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Implicit–explicit time integration of a high-order particle-in-cell method with hyperbolic divergence cleaning

G.B. Jacobs, J.S. Hesthaven
2009 Computer Physics Communications  
A high-order implicit-explicit additive Rung-Kutta time integrator is implemented in a particle-in-cell method based on a high-order discontinuous Galerkin Maxwell solver for simulation of plasmas.  ...  The method satisfies Gauss law using a hyperbolic divergence cleaner that transports divergence out of the computational domain at several times the speed of light.  ...  We conclude finally that the implicit-explicit method should be generally applicable to particle-mesh methods that have a discrepancy in stiffness between the continuum and particle phase.  ... 
doi:10.1016/j.cpc.2009.05.020 fatcat:npc772tjwbce5i44dfxsa357ne

A particle-in-cell method for the simulation of plasmas based on an unconditionally stable field solver

Eric M. Wolf, Matthew Causley, Andrew Christlieb, Matthew Bettencourt
2016 Journal of Computational Physics  
We propose a new particle-in-cell (PIC) method for the simulation of plasmas based on a recently developed, unconditionally stable solver for the wave equation.  ...  We describe the implementation in one and two dimensions for both electrostatic and electromagnetic cases, and present the results of several standard test problems, showing good agreement with theory  ...  with hyperbolic divergence cleaning.  ... 
doi:10.1016/j.jcp.2016.08.006 fatcat:ieqgy2fp5vfgpc56bgygatbrna

A geometric multigrid library for quadtree/octree AMR grids coupled to MPI-AMRVAC [article]

Jannis Teunissen, Rony Keppens
2019 arXiv   pre-print
Periodic, Dirichlet, and Neumann boundary conditions can be handled, as well as free-space boundary conditions for 3D Poisson problems, for which we use an FFT-based solver on the coarse grid.  ...  Several test cases are presented in which the multigrid routines are used to control the divergence of the magnetic field in magnetohydrodynamic simulations.  ...  The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation -Flanders (FWO) and the Flemish Government -department  ... 
arXiv:1901.11370v2 fatcat:j5wgmrw6ofbfzpgynkp4fknmeu

Mesh-free Hamiltonian implementation of two dimensional Darwin model

Lorenzo Siddi, Giovanni Lapenta, Paul Gibbon
2017 Physics of Plasmas  
needs additional 55 'divergence cleaning' techniques to enforce the Coulomb 56 gauge condition ∇ · A 2,3 .  ...  12 procedures typically required by particle-in-cell (PIC) methods.  ...  In 468 contrast to most Darwin PIC codes, no divergence clean-469 ing is needed with the present method.  ... 
doi:10.1063/1.4994705 fatcat:77kmwf72hvbqrgmbg63u2cryua

Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation

Denis Eremin, Torben Hemke, Ralf Peter Brinkmann, Thomas Mussenbrock
2013 Journal of Physics D: Applied Physics  
The algorithm described here avoids iterative schemes needed for the divergence cleaning and represents a fast and efficient solver, which can be used in fluid and kinetic models for self-consistent description  ...  The Darwin approximation offers a simple and efficient way of carrying out electromagnetic simulations as it removes the Courant condition plaguing explicit electromagnetic algorithms and can be implemented  ...  fields designed in 382 this work can be also used in a Particle-in-Cell code.  ... 
doi:10.1088/0022-3727/46/8/084017 fatcat:cpf3urkwnjdj3m3fw3xankvgjy

Magnetic Fluctuations in Gyrokinetic Simulations of Tokamak Scrape-Off Layer Turbulence [article]

Noah Mandell
2021 arXiv   pre-print
be handled in a robust, stable, and efficient manner in the gyrokinetic module of the Gkeyll code.  ...  We also formulate the gyrokinetic system in field-aligned coordinates for modeling realistic edge and scrape-off layer geometries in experiments.  ...  We use periodic boundary conditions in z and zero-flux boundary conditions in v . Figure 3 . 2 : 32 Φ h (blue) and ∂A h /∂t (yellow) for the case withβ = 10 and k ⊥ ρ s = 0.01.  ... 
arXiv:2103.16062v1 fatcat:vwko7fzlhzeevczpwakvn67yye

A high resolution wave propagation scheme for ideal Two-Fluid plasma equations

A. Hakim, J. Loverich, U. Shumlak
2006 Journal of Computational Physics  
In the first approach Maxwell equations are rewritten in their mixed-potential form.  ...  In the second approach the so-called perfectly hyperbolic form of Maxwell equations are used which explicitly incorporate the divergence equations into the time stepping scheme.  ...  Acknowledgments The authors acknowledge computer time on the Ladon Supercomputer belonging to the Mechanical Engineering Department of the University of Washington, Seattle.  ... 
doi:10.1016/j.jcp.2006.03.036 fatcat:wtzcar3cszhvppdszu72dnl42m

