Modeling neutral particle dynamics using kinetic discontinuous Galerkin method

In this work, we present a discontinuous Galerkin code to model the Boltzmann equation for neutral particle dynamics. Neutral atoms and molecules are crucial in fusion devices as they determine fueling efficiency and mitigate heat fluxes to the divertor [1, 2]. Kinetic Monte Carlo codes capture the full dynamics but suffer from statistical noise and high computational cost — linked to the number of particles needed — in large devices and/or regimes with large variations in neutral densities, affecting scalability [3, 4]. We propose a continuum kinetic neutral model using the discontinuous Galerkin method, which offers high-order accuracy, parallel scalability and the ability to model complex geometries [5]. This allows our code to overcome noise limitations, improve scalability for large-scale simulations and tackle complex divertor geometries. The poster discusses the theoretical background and test cases showing conservation properties in solving the Boltzmann equation in 1X1V. The method is also validated against analytic theory for ionization and charge exchange in 1X1V. Ongoing work on unstructured grids and utilizing GPUs is discussed.

References

[1] S. Mordijck, Nucl. Fusion 60, 082006 (2020)

[2] P. C. Stangeby, The Plasma Boundary of Magnetic Fusion Devices (2000)

[3] I. Josepch et al, Nucl. Mater. Energy 12, 813-81 (2017)

[4] D. V. Borodin et al, Nucl. Fusion 62 086051 (2022)

[5] J. Hesthaven, Nodal Discontinuous Galerkin Methods (2008)