44227 Dortmund Germany. stefan.kast@tu-dortmund.de. Centre for Molecular Informatics Department of Chemistry University of Cambridge Lensfield Road Cambridge CB2 1EW United Kingdom. kcb27@cam.ac.uk. Centre for Molecular Informatics Department of Chemistry

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A trust region method based on a new affine scaling technique for simple bounded optimization

A trust region method based on a new affine scaling techniqu...

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作者： Wang, Xiao Yuan, Ya-Xiang State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Chinese Academy of Sciences PO Box 2719 Beijing 100190 China

In this paper, we propose a new trust region affine scaling method for nonlinear programming with simple bounds. Our new method is an interior-point trust region method with a new scaling technique. The scaling matrix depends on the distances of the current iterate to the boundaries, the gradient of the objective function and the trust region radius. This scaling technique is different from the existing ones. It is motivated by our analysis of the linear programming case. The trial step is obtained by minimizing the quadratic approximation to the objective function in the scaled trust region. It is proved that our algorithm guarantees that at least one accumulation point of the iterates is a stationary point. Preliminary numerical experience on problems with simple bounds from the CUTEr collection is also reported. The numerical performance reveals that our method is effective and competitive with the famous algorithm LANCELOT. It also indicates that the new scaling technique is very effective and might be a good alternative to that used in the subroutine fmincon from Matlab optimization toolbox. © 2013 Copyright Taylor and Francis Group, LLC.

关键词： Nonlinear programming

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