High-order computational method applied to the multi-fluid plasma model

High-order accurate finite element methods are important for problems that have strong anisotropies and complicated geometries and for stiff equation systems that are coupled through large source terms. Magnetized plasma simulations of realistic devices using the multi-fluid plasma model are examples that benefit from high-order accuracy. The multi-fluid plasma model only assumes local thermodynamic equilibrium within each fluid, e.g. ion and electron fluids for the two-fluid plasma model. Physical parameters indicate the importance of the two-fluid effects: electron to ion mass ratio, ion skin depth, and ion Larmor radius. The algorithm
¹
implements a discontinuous Galerkin method with an approximate Riemann solver to compute the fluxes of the fluids and electromagnetic fields at the computational cell interfaces. The multi-fluid plasma model has time scales on the order of the electron and ion cyclotron frequencies, the electron and ion plasma frequencies, the electron and ion sound speeds, and the speed of light. The multi-fluid plasma algorithm is implemented in a flexible code framework (WARPX) that allows easy extension of the physical model to include multiple fluids and additional physics. The code runs on multi-processor machines and is being adapted with OpenCL to many-core systems, characteristic of the next generation of high performance computers. WARPX has demonstrated a three-fluid (electrons, ions, and neutrals) simulation of a plasma sheath formation. Atomic reactions are incorporated that describe the effects of collisions between the species explicitly, allowing for the identification of regions of ionization/recombination, and interspecies momentum and energy transfer. The algorithm is validated with several test problems including the GEM challenge magnetic reconnection problem and the generation of dispersive plasma waves which are compared to analytical dispersion diagrams. The algorithm is applicable to study advanced physics calculations of plasma dynamics including magnetic plasma confinement and astrophysical plasmas. Three-dimensional solutions of the Z-pinch and the field reversed configuration (FRC) magnetic plasma confinement configurations are presented.