#### Alladi Ramakrishnan Hall

#### High Order Numerical Schemes for Magnetohydrodynamics on Geodesic Mesh

#### Sudip K. Garain

##### Korea Astronomy and Space Science Institute

*Many of the space physics and astrophysics systems are spherical. The numerical simulations of most of such systems use spherical polar coordinate system. However, computations are heavily affected because the mesh in this coordinate system results in vanishingly small timesteps, and a loss of accuracy close to the poles. In this presentation, we describe a meshing for spherical problems which is truly isotropic in angular space and avoids the coordinate singularity present in the spherical coordinate system. We further describe the numerical technique for achieving high order spatial reconstruction using WENO for the zone-centered variables as well as divergence free reconstruction of the face-centered magnetic field components. Using several stringent test problems, we demonstrate that our simulation technique achieves its design accuracies (upto fourth order) and performs stably. Finally, as an application, we present preliminary results of the 3D numerical simulation for sub-Keplerian accretion flow.*

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