Coupled Vlasov and two-fluid codes on GPUs

We present a way to combine Vlasov and two-fluid codes for the simulation of a collisionless plasma in large domains while keeping full information on the velocity distribution in localised areas of interest. This is made possible by solving the full Vlasov equation in one region while the remaining area is treated by a 5-moment two-fluid code. In such a treatment, the main challenge of coupling kinetic and fluid descriptions is the interchange of physically correct boundary conditions between the different plasma models. In contrast to other treatments, we do not rely on any specific form of the distribution function, e.g. a Maxwellian type. Instead, we combine an extrapolation of the distribution function and a correction of the moments based on the fluid data. Thus, throughout the simulation both codes provide the necessary boundary conditions for each other. A speed-up factor of around 10 is achieved by using GPUs for the computationally expensive solution of the Vlasov equation. Additional major savings are obtained due to the coupling where the amount of savings roughly corresponds to the fraction of the domain where the kinetic equations are solved. The coupled codes were then tested on the propagation of whistler waves and on the GEM reconnection challenge.

[1]  Doron Levy,et al.  A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations , 2000, SIAM J. Sci. Comput..

[2]  Gábor Tóth,et al.  Sun‐to‐thermosphere simulation of the 28–30 October 2003 storm with the Space Weather Modeling Framework , 2007 .

[3]  H. Schmitz,et al.  Kinetic Vlasov simulations of collisionless magnetic reconnection , 2006 .

[4]  Stéphane Dellacherie,et al.  Kinetic-Fluid Coupling in the Field of the Atomic Vapor Laser Isotopic Separation: Numerical Results in the Case of a Monospecies Perfect Gas , 2003 .

[5]  Holger Schmitz,et al.  Darwin-Vlasov simulations of magnetised plasmas , 2006, J. Comput. Phys..

[6]  Shi Jin,et al.  Asymptotic‐preserving schemes for kinetic–fluid modeling of disperse two‐phase flows with variable fluid density , 2013, J. Comput. Phys..

[7]  Stefano Markidis,et al.  Two-way coupling of a global Hall magnetohydrodynamics model with a local implicit particle-in-cell model , 2014, J. Comput. Phys..

[8]  K. Yee.  Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media , 1966 .

[9]  P. Bertrand,et al.  Conservative numerical schemes for the Vlasov equation , 2001 .

[10]  Holger Schmitz,et al.  Comparison of time splitting and backsubstitution methods for integrating Vlasov's equation with magnetic fields , 2006, Comput. Phys. Commun..

[11]  A. Taflove,et al.  Numerical Solution of Steady-State Electromagnetic Scattering Problems Using the Time-Dependent Maxwell's Equations , 1975 .

[12]  N. Shankar,et al.  An estimation of the plasma parameters in the solar corona using quasi-periodic metric type III radio burst emission , 2005 .

[13]  Eric Sonnendrücker,et al.  Conservative semi-Lagrangian schemes for Vlasov equations , 2010, J. Comput. Phys..

[14]  Vladimir Kolobov,et al.  Towards adaptive kinetic-fluid simulations of weakly ionized plasmas , 2012, J. Comput. Phys..

[15]  Axel Klar,et al.  Transition from Kinetic theory to macroscopic fluid equations: A problem for domain decomposition and a source for new algorithms , 2000 .

[16]  Michael Hesse,et al.  Geospace Environmental Modeling (GEM) magnetic reconnection challenge , 2001 .

[17]  Erwin Laure,et al.  The Fluid-Kinetic Particle-in-Cell method for plasma simulations , 2013, J. Comput. Phys..

[18]  L. Leslie,et al.  Three-Dimensional Mass-Conserving Semi-Lagrangian Scheme Employing Forward Trajectories , 1995 .

[19]  Luc Mieussens,et al.  A multiscale kinetic-fluid solver with dynamic localization of kinetic effects , 2009, J. Comput. Phys..

[20]  P. Smereka,et al.  Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth , 2003 .

[21]  Vlasov simulations of collisionless magnetic reconnection without background density , 2006, physics/0612082.

[22]  Patrick Le Tallec,et al.  Coupling Boltzmann and Navier-Stokes Equations by Half Fluxes , 1997 .

[23]  Rainer Grauer,et al.  Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws , 2005, Parallel Comput..

[24]  Kanya Kusano,et al.  Multi-scale plasma simulation by the interlocking of magnetohydrodynamic model and particle-in-cell kinetic model , 2007, J. Comput. Phys..

[25]  Uri Shumlak,et al.  A high resolution wave propagation scheme for ideal Two-Fluid plasma equations , 2006, J. Comput. Phys..

[26]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .