GAMERA-OP: A three-dimensional finite-volume MHD solver for orthogonal curvilinear geometries

TL;DR

GAMERA-OP is a high-order, flexible 3D MHD solver designed for orthogonal curvilinear geometries, ensuring divergence-free magnetic fields and accurate handling of complex geometries for space and astrophysical plasma simulations.

Contribution

It introduces a novel finite-volume MHD solver with geometry-consistent high-order reconstruction, divergence preservation, and modular design tailored for orthogonal curvilinear coordinates.

Findings

Demonstrates high accuracy and low numerical diffusion across benchmarks.

Effectively handles coordinate singularities and rotating flows.

Maintains divergence-free magnetic fields with constrained transport.

Abstract

We present GAMERA-OP (Orthogonal-Plus), a three-dimensional finite-volume magnetohydrodynamics (MHD) solver for orthogonal curvilinear geometries. The solver advances magnetic fields using constrained transport to preserve $\nabla\!\cdot\!\mathbf{B}=0$ to machine precision and employs geometry-consistent high-order reconstruction with an enhanced Partial Donor Cell method (e-PDM) that accounts for geometry curvature. Flexible numerics include various numerical fluxes and time integrators. In axial symmetric coordinates, angular momentum are preserved to round-off, and a ring-averaging treatment near the axis relaxes CFL constraints while maintaining divergence-free magnetic fields. Optional capabilities include the semi-relativistic (Boris) correction, background-field splitting, and an anisotropic MHD formulation. Rewritten in C, the code adopts a modular design that simplifies case setup and facilitates the addition of physics modules and coupling to other first-principles codes. Standard benchmarks across multiple geometries verify the code's high accuracy, low numerical diffusion, and robust handling of coordinate singularities and rotating flows. GAMERA-OP provides a practical, high-order framework for space and astrophysical plasma applications where orthogonal curvilinear coordinates and exact angular-momentum conservation are advantageous.