Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences

Area of Science:

• Computational astrophysics
• Space physics
• Geophysics
• Magnetohydrodynamics (MHD)

Background:

• Astrophysical and geophysical problems often involve fluid flows near spherical objects like stars and planets.
• Traditional polar (latitude-longitude) meshes suffer from singularities and non-uniform zone sizes, leading to accuracy loss and computational inefficiency.
• Geodesic meshes offer a solution to anisotropy but increase code complexity.

Purpose of the Study:

• To present a novel finite volume implementation for solving Euler and Magnetohydrodynamics (MHD) equations.
• To utilize a triangular geodesic mesh (TGM) for enhanced accuracy and efficiency in astrophysical fluid flow simulations.
• To address the limitations of polar meshes in modeling phenomena around spherical celestial bodies.

Main Methods:

• Development of a finite volume method on a triangular geodesic mesh (TGM).
• Implementation of Euler and MHD systems of equations with fourth-order accuracy in space and time.
• Detailed discussion on TGM generation, domain decomposition, 3D conservative reconstruction, and time-stepping schemes.

Main Results:

• Achieved fourth-order accuracy in both space and time for fluid flow simulations.
• Demonstrated conservation of the magnetic field's divergence to machine precision.
• Successfully implemented a computational scheme that overcomes the drawbacks of polar meshes.

Conclusions:

• The new finite volume method on a TGM provides an accurate and efficient approach for astrophysical fluid dynamics.
• This method effectively handles the challenges posed by spherical geometries and complex fluid behaviors.
• The TGM approach offers significant advantages for simulating phenomena in astrophysics, space physics, and geophysics.