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

TL;DR

GAMERA-OP extends MHD finite-volume methods to orthogonal curvilinear geometries with constrained transport on a Yee-like grid to enforce $\nabla\cdot\mathbf{B}=0$ to machine precision and exact angular-momentum conservation. It introduces geometry-consistent high-order reconstruction via the enhanced PDM (e-PDM) limiter, multiple flux options including gas-kinetic and Rusanov, and two time integrators (AB2 and SSPRK3). The solver includes axis/pole treatments (ring-average), semi-relativistic corrections, background-field splitting, and anisotropic MHD support, all implemented in C with a modular design. A broad suite of tests across Cartesian, cylindrical, and spherical geometries demonstrates high accuracy, low diffusion, and robust handling of coordinate singularities and rotating flows, with performance improvements over previous GAMERA/LFM implementations. GAMERA-OP provides a practical, extensible platform for space and astrophysical plasma problems where orthogonal coordinates and angular-momentum conservation are advantageous.

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.

Figures (15)

• Figure 1: (a) The locations of the volume centered fluid variables $\boldsymbol{U}$, the face-centered magnetic fields $\boldsymbol{B}$, and the edge-centered electric fields $\boldsymbol{E}$. (b) A schematic showing the evaluation of the electric fields $E_3$ in a 2D slice ($x_1$-$x_2$ plane).
• Figure 2: (a) A seventh-order reconstruction profile evaluating $f_{i+\frac{1}{2}}$. (b) A schematic showing the PDM limiter procedure for curvilinear coordinates.
• Figure 3: Seventh-order reconstruction weights for the second active face $f_{i+\frac{1}{2}}^L$ in a uniform cylindrical radial grid versus a Cartesian grid.
• Figure 4: (a) Time step comparison for the two-dimensional field–loop advection problem on a cylindrical grid (see Section \ref{['loop 1/2D']}). (b) Magnetic energy distribution for the Cartesian–based method in the two-dimensional field–loop advection across the axis ($R=0$). (c) Same as panel (b), computed with GAMERA-OP.
• Figure 5: $L_1$ error of radial advection test as a function of grid resolution $N$