Novel approach to general curvilinear coordinates for plasma fluid applications

In general geometry, plasma fluid equations include nonlinear geometric sources associated with fictitious forces, which pose significant challenges to computer simulations. We reformulate the plasma fluid hierarchy to rigorously preserve geometry and conservation properties critical to numerical simulations, while concealing the geometric sources. Our method extends the anti-symmetry approach, which frames plasma dynamics as infinitesimal rotations instead of fluxes or advection in traditional Eulerian or Lagrangian descriptions. In their discrete form, the reformulated models conserve mass, momentum, and energy naturally, by simple analogy with the continuous equations. Crucially, these conservation properties are independent of specific numerical schemes, and enable maximum flexibility by decoupling magnetic geometry, coordinate systems, and numerical discretization. As a testbed, we apply the novel representation to the extended magnetohydrodynamic system, which involves a complete set of curvilinear operations. The numerical implementation harnesses a Python-based, symbolic mathematics framework to generate GPU-accelerated curvilinear vector calculus routines, with the equations of motion implemented using the ALMA numerical engine. Excellent strong and weak parallel scalability is demonstrated in GPU supercomputers. The approach is validated with test cases drawn from different fusion subfields, including magnetic reconnection, gravity-driven instabilities, and liquid metal flows relevant to fusion reactor blankets. This work offers a new, powerful paradigm for plasma modeling in complex geometries, significantly increasing simulation code fidelity, robustness, speed, and versatility.