Simulations of plasmas and fluids using anti-symmetric models

•Novel fluid representation preserves force operator symmetry in discrete space.•Numerical toolkit adapted for hybrid supercomputers is used to create Navier-Stokes, MHD, and Braginskii codes.•Accompanying multigrid solver is used to diagonalize Poisson problems with 239 unknowns.•Good strong and weak scaling demonstrated in petascale supercomputers.•Anti-symmetry method can outperform classic flux-limiter schemes in solution smoothness and physicality.