Fully Compressible Magnetohydrodynamic Simulations of Solar Convection Zones with CHORUS++

Fully Compressible Magnetohydrodynamic Simulations of Solar and Jovial Convection Zones with CHORUS++ By Aidan Paoli1, Russell Hankey2, Chunlei Liang3 The objective of this study is to develop a fully compressible magnetohydrodynamic solver for fast simulations of global dynamo of the Sun using unstructured grids and GPUs. Accurately modeling the Sun’s convective layers is vital to predicting the Sun’s behavior including solar dynamo and sunspot cycles. Similarly, to better understand convection in gas giants like Jupiter and Saturn requires global simulations of their convective layers. Global simulations modeling convective layers inside stars and planets are computationally strenuous. Currently there are many efficient codes capable of conducting these large simulations, however many make assumptions of anealastic density distribution. The anelastic assumption is able to produce accurate results for low mach numbers, however it fails in regions where the mach number approaches one and fully compressible flow needs to be considered. Many of these codes are also required to use a structured grid for the use of spherical harmonics. To avoid these issues, a Compressible High ORder Unstructured Spectral difference (CHORUS) code was created by Wang et al [1]. CHORUS is a fully compressible, high order, spectral difference code for simulating fluid dynamics inside stars and planets. CHORUS++ augmented the CHORUS code to adopt higher degree of polynomials by using cubed-sphere meshing and transfinite mapping to perform simulations on unstructured grids [2]. Two hydrodynamic benchmark tests of Jupiter and Sun were used to test the CHORUS code [1,2]. Recently, CHORUS++ was further developed for parallel magnetohydrodynamic (MHD) solutions on GPUs at Clarkson University. Two benchmark tests resembling the MHD in Jupiter were originally proposed by Jones et al [3]. This study presents CHORUS-MHD solutions of a dynamo benchmark problem similar to the one proposed by Jones et al. Subsequently, we extend the solar benchmark problems presented by Chen et al [1] to unsteady solar dynamo problems. The CHORUS-MHD code is further accelerated by GPUs and used to successfully solve these solar dynamo benchmark problems. Both Jupiter and solar benchmark problems are run using a 6th-order spectral difference method, on multiple GPUs. CHORUS-MHD can be further used to simulate the sunspot cycle and model the polar vortices of the Sun [4] because of its flexibility in meshing. References: [1] J. Wang, C. Liang and M. S. Miesch, A Compressible High-Order Unstructured Spectral Difference Code for Stratified Convection in Rotating Spherical Shells, Journal of Computational Physics, Vol 290, pp 90-111, 2015. [2] K. Chen, C. Liang and M. Wan, Arbitrarily high-order accurate simulations of compressible rotationally constrained convection using a transfinite mapping on cubed-sphere grids, Physics of Fluids, Vol 35, 086120, 2023. [3] C.A. Jones, P. Boronski, A.S. Brun, G.A. Glatzmaier, T. Gastine, M.S. Miesch, J. Wicht, Anelastic convection-driven dynamo benchmarks, Icarus, Volume 216, 2011,Pages 120-135, [4] M. Dikpati, B. Raphaldini, S. W. McIntosh, and P. A. Gilman, A magnetohydrodynamic mechanism for the formation of solar polar vortices, Proceedings of the National Academy of Sciences, 121 (47) e2415157121. Paper Authors: 1Undergraduate Research Assistant, Department of Mechanical and Aerospace Engineering, Clarkson University, AIAA Student Member 2Graduate Research Assistant, Department of Mechanical and Aerospace Engineering, Clarkson University, AIAA Student Member 3Professor of Mechanical and Aerospace Engineering, Clarkson University, AIAA Associate Fellow