Accurate numerical solutions to the forward problem of local helioseismology
Chris Hanson (Max-Planck-Institut für Sonnensystemforschung), Michael Leguebe (Max-Planck-Institut für Sonnensystemforschung), MPS and INRIA Collaboration (Max-Planck-Institut für Sonnensystemforschung and INRIA Bordeaux)

We compute acoustic Green’s functions in an axisymmetric solar background model, which may include a meridional flow and differential rotation. The wave equation is solved in the frequency domain using a finite element solver. A transparent boundary condition for the waves is implemented in the chromosphere, which represents a great improvement in computational efficiency compared to implementations based on ‘sponge layers’. We perform various convergence studies that demonstrate that wave travel times can be computed with an accuracy of 0.001 s. This high level of numerical accuracy is required to interpret travel times in the deep interior, and is achieved thanks to a refined mesh in the near surface layers and around the source of excitation. The wave solver presented here lays the ground for future iterative inversion methods for flows in the deep solar interior.