Generalizations of Arakawa's Jacobian
Journal of Computational Physics
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Statistical relevance of vorticity conservation in the Hamiltonian particle-mesh method
Journal of Computational Physics
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The results of statistical analysis of simulation data obtained from long time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization used. This is illustrated for quasi-geostrophic flow with topographic forcing, for which a well established statistical mechanics exists. Statistical mechanical theories are constructed for the discrete dynamical systems arising from three discretizations due to Arakawa [Arakawa, Computational design for long-term numerical integration of the equations of fluid motion: two-dimensional incompressible flow. Part I. J. Comput. Phys. 1 (1966) 119-143] which conserve energy, enstrophy or both. Numerical experiments with conservative and projected time integrators show that the statistical theories accurately explain the differences observed in statistics derived from the discretizations.