Simulations of Global Solar Convection with a Fully Compressible CHORUS++ Code

Fluid-dynamics simulations of global solar convection are a critically important tool for assessing the dynamics of the solar interior. However, simulation studies with a fully compressible hydrodynamics code are not yet common. The Compressible High-Order Unstructured Spectral differencing (CHORUS++) code solves robustly and efficiently the fully compressible hydrodynamics equations using a compact local spectral method and semiunstructured grid system. Using the CHORUS++ code, we simulate the solar interior plasma flows from 0.7 to 0.99 of the solar radius using the values of the solar total luminosity and the sidereal rotation rate. In this paper, we analyze the simulated global flow structures before the statistically stable state to assess the compressibility of the plasma flows obtained with the fully compressible hydrodynamic code. The divergence of mass flux with the compressible model is overall small in the examined state before reaching the equilibrium state of the convection, which implies that the differences between the fully compressible flows and those obtained with the anelastic, incompressible, or linear-equation models are small in the simulated inner part of the convection zone. Although a fully relaxed stationary convection has not been achieved yet in the examined state, the model qualitatively reproduces the solar-type differential rotation. Simulations for longer periods are needed to achieve the system relaxation state. This work, assessing the early phase of the hydrodynamic evolution of solar convection, is our first step toward a better understanding of the nature of solar convection and the dynamo processes.