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Accurate spectral numerical schemes for kinetic equations with energy diffusion

Jon Wilkening, Antoine J. Cerfon, Matt Landreman
2015 Journal of Computational Physics  
We consider a model one-dimensional partial differential equation describing energy diffusion in velocity space due to Fokker-Planck collisions.  ...  kinetic equations in plasma physics.  ...  via energy diffusion.  ... 
doi:10.1016/j.jcp.2015.03.039 fatcat:okgscx2xgvf4fcx6lntec6r4xm

Conservative and positivity-preserving semi-Lagrangian kinetic schemes with spectrally accurate phase-space resolution

Yaman Guclu, Andrew J. Christlieb, William N. G. Hitchon
2013 2013 Abstracts IEEE International Conference on Plasma Science (ICOPS)  
For sufficiently smooth profiles on a periodic domain, this new scheme shows spectral convergence to the exact solution.  ...  While being strictly mass conservative, the proposed algorithm does not exactly conserve the total energy, the sum of kinetic and potential energy.  ...  For sufficiently smooth profiles on a periodic domain, this new scheme shows spectral convergence to the exact solution.  ... 
doi:10.1109/plasma.2013.6635219 fatcat:oxs4c2rrunfbfcy4wtfvgbebs4

Coarsening kinetics from a variable-mobility Cahn-Hilliard equation: Application of a semi-implicit Fourier spectral method

Jingzhi Zhu, Long-Qing Chen, Jie Shen, Veena Tikare
1999 Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics  
An efficient semi-implicit Fourier spectral method is implemented to solve the Cahn-Hilliard equation with a variable mobility.  ...  We studied the coarsening kinetics of interconnected two-phase mixtures using a Cahn-Hilliard equation with its mobility depending on local compositions.  ...  ACKNOWLEDGMENTS The authors are grateful for financial support from the Sandia National Laboratory and the National Science Foundation under Grant Nos. DMR 96-33719 and DMS 9721413.  ... 
doi:10.1103/physreve.60.3564 pmid:11970189 fatcat:d3zkbltwebckjhwqhmfetnvnmi

Page 3283 of Mathematical Reviews Vol. , Issue 2004d [page]

2004 Mathematical Reviews  
Summary: “In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution.  ...  methods for one-dimensional kinetic models of granular flows and numerical quasi elastic limit.  ... 

Page 2618 of Mathematical Reviews Vol. , Issue 98D [page]

1998 Mathematical Reviews  
Many schemes suffer from this numerical diffusion, which is responsible for a bad reso- lution of shocks and contact discontinuities.  ...  Comparisons for well-known test cases indicate that the gas-kinetic BGK scheme is a promising approach in the design of numerical schemes for hyperbolic conservation laws.” 98d:76130 76M25 65M70 65N35  ... 

Non-modal analysis of spectral element methods: Towards accurate and robust large-eddy simulations

Pablo Fernandez, Rodrigo C. Moura, Gianmarco Mengaldo, Jaime Peraire
2019 Computer Methods in Applied Mechanics and Engineering  
We introduce a non-modal analysis technique that characterizes the diffusion properties of spectral element methods for linear convection-diffusion systems.  ...  The answer to these two questions can in turn provide crucial guidelines to construct more robust and accurate schemes for complex under-resolved flows, commonly found in industrial applications.  ...  Acknowledgments The authors acknowledge the Air Force Office of Scientific Research (FA9550-16-1-0214) and Pratt & Whitney for supporting this effort.  ... 
doi:10.1016/j.cma.2018.11.027 fatcat:xemmosfdpreuhcsrsrhydx635i

Calculation of isotropic turbulence using a pure Lagrangian vortex method

R. Yokota, T.K. Sheel, S. Obi
2007 Journal of Computational Physics  
The core spreading method and particle strength exchange were selected as the viscous diffusion scheme.  ...  The vortex method is applied to the calculation of a decaying homogeneous isotropic turbulence of Re k = 25, 50 and the results are compared with a spectral method calculation.  ...  [1] used the vortex-in-cell for the viscous diffusion scheme and compared with a spectral method for N = 128 3 grid points.  ... 
doi:10.1016/j.jcp.2007.06.003 fatcat:v2dqeuo5afa6fm47e6bwjxtkle

Page 5136 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
Summary: “A new cell-centered diffusion differencing scheme for the quadrilateral meshes associated with Lagrangian hydrodynam- ics codes is described.  ...  high-order spectral methods for one- and two-dimensional Euler equations.  ... 

