The development of numerical models and tools which have operational space weather potential is an increasingly important area of research. This study presents recent Canadian efforts toward the development of a numerical framework for Sun-to-Earth simulations of solar wind disturbances. This modular three-dimensional (3D) simulation framework is based on a semi-empirical data-driven approach to describe the solar corona and an MHD-based description of the heliosphere. In the present configuration, the semi-empirical component uses the Potential Field Source Surface (PFSS) and Schatten Current Sheet (SCS) models to derive the coronal magnetic field based on observed magnetogram data. Using empirical relations, solar wind properties are associated with this coronal magnetic field. Together with a Coronal Mass Ejection (CME) model, this provides inner boundary conditions for a global MHD model which is used to describe interplanetary propagation of the solar wind and CMEs. The proposed MHD numerical approach makes use of advanced numerical techniques. The 3D MHD code employs a finite-volume discretization procedure with limited piecewise linear reconstruction to solve the governing partial-differential equations. The equations are solved on a body-fitted hexahedral multi-block cubed-sphere mesh and an efficient iterative Newton method is used for time-invariant simulations and an explicit time-marching scheme is applied for unsteady cases. Additionally, an efficient anisotropic block-based refinement technique provides significant reductions in the size of the computational mesh by locally refining the grid in selected directions as dictated by the flow physics. The capabilities of the framework for accurately capturing solar wind structures and forecasting solar wind properties at Earth are demonstrated. Furthermore, a comparison with previously reported results and future space weather forecasting challenges are discussed.
An anisotropic output-based adaptive mesh refinement scheme is proposed for the numerical prediction of inviscid and viscous flows on three-dimensional multi-block meshes using parallel distributed-memory computer architecture. A finite-volume discretization procedure with limited piecewise linear reconstruction is used in combination with a secondorder implicit time-marching algorithm to solve the governing partial differential equations on body-fitted hexahedral meshes. The anisotropic block-based refinement provides significant reductions in the size of the computational mesh by locally refining the grid only in selected directions as dictated by the flow physics and the predicted solution. The adjointbased error estimation enables formal evaluation of a posteriori estimates of the errors in solution-dependent engineering functionals in terms of local estimates of the truncation error as measured by the solution residual error. These errors are calculated by solving an adjoint problem related to the functional of interest and using the solution of the adjoint problem to appropriately weigh primal flow quantity residual errors evaluated on a finer mesh using an h-refinement strategy. The resulting dual-weighted error estimate is used to direct the local mesh adaptation and the error-driven refinement strategy creates meshes which are customized for the accurate calculation of the functionals of interest. The performance of the output-based mesh refinement scheme is demonstrated for several representative steady time-invariant inviscid flows governed by the Euler equations and viscous flows governed by the Navier-Stokes equations.
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