Discrete Unified Gas Kinetic Scheme for MHD Flows - an Implementation in OpenFOAM
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The Discrete Unified Gas Kinetic Scheme (DUGKS) was first proposed by [1] for low- speed isothermal flows and later extended to compressible flows in [2]. We build upon the OpenFOAM implementation of [3] to enable the simulation of MHD flows, by adding a force term to the Boltzmann-BGK Equation, which when integrated over the second order moment yields the Maxwell stress tensor. We solve the induction equation for the magnetic field using the macroscopic velocity and density field values computed by the DUGKS algorithm. This approach allows us to simulate the one-fluid, one-temperature plasma model over the entire Knudsen number regime. Verification in the continuum regime is performed against the analytical solution of the Hartmann flow, while the Brio-Wu shock tube problem results are compared to the well-documented astrophysics solver Athena [4]. REFERENCES [1] Z. Guo, K. Xu and R. Wang, Discrete unified gas kinetic scheme for all Knudsen number flows: Low-speed isothermal case, Phys. Rev. E, Vol. 88, 033305, 2013. [2] Z. Guo, R. Wang and K. Xu, Discrete unified gas kinetic scheme for all Knudsen number flows. II. Thermal compressible case, Phys. Rev. E, Vol. 91, 033313, 2015. [3] L. Zhu, S. Chen, and Z. Guo, dugksFoam: An open source OpenFOAM solver for the Boltzmann model equation, Commun. Comput. Phys., Vol. 213, pp. 155–164, 2017. [4] J. M. Stone, K. Tomida, C. J. White and K. G. Felker, The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers, Astrophys. J. Suppl. S., Vol. 249, 4, 2020.