A SURVEY OF FINITE-DIFFERENCE SCHEMES FOR THE PRIMITIVE EQUATIONS FOR A BAROTROPIC FLUID

Abstract Ten different finite-difference schemes for the numerical integration of the primitive equations for the free-surface model are tested for stability and accuracy. The integrations show that the quadratic conservative and the total energy conservative schemes are more stable than the usual second-order conservative scheme. But the most stable schemes are those in which the finite-difference approximations to the advection terms are calculated over nine grid points in space and therefore contain a form of smoothing, and the generalized Arakawa scheme, which for nondivergent flow conserve mean vorticity, mean kinetic energy, and mean square vorticity. If the integrations are performed for more than 3 days, it is shown that more than 15 grid points per wavelength are probably needed to describe with accuracy the movement and development of the shortest wave that initially is carrying a significant part of the energy. This is true even if a fourth-order scheme in space is used. Long-term integrations ...

[1]  R. D. Richtmyer,et al.  A Method for the Numerical Calculation of Hydrodynamic Shocks , 1950 .

[2]  F. Shuman.  Numerical Experiments with the Primitive Equations , 1960 .

[3]  P. Lax,et al.  Systems of conservation laws , 1960 .

[4]  D. Richtmyer,et al.  A Survey of Difference Methods for Non-Steady Fluid Dynamics , 1962 .

[5]  K. Miyakoda,et al.  Contribution to the numerical weather prediction:computation with finite difference. , 1962 .

[6]  K. Bryan,et al.  A Numerical Investigation of a Nonlinear Model of a Wind-Driven Ocean , 1963 .

[7]  Douglas K. Lilly,et al.  ON THE COMPUTATIONAL STABILITY OF NUMERICAL SOLUTIONS OF TIME-DEPENDENT NON-LINEAR GEOPHYSICAL FLUID DYNAMICS PROBLEMS , 1965 .

[8]  Syukuro Manabe,et al.  NUMERICAL RESULTS FROM A NINE-LEVEL GENERAL CIRCULATION MODEL OF THE ATMOSPHERE1 , 1965 .

[9]  Studies on numerical weather prediction , 1965 .

[10]  Yoshio Kurihara,et al.  ON THE USE OF IMPLICIT AND ITERATIVE METHODS FOR THE TIME INTEGRATION OF THE WAVE EQUATION , 1965 .

[11]  C. Jelesnianski,et al.  NUMERICAL COMPUTATIONS OF STORM SURGES WITHOUT BOTTOM STRESS , 1966 .

[12]  T. Matsuno.  Numerical Integrations of the Primitive Equations by a Simulated Backward Difference Method , 1966 .

[13]  DIFFERENCE SYSTEM AND BOUNDARY CONDITIONS FOR THE PRIMITIVE-EQUATION BAROTROPIC FORECAST , 1966 .

[14]  K. Bryan.  A SCHEME FOR NUMERICAL INTEGRATION OF THE EQUATIONS OF MOTION ON AN IRREGULAR GRID FREE OF NONLINEAR INSTABILITY , 1966 .

[15]  A. Arakawa.  Computational design for long-term numerical integration of the equations of fluid motion: two-dimen , 1997 .

[16]  LONG-TERM INTEGRATION OF THE BAROTROPIC EQUATIONS BY THE LAX-WENDROFF METHOD* , 1966 .

[17]  Energy‐preserving integrations of the primitive equations on the sphere , 1967 .

[18]  Y. Kurihara,et al.  NUMERICAL INTEGRATION OF A NINE-LEVEL GLOBAL PRIMITIVE EQUATIONS MODEL FORMULATED BY THE BOX METHOD , 1967 .

[19]  W. Gates.  A Numerical Study of Transient Rossby Waves in a Wind-Driven Homogeneous Ocean , 1968 .