MAGNETOHYDRODYNAMIC MODELING OF SOLAR SYSTEM PROCESSES ON GEODESIC GRIDS

V. Florinski, X. Guo, D. S. Balsara, C. Meyer
2013 Astrophysical Journal Supplement Series  
The code employs HLL-type approximate Riemann solvers and includes facilities to control the divergence of magnetic field and maintain pressure positivity.  ...  Multiple populations of plasma and neutral particles, coupled via charge-exchange interactions, can be simulated simultaneously with this model.  ...  For explicit methods, this requires a small global time step to satisfy the Courant stability condition for a system of hyperbolic conservation laws for the entire grid (implicit or semi-implicit methods  ... 
doi:10.1088/0067-0049/205/2/19 fatcat:izuzl3kj6zg7tpm4l65xqsrjfu

Three-dimensional microscale simulation of colloidal particle transport and deposition in model porous media with converging/diverging geometries

Yajie Li, Azita Ahmadi, Aziz Omari, Hongting Pu
2018 Colloids and Surfaces A: Physicochemical and Engineering Aspects  
The declining trend observed for high Pe is in good agreement with experimental and simulation results found in the literature.  ...  microscale simulation of colloidal particle transport and deposition in model porous media with converging/diverging geometries -Colloids and Surfaces The microscale simulation of colloidal particle transport  ...  Acknowledgement This work was supported in part by the China Scholarship Council (CSC) under the Grant CSC N°201506260062.  ... 
doi:10.1016/j.colsurfa.2018.02.034 fatcat:mshirs4fqndzdn3iouqnbo4ccq

Modeling and Simulating Flowing Plasmas and Related Phenomena

S. A. Ledvina, Y.-J. Ma, E. Kallio
2008 Space Science Reviews  
The magnetohydrodynamic (MHD), test-particle/Monte-Carlo and hybrid models used in simulating flowing plasmas are described.  ...  Solving (1.1)-(1.2) together with Maxwell's equations (1.3)-(1.6) for every electron and ion in a plasma is an intractable task.  ...  Some simulations will use periodic boundary conditions on the side boundaries. This can be potentially dangerous.  ... 
doi:10.1007/s11214-008-9384-6 fatcat:yttni2uyerbqpmiegsdyuibt3a

Computational analysis of transport in three-dimensional heterogeneous materials

Gianluca Boccardo, Eleonora Crevacore, Alberto Passalacqua, Matteo Icardi
2020 Computing and Visualization in Science  
Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical  ...  Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.  ...  Acknowledgements MI acknowledge the financial support of AVL and the computational resources provided by the Warwick Centre for Scientific Computing.  ... 
doi:10.1007/s00791-020-00321-6 fatcat:gyl26hpty5furmyob6hvf34myy

Computational analysis of transport in three-dimensional heterogeneous materials [article]

Gianluca Boccardo, Eleonora Crevacore, Alberto Passalacqua, Matteo Icardi
2019 arXiv   pre-print
Transport equations are thus solved in a finite-volume formulation with quasi-periodic boundary conditions to simplify the upscaling problem by solving simple closure problems consistent with the classical  ...  Then, heat transfer problems are considered in a pipe with layers of deposited particles of different heights, and in heterogeneous anisotropic materials.  ...  Acknowledgements MI acknowledge the financial support of AVL and the computational resources provided by the Warwick Centre for Scientific Computing.  ... 
arXiv:1909.02830v1 fatcat:qqmhhqkfwvb7dnb33r267vz2pe

Two-way coupling of magnetohydrodynamic simulations with embedded particle-in-cell simulations

K.D. Makwana, R. Keppens, G. Lapenta
2017 Computer Physics Communications  
In this two-way coupling we follow the work of Daldorff et al. in which the PIC domain receives its initial and boundary conditions from MHD variables (MHD to PIC coupling) while the MHD simulation is  ...  We describe a method for coupling an embedded domain in a magnetohydrodynamic (MHD) simulation with a particle-in-cell (PIC) method.  ...  For the wave simulations shown below, we use the diffusive approach of [24] , [27] , whereas for the reconnection simulations we follow a hyperbolic divergence cleaning method (glm3) as in [22] [28  ... 
doi:10.1016/j.cpc.2017.08.003 fatcat:duhusbdjffdfbpw7vwwtlbksnm

A discontinuous Galerkin method for the Vlasov–Poisson system

R.E. Heath, I.M. Gamba, P.J. Morrison, C. Michler
2012 Journal of Computational Physics  
of the electric field through mesh interfaces and boundary conditions.  ...  In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions.  ...  The piecewise approximation is then used in conjunction with a slope limiter to reconstruct a local polynomial approximation of f for each cell in the mesh.  ... 
doi:10.1016/j.jcp.2011.09.020 fatcat:hvpvpcckeffqtnvpfukwy4n2ze

A discontinuous Galerkin method for the Vlasov-Poisson system [article]

R. E. Heath, I.M. Gamba, P.J. Morrison, C. Michler
2011 arXiv   pre-print
of the electric field through mesh interfaces and boundary conditions.  ...  In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions.  ...  The piecewise approximation is then used in conjunction with a slope limiter to reconstruct a local polynomial approximation of f for each cell in the mesh.  ... 
arXiv:1009.3046v2 fatcat:no3bgdc25rarhgjta3m5lsyfx4
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