Fully-implicit finite volume method for the ideal two-fluid plasma model

Abstract We present a novel numerical model that simulates ideal two-fluid plasmas coupled to the full set of Maxwell’s equations with application to space and laboratory plasmas. We use a fully-implicit finite volume method for unstructured meshes, that uses an advection upstream splitting method (i.e., AUSM + -up) for all speeds to discretize the numerical fluxes of the fluids. In addition, we discretize Maxwell’s equations with a modified-Rusanov scheme. The electromagnetic numerical dissipation is scaled using the scales of the fluid-electromagnetics coupled problem that are found to be very different from those of the uncoupled problem. Our numerical scheme guarantees that the elliptical constraints of Maxwell’s equations are satisfied by using hyperbolic divergence cleaning. We validate the performance and accuracy of our model by simulating the following conventional cases: a circularly polarized wave, a Brio–Wu type shock tube, and a two-fluid plasma reconnection with the GEM challenge set up. Our model reveals the complexity of the two-fluid model compared to magnetohydrodynamics (MHD) models, as the inclusion of charge separation, the displacement current and the electron dynamics present are ignored by the MHD simplifications. The two-fluid model shows the presence of electromagnetic and plasma waves and the effect that they have in even the simplest cases. We also compare our model to other available two-fluid models and find our results to be in good agreement.

[1]  T. Amano,et al.  A SECOND-ORDER DIVERGENCE-CONSTRAINED MULTIDIMENSIONAL NUMERICAL SCHEME FOR RELATIVISTIC TWO-FLUID ELECTRODYNAMICS , 2016, 1607.08487.

[2]  Andrea Lani,et al.  Effect of Radiation on Chromospheric Magnetic Reconnection: Reactive and Collisional Multi-fluid Simulations , 2017 .

[3]  Andrea Lani,et al.  An object oriented and high performance platform for aerothermodynamics simulation , 2008 .

[4]  J. Goedbloed,et al.  Principles of Magnetohydrodynamics , 2004 .

[5]  S. Baboolal.  Finite-difference modeling of solitons induced by a density hump in a plasma multi-fluid , 2001 .

[6]  D. Bonfiglio,et al.  Dominant electrostatic nature of the reversed field pinch dynamo. , 2005, Physical review letters.

[7]  R. J. Mason,et al.  An electromagnetic field algorithm for 2d implicit plasma simulation , 1987 .

[8]  Uri Shumlak,et al.  A discontinuous Galerkin method for the full two-fluid plasma model , 2005, Comput. Phys. Commun..

[9]  Takanobu Amano,et al.  Divergence-free approximate Riemann solver for the quasi-neutral two-fluid plasma model , 2015, J. Comput. Phys..

[10]  Uri Shumlak,et al.  A blended continuous-discontinuous finite element method for solving the multi-fluid plasma model , 2016, J. Comput. Phys..

[11]  Andrea Lani,et al.  Conservative Residual Distribution Method for Viscous Double Cone Flows in Thermochemical Nonequilibrium , 2013 .

[12]  Dinshaw S. Balsara,et al.  A high-order relativistic two-fluid electrodynamic scheme with consistent reconstruction of electromagnetic fields and a multidimensional Riemann solver for electromagnetism , 2016, J. Comput. Phys..

[13]  Andrea Lani,et al.  A finite volume implicit time integration method for solving the equations of ideal magnetohydrodynamics for the hyperbolic divergence cleaning approach , 2011, J. Comput. Phys..

[14]  Meng-Sing Liou,et al.  A sequel to AUSM, Part II: AUSM+-up for all speeds , 2006, J. Comput. Phys..

[15]  R. J. Mason,et al.  Hybrid Two-Dimensional Electron Transport in Self-Consistent Electromagnetic Fields , 1986, IEEE Transactions on Plasma Science.

[16]  Andrea Lani,et al.  A GPU-enabled Finite Volume solver for global magnetospheric simulations on unstructured grids , 2014, Comput. Phys. Commun..

[17]  Andrea Lani,et al.  Collisional radiative coarse-grain model for ionization in air , 2013 .

[18]  Harish Kumar,et al.  Entropy Stable Numerical Schemes for Two-Fluid Plasma Equations , 2011, J. Sci. Comput..

[19]  Uri Shumlak,et al.  Analytical and computational study of the ideal full two-fluid plasma model and asymptotic approximations for Hall-magnetohydrodynamics , 2011 .

[20]  Andrea Lani,et al.  A fully-implicit finite-volume method for multi-fluid reactive and collisional magnetized plasmas on unstructured meshes , 2016, J. Comput. Phys..

[21]  Claus-Dieter Munz,et al.  A three-dimensional finite-volume solver for the Maxwell equations with divergence cleaning on unstructured meshes , 2000 .

[22]  Andrea Lani,et al.  Multi-fluid Modeling of Magnetosonic Wave Propagation in the Solar Chromosphere: Effects of Impact Ionization and Radiative Recombination , 2016, 1611.08439.

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

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

[25]  Giovanni Lapenta,et al.  Role of electric fields in the MHD evolution of the kink instability , 2017 .

[26]  M. Liou,et al.  A New Flux Splitting Scheme , 1993 .

[27]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[28]  Uri Shumlak,et al.  Approximate Riemann solver for the two-fluid plasma model , 2003 .