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A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives [article]

Gino I. Montecinos
2020 arXiv   pre-print
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented.  ...  The solution to these problems is carried through an implicit Taylor series expansion, which allows the scheme to works very well for stiff source terms.  ...  The aim of this article is to present a numerical scheme for balance laws, centred, universal and based on the implicit Taylor series expansion and the conventional Cauchy-Kowalewskaya procedure which  ... 
arXiv:2010.10659v1 fatcat:hhu5c7rl2bhhzimtosoi7fnwve

Investigation of Numerical Dissipation in Classical and Implicit Large Eddy Simulations

Moutassem El Rafei, László Könözsy, Zeeshan Rana
2017 Aerospace (Basel)  
Therefore, the objective of the present study is to examine the resolving power of Monotonic Upwind Scheme for Conservation Laws (MUSCL) scheme with three different slope limiters: one second-order and  ...  two third-order used within the framework of Implicit Large Eddy Simulations (ILES).  ...  The MEA approach is based on Taylor series expansions of each component of the discretized convective term.  ... 
doi:10.3390/aerospace4040059 fatcat:hfd74b4ppbbc3f5qh4t63q37aq

N-body simulations of gravitational dynamics

W. Dehnen, J. I. Read
2011 The European Physical Journal Plus  
We describe the astrophysical and numerical basis of N-body simulations, both of collisional stellar systems (dense star clusters and galactic centres) and collisionless stellar dynamics (galaxies and  ...  We explain and discuss the state-of-the-art algorithms used for these quite different regimes, attempt to give a fair critique, and point out possible directions of future improvement and development.  ...  Left: Illustration of the geometry for the Taylor expansion used with the fast multipole method.  ... 
doi:10.1140/epjp/i2011-11055-3 fatcat:scevhtqoq5cbzb4aokzvg2hliu

Enabling strain hardening simulations with dislocation dynamics

A Arsenlis, W Cai, M Tang, M Rhee, T Oppelstrup, G Hommes, T G Pierce, V V Bulatov
2007 Modelling and Simulation in Materials Science and Engineering  
of data and work on parallel computers.  ...  Numerical algorithms for discrete dislocation dynamics simulations are investigated for the purpose of enabling strain hardening simulations of single crystals on massively parallel computers.  ...  Conversely, the computational cost of keeping high orders of multipole moments is wasted if the Taylor series expansions are truncated at lower orders.  ... 
doi:10.1088/0965-0393/15/6/001 fatcat:o2dz36zu2nebjdnsbzl3r6f5xe

Optimized pseudo-Padé Fourier migrator in terms of propagation angles

Cong Tang, Li-Yun Fu, Wenyong Pan, Qingqing Li, Jianping Huang
2020 IEEE Access  
The broadband wave-equation migrator is developed based on the pseudo-Padé approximation, where the Padé coefficients are independent of spatial coordinates, leading to a pure Fourier transform-based matching  ...  We benchmark the OPF1 migrator with other typical migrators based on the exact dispersion equation.  ...  (A-3) With the Taylor series expansion of the arctangent terms of (A-3) inside the bracket for k 0 zO(n) 2(k z +k z ) ≤ 1 (A-4) and taking the first-order term, we obtain arctan k 0 zO(n) 2(k z +k z )  ... 
doi:10.1109/access.2020.2973042 fatcat:kff76am4ojefhgqmpm5mpqdm3e

SOME EXPERIMENTS WITH STABILITY ANALYSIS OF DISCRETE INCOMPRESSIBLE FLOWS IN THE LID-DRIVEN CAVITY

J. J. Gervais, D. Lemelin, R. Pierre
1997 International Journal for Numerical Methods in Fluids  
The algorithm is applied to a second-order oscillator and to a ow-structure interaction problems. Open issues and extensions to general random distributions are presented.  ...  We present a fast Polynomial Chaos algorithm to model the input uncertainty and its propagation in incompressible ow simulations.  ...  ACKNOWLEDGEMENTS This paper is based on material presented by the last author (G.K.) as keynote lecture in ECCOMAS 2001, marking the 80th birthday of Prof. O.C. Zienkiewicz.  ... 
doi:10.1002/fld.500 fatcat:tf2jeastazglhmioac2wbst2ay

ADER scheme on unstructured meshes for shallow water: simulation of tsunami waves

Cristóbal E. Castro, Eleuterio F. Toro, Martin Käser
2012 Geophysical Journal International  
Here we present an arbitrary high-order finite volume scheme based on the ADER approach on 2-D unstructured meshes that preserves steady state solutions with arbitrarily high order of accuracy.  ...  However, most of them are based on a 1-D quadrature rule and are suitable only for Cartesian grids.  ...  This work was also supported through the Cluster of Excellence 'CliSAP' (EXC177), University of Hamburg, funded through the DFG.  ... 
doi:10.1111/j.1365-246x.2012.05471.x fatcat:4uxdgqzsvbea3blkpjupkuo2h4

Improving finite-volume diffusive fluxes through better reconstruction

Chandan B. Sejekan, Carl F. Ollivier-Gooch
2016 Computers & Fluids  
interpolation scheme along with a high-accuracy jump term to enhance stability of the system.  ...  We propose a novel reconstruction method and flux discretization to improve diffusive flux accuracy on cell-centred, isotropic unstructured meshes.  ...  Acknowledgements I owe my gratitude to all those people who have made this thesis possible and because of whom my graduate experience has been one that I will cherish forever.  ... 
doi:10.1016/j.compfluid.2016.08.002 fatcat:wubbfdyamzbllmf77gkgsais24

