High-order finite element method for plasma modeling

Abstract

High-order accurate finite element methods provide unique benefits for problems that have strong anisotropies and complicated geometries and for stiff equation systems that are coupled through large source terms, e.g. Lorentz force, collisions, or atomic reactions. Magnetized plasma simulations of realistic devices using the kinetic or the multi-fluid plasma models 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. The algorithm 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. A general model for atomic reactions has been developed and is incorporated in the multi-fluid plasma model. 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. The algorithm is applicable to study advanced physics calculations of plasma dynamics including magnetic plasma confinement and astrophysical plasmas. The discontinuous Galerkin method has also been applied to solve the Vlasov-Poisson kinetic model. Recently, a blended finite element algorithm has been developed and implemented which exploits the expected physical behavior to apply either a discontinuous or continuous finite element representation, which improves computational efficiency without sacrificing accuracy.