Numerical solution of the Laplace equation for magnetosheath modeling using data-driven boundary conditions

The magnetic field in the magnetosheath is approximately current-free and can therefore be described by a scalar potential satisfying the Laplace equation. A key difficulty in solving the Laplace equation numerically is the closure of the computational domain, as the downstream magnetosheath field is generally unknown. Here, we address this challenge by prescribing magnetic field data on the boundaries, obtained from an analytical model and a global plasma simulation. The Laplace equation is solved using a finite-difference Jacobi scheme with Neumann boundary conditions and a consistent treatment of curved boundaries. The method is demonstrated for Mercury’s magnetosheath using hybrid plasma simulation data under average solar wind conditions, showing that the large-scale field can be reconstructed self-consistently from the boundary constraints.