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
2010 Numerical Mathematics and Advanced Applications 2009  
We develop a hybrid scheme consisting of a combination of a second order MUSCL scheme and a high order finite difference scheme.  ...  Numerical experiments will be done for simple linear problems, the Burger's equation, and for the Euler equations with high Mach numbers. 24 This contribution deals with the modeling of soft biological  ...  A one dimensional fractional diffusion model is considered, where the usual second-order derivative gives place to a fractional derivative of order alpha, 1< alpha < 2.  ... 
doi:10.1007/978-3-642-11795-4_6 fatcat:nx4nvuxaxfbcdjknopny53ck5e

Current and Emerging Time-Integration Strategies in Global Numerical Weather and Climate Prediction

Gianmarco Mengaldo, Andrzej Wyszogrodzki, Michail Diamantakis, Sarah-Jane Lock, Francis X. Giraldo, Nils P. Wedi
2018 Archives of Computational Methods in Engineering  
order to obtain a solution otherwise not readily available in closed (i.e., analytic) form.  ...  In addition, the potential for the co-design of time-stepping algorithms and underlying high performance computing hardware, a keystone to accelerate the computational performance of future NWP and climate  ...  FXG gratefully acknowledges the support of the U.S. Office  ... 
doi:10.1007/s11831-018-9261-8 fatcat:mj7vbyhttjd7lid7xwrgztdayu

Full sphere hydrodynamic and dynamo benchmarks

P. Marti, N. Schaeffer, R. Hollerbach, D. Cébron, C. Nore, F. Luddens, J.-L. Guermond, J. Aubert, S. Takehiro, Y. Sasaki, Y.-Y. Hayashi, R. Simitev (+3 others)
2014 Geophysical Journal International  
Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed  ...  The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for  ...  The spatial discretization is based on a centred-difference-like stencil that is second-order accurate for regular tetrahedra.  ... 
doi:10.1093/gji/ggt518 fatcat:wudpy4ltevcgnlxh2jx54vtw44

Simulation Techniques for Cosmological Simulations

K. Dolag, S. Borgani, S. Schindler, A. Diaferio, A. M. Bykov
2008 Space Science Reviews  
Simulations of baryonic matter in the Universe often use hydrodynamic codes based on both particle methods that discretise mass, and grid-based methods.  ...  The fundamental problem of accurate constraints on the cosmological parameters, within a given cosmological model, requires precise modelling of the observed structure.  ...  A.D. also gratefully acknowledges partial support from the PRIN2006 grant "Costituenti fondamentali dell'Universo" of the Italian Ministry of University and Scientific Research and from the INFN grant  ... 
doi:10.1007/s11214-008-9316-5 fatcat:4mkjel2uxjbuxb4wg5endv7wwi

Advanced operator splitting-based semi-implicit spectral method to solve the binary phase-field crystal equations with variable coefficients

György Tegze, Gurvinder Bansel, Gyula I. Tóth, Tamás Pusztai, Zhongyun Fan, László Gránásy
2009 Journal of Computational Physics  
A combination of non-trivial splitting with spectral semi-implicit solution leads to sets of algebraic equations of diagonal matrix form.  ...  For example, a combination of the coarse grained formulation based on the renormalization group technique with adaptive gridding can certainly enhance substantially the simulation domain [18] [19] [20]  ...  P. is a grantee of the Bolyai János Scholarship. G. B. acknowledges EPSRC for financial support.  ... 
doi:10.1016/j.jcp.2008.11.011 fatcat:ie6fnri4ebhvlcshbum43rcvtu

SWIFF: Space weather integrated forecasting framework

Giovanni Lapenta, Viviane Pierrard, Rony Keppens, Stefano Markidis, Stefaan Poedts, Ondřej Šebek, Pavel M. Trávníček, Pierre Henri, Francesco Califano, Francesco Pegoraro, Matteo Faganello, Vyacheslav Olshevsky (+8 others)
2013 Journal of Space Weather and Space Climate  
The phenomena of space weather span a tremendous scale of densities and temperature with scales ranging 10 orders of magnitude in space and time.  ...  SWIFF is a project funded by the Seventh Framework Programme of the European Commission to study the mathematical-physics models that form the basis for space weather forecasting.  ...  This research has received funding from the European Commission's FP7 Program with the grant agreement SWIFF (Project No. 2633430, swiff.eu  ... 
doi:10.1051/swsc/2013027 fatcat:uwr45cwqpzg5xmgavgh43oqhsi

Hierarchies of Balance Conditions for thef-Plane Shallow-Water Equations

A. R. Mohebalhojeh, D. G. Dritschel
2001 Journal of the Atmospheric Sciences  
vided by expanding the nonlinear terms of (11c) and (11b) in a Taylor series around ¢ = 0 and then removing all terms oscillating with gravity-wave frequencies.  ...  effort to simplify Baer—Tribbia’s (1977) nonlinear normal-mode initialization (NNMI) method, which was based on a formal multiple-timescale Rossby number expansion.  ... 
doi:10.1175/1520-0469(2001)058<2411:hobcft>2.0.co;2 fatcat:puemzo2fifamjckuo7epvvmthe
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