A Provably Positive, Divergence-free Constrained Transport Scheme for the Simulation of Solar Wind

Abstract

Abstract In this paper, we present a provably positive, divergence-free constrained transport (CT) scheme to simulate the steady-state solar wind ambient with the three-dimensional magnetohydrodynamics numerical model. The positivity can be lost in two ways: one way is in the reconstruction process, and the other is in the updating process when the variables are advanced to the next time step. We adopt a self-adjusting strategy to bring the density and pressure into the permitted range in the reconstruction process, and use modified wave speeds in the Harten–Lax–van Leer flux to ensure the positivity in the updating process. The CT method can keep the magnetic fields divergence-free if the magnetic fields are divergence-free initially. Thus, we combine the least-squares reconstruction of the magnetic fields with the divergence-free constraints to make the magnetic fields globally solenoidal initially. Furthermore, we adopt a radial basis function method to interpolate variables at boundaries that can keep the magnetic field locally divergence-free. To verify the capability of the model in producing structured solar wind, the modeled results are compared with Parker Solar Probe (PSP) in situ observations during its first two encounters, as well as Wind observations at 1 au. Additionally, a solar maximum solar wind background is simulated to show the property of the model’s ability to preserve the positivity. The results show that the model can provide a relatively satisfactory comparison with PSP or Wind observations, and the divergence error is about 10−10 for all of the tests in this paper.