Fourth-order accurate numerical modeling of the multi-fluid plasma equations with adaptive mesh refinement

This work develops a multi-fluid plasma modeling capability in extension of a parallel, adaptive, fourth-order, finite-volume method, computational fluid dynamics algorithm. The governing equations of the multi-fluid plasma model are derived from moments of the Boltzmann equation, under the assumption of local thermodynamic equilibrium. Maxwell's equations describe the electromagnetic field evolution and are coupled to the fluid equations of charged species. The present work concentrates on two, charged, collisionless fluids as the first step, although the algorithm is designed to accommodate more fluids, both charged and neutral, and collisions between fluids; the extension to multiple fluids is straightforward. The numerical algorithm featuring parallel, high-order (>= 4 for smooth flows), adaptive mesh refinement is expected to help cope with the inherent stiffness of the physics involved. The standard, fourth-order Runge-Kutta scheme is used to evolve the solution in time. The current study is primarily focused on verification and testing of the new, adaptive algorithm; we demonstrate 4th-order accuracy using problems with exact solutions and benchmark our solutions for common plasma simulations against references from literature. Using the 4th-order scheme, our multi-fluid model is shown to provide accurate solutions to plasma problems using half the cell count as traditional, 2nd-order methods. Furthermore, adaptive mesh refinement is successfully applied to three, plasma test problems, providing a significant reduction in mesh size. In subsequent work, an optimized version of our multi-fluid plasma algorithm will be applied to plasma test cases with more practical configurations, with a rigorous assessment of the improvements to computational efficiency afforded by our adaptive, higher-order scheme. (c) 2023 Elsevier B.V. All rights reserved.

Automated summary

This work presents the development of a multi-fluid plasma modeling capability based on a parallel, adaptive, fourth-order finite-volume method in computational fluid dynamics. The model couples the governing equations derived from the moments of the Boltzmann equation with Maxwell's equations, considering local thermodynamic equilibrium. The accuracy and efficiency of the algorithm are verified using problems with exact solutions, and it is shown that the multi-fluid model provides accurate solutions with half the cell count compared to traditional 2nd-order methods. Additionally, successful application of adaptive mesh refinement is demonstrated, resulting in a significant reduction in mesh size for plasma simulations.