Abstract

A physics-based-adaptive plasma model and an appropriate computational algorithm are developed to numerically simulate plasma phenomena in high fidelity. %The physics-based-adaptive plasma model is dynamically refined based on the local conditions to provide uniform model fidelity throughout the domain at all times of the simulation. The physics-based-adaptive plasma model can be dynamically refined based on the local plasma conditions to increase model fidelity uniformity throughout the domain at all times of the simulation. %The adaptive plasma model uses continuum representations of the plasma, which include a kinetic Boltzmann model for the highest fidelity, multi-fluid plasma models (13N-moment and 5$N$-moment), and single-fluid MHD models for the lowest fidelity. The adaptive plasma model uses continuum representations of the plasma, which include a kinetic Vlasov model for the highest fidelity, multi-fluid 5$N$-moment plasma model, and single-fluid MHD model for the lowest fidelity. The models include evolution equations for the electromagnetic fields, electron species, ion species, and neutral species. A nodal discontinuous Galerkin finite element method is implemented and is coupled with various implicit and explicit Runge-Kutta methods. Various model coupling techniques are investigated for a 5$N$-moment multi-fluid models with a Vlasov-Maxwell model, and a 5$N$-moment two-fluid model with an MHD model. Continuum plasma models using consistent normalizations and identical spatial representations provide straightforward and accurate coupling between the models. %The solution approach offers the potential for high-order accuracy and computational efficiency. The solution approach offers high-order accuracy and computational efficiency. Target compute platforms are heterogeneous computer architectures using a compute model that minimizes data movement.

Highlights

  • There are a wide variety of computational plasma models available which balance physical accuracy with simplifying approximations

  • The investigation is performed using a high-order discontinuous Galerkin finite element method [13,14,15], involving the continuum kinetic multi-species plasma model, 5N-moment multi-fluid plasma model, and magnetohydrodynamics (MHD) models, implemented in the WARPXM (Washington Approximate Riemann Plasma) codes [12, 16, 17], which provides a general framework for performing parallel computational plasma physics simulations

  • Spatial coupling of different plasma models is facilitated by derivations of the governing equations that use a consistent formulation and normalization, which allows direct translation between models of higher and lower physical fidelity

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Summary

INTRODUCTION

There are a wide variety of computational plasma models available which balance physical accuracy with simplifying approximations. The investigation is performed using a high-order discontinuous Galerkin finite element method [13,14,15], involving the continuum kinetic multi-species plasma model, 5N-moment multi-fluid plasma model, and magnetohydrodynamics (MHD) models, implemented in the WARPXM (Washington Approximate Riemann Plasma) codes [12, 16, 17], which provides a general framework for performing parallel computational plasma physics simulations. There has been work to couple different numerical methods [23] investigating a blended finite element method to solve the five moment multi-fluid plasma model [12]. In this work, coupling procedures between plasma models are presented, including between the MHD and 5N-moment multi-fluid models as well as between the 5N-moment multifluid model and continuum kinetics. An implementation of the kinetic model on a mixed structured/unstructured mesh is described that facilitates coupling to the 5N-moment multi-fluid plasma model.

PLASMA MODELS
Normalized Equation System
NUMERICAL DISCRETIZATION USING DISCONTINUOUS GALERKIN
Conservation Form Fluxes
Domains for Continuum Kinetic Plasma Models
Numerical Fluxes
Temporal Advance
MODEL COMPATIBILITY AND CONSERVATION PROPERTIES
Approach 1
Approach 2
Approach 3
CONTINUUM KINETIC PLASMA MODEL VALIDATION
Landau Damping
Two-Stream Instability
NUMERICAL TESTS WITH DIRECT VARIABLE TRANSLATION
Double Rarefaction Waves
COMPARISON OF CONSERVATIVE NUMERICAL FLUXES AND DIRECT VARIABLE TRANSLATION
CONCLUSION
DATA AVAILABILITY STATEMENT
Full Text
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