Helioseismic Modeling of Background Flows

We present a 3-dimensional (3D) numerical solver of the linearized compressible Euler equations (GALE -- Global Acoustic Linearized Euler), used to model acoustic oscillations throughout the solar interior. The governing equations are solved in conservation form on a fully global spherical mesh ($0 \le \phi \le 2\pi$, $0 \le \theta \le \pi$, $0 \le r \le R_{\odot}$) over a background state generated by the standard Solar Model S. We implement an efficient pseudo-spectral computational method to calculate the contribution of the compressible material derivative dyad to internal velocity perturbations, computing oscillations over arbitrary 3D background velocity fields. This model offers a foundation for a "forward-modeling" approach, using helioseismology techniques to explore various regimes of internal mass flows. We demonstrate the efficacy of the numerical method presented in this paper by reproducing observed solar power spectra, showing rotational splitting due to differential rotation, and applying local helioseismology techniques to measure travel times created by a simple model of single-cell meridional circulation.