Pseudo spectral collocation with Maxwell polynomials for kinetic equations with energy diffusion

Tonatiuh Sánchez-Vizuet, Antoine J Cerfon
2018 Plasma Physics and Controlled Fusion  
Taking a one-dimensional equation describing energy diffusion due to Fokker-Planck collisions with a Maxwell-Boltzmann background distribution as the test bench for the performance of the scheme, we find  ...  We study the approximation and stability properties of a recently popularized discretization strategy for the speed variable in kinetic equations, based on pseudo spectral collocation on a grid defined  ...  Berkeley) for his valuable comments and insights, and for providing the spectral transform data that made the convergence studies in this article possible. T.S-V and A.J.C. were supported by the U.S.  ... 
doi:10.1088/1361-6587/aa963a fatcat:263t3wo47vgvhfec3nvml7xxnq

Spectral Viscosity for Shallow Water Equations in Spherical Geometry

Anne Gelb, James P. Gleeson
2001 Monthly Weather Review  
A spherical spectral viscosity operator is proposed as an alternative to standard horizontal diffusion terms in global atmospheric models.  ...  Implementation in NCAR's Spectral Transform Shallow Water Model and application to a suite of standard test cases demonstrates improvement in resolution and numerical conservation of invariants at no extra  ...  Assistance provided by John Truesdale, David Williamson, and Jim Hack with NCAR's STSWM computer code and documentation is gratefully acknowledged.  ... 
doi:10.1175/1520-0493(2001)129<2346:svfswe>2.0.co;2 fatcat:esgqfv5zvvboncnc672ladahdy

Semi-Lagrangian Exponential Integration with application to the rotating shallow water equations [article]

Pedro da Silva Peixoto, Martin Schreiber
2019 arXiv   pre-print
We show experiments for the planar rotating shallow water equations.  ...  The general formulation is built from the solution of an integration factor problem with respect to the problem written with a material derivative, so that the exponential integration scheme naturally  ...  We would also like to thank Saulo Barros for discussions with respect to semi-Lagrangian spectral schemes. Appendix A.  ... 
arXiv:1904.09189v1 fatcat:ty5nqrgicna3holvgdl2bcfe4a

On the role of numerical dissipation in stabilising under-resolved turbulent simulations using discontinuous Galerkin methods [article]

Juan Manzanero, Esteban Ferrer, Gonzalo Rubio, Eusebio Valero
2018 arXiv   pre-print
First, we analyse these methods using a linear von Neumann analysis (for a linear advection-diffusion equation) to characterise their properties in wave-number space.  ...  Combining the SVV technique with a low dissipation Riemann solver, we obtain a scheme capable of maintaining low dissipation levels for laminar flows, whilst providing the correct dissipation for all wave-number  ...  In the linear advection equation, energy conserving schemes are achieved with an appropriate choice of the numerical Riemann solver.  ... 
arXiv:1805.10519v1 fatcat:ntdhv4swu5aohn27u7gsu7o3hm

OUP accepted manuscript

2019 Monthly notices of the Royal Astronomical Society  
The low numerical diffusion of the scheme reduces the numerical errors by orders of magnitude in comparison to classical schemes with piecewise constant spectral representations.  ...  We present an efficient novel numerical scheme to accurately compute the evolution of the particle distribution function by solving the Fokker-Planck equation with a low number of spectral bins (10 - 20  ...  ACKNOWLEDGEMENTS The authors thank Andy Strong and Stefanie Walch for fruitful discussions. We also thank the anonymous referee for very constructive comments that helped to improve the manuscript.  ... 
doi:10.1093/mnras/stz2961 fatcat:2lu65l62cnag3jjc7eq4esinw4

A kinetic energy backscatter algorithm for use in ensemble prediction systems

Glenn Shutts
2005 Quarterly Journal of the Royal Meteorological Society  
The input of small-scale kinetic energy by the backscatter algorithm also helps to correct a known problem with the energy spectrum in the ECMWF model-the absence of the observed −5/3 spectral slope in  ...  The rate of energy backscatter to scales near the truncation limit is controlled by a total energy dissipation function involving contributions from numerical diffusion, mountain drag and deep convection  ...  ACKNOWLEDGEMENTS I thank Peter Bechtold and Martin Leutbecher for considerable technical assistance during the course of this work, as well as Anton Beljaars, Roy Kershaw, Peter Janssen,  ... 
doi:10.1256/qj.04.106 fatcat:cpad2y2g7vb6pdniswtq6ma6wq

Comparison of Horizontal Difference Schemes for the Shallow Water Equations on a Sphere

Gary L. Russell, Kenji Takano, Frank Abramopoulos
1986 Journal of the Meteorological Society of Japan  
The accuracy of horizontal difference schemes used in the hydrodynamics parts of General Circulation Models are compared by means of numerical experiments for the shallow water equations on a sphere.  ...  Overall, Takano and Wurtele's partial fourth order energy and potential enstrophy conserving sdheme on the C grid is most accurate.  ...  Acknowledgements The authors wish to thank Eugenia Kalnay for several useful discussions and to Lawrence Takacs for a copy of the NASA/GLA fourth order A grid scheme.  ... 
doi:10.2151/jmsj1965.64a.0_327 fatcat:3ixzn5lckrcbhgghv54unhyo3y
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