Description
Plasma fluid equations feature nonlinear geometric source terms associated with fictitious forces, which pose significant challenges for robust and accurate high-fidelity simulations. We present a reformulation of the fluid hierarchy that rigorously preserves conservation properties while concealing explicit geometric source terms. The approach recasts the governing equations into forms that are directly analogous to their discrete counterparts even in general curvilinear coordinates. Geometry effects are embedded implicitly through metric factors and differential operators, rather than appearing as explicit force terms. This strategy avoid explicit Christoffel symbols or metric derivatives, which may lead to fragile discretizations and difficulty in preserving discrete conservation. The novel representation naturally conserves mass, angular momentum, and energy in discrete space by direct analogy with the continuum equations. Importantly, these conservation properties impose only minimal and physically transparent requirements on the numerical discretization: anti-symmetry of the first-derivative operator and orthogonality of scalar and cross-product operations. No special geometric reconstruction, flux correction, or coordinate-specific tuning is required. As a result, the formulation cleanly decouples magnetic geometry, coordinate systems, and numerical discretization, enabling maximum flexibility while preserving physics fidelity. As a testbed, we apply this framework to the resistive magnetohydrodynamic system, which involves a complete set of curvilinear operations. The correctness and robustness of the approach are verified using steady-state liquid-metal flow configurations and the classic Orszag–Tang vortex problem. These results demonstrate that complex curvilinear plasma dynamics can be simulated using structure-preserving discretizations that remain simple, robust, and well suited for GPU-accelerated architectures. --This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, Theory Program, under Award DE-FG02-95ER54309.