Computationally efficient schemes and boundary conditions for a fine-mesh barotropic model based on the shallow-water equations

Two types of computationally efficient semi-implicit and leap-frog schemes for integrating the shallow-water equations are presented. Their accuracy and stability are investigated, both for the pure initial value problem and for limited-area forecasts. The proper formulation of boundary conditions for the latter case is also discussed. Two sets of stable and sufficiently accurate boundary conditions are given. The practical usefulness of these conditions is also supported by computer experiments. DOI: 10.1111/j.2153-3490.1973.tb01601.x

[1]  Gino Moretti,et al.  Importance of Boundary Conditions in the Numerical Treatment of Hyperbolic Equations , 1969 .

[2]  H. Kreiss,et al.  Über das Verfahren der zentralen Differenzen zur Lösung des Cauchyproblems für partielle Differentialgleichungen , 1963 .

[3]  G. Platzman.  The computational stability of boundary conditions in numerical integration of the vorticity equation , 1954 .

[4]  Difference approximations for initial boundary-value problems , 1971, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[5]  Lewis F. Richardson,et al.  Weather Prediction by Numerical Process , 1922 .

[6]  Hsuan-Heng Wang,et al.  Experiments with a Regional Fine-Mesh Prediction Model , 1970 .

[7]  Arne Sundström.  STABILITY THEOREMS FOR THE BAROTROPIC VORTICITY EQUATION , 1969 .

[8]  H. Kreiss,et al.  Stability Theory of Difference Approximations for Mixed Initial Boundary Value Problems. II , 1972 .

[9]  G. E. Hill.  Grid Telescoping in Numerical Weather Prediction , 1968 .

[10]  Heinz-Otto Kreiss,et al.  Difference approximations for initial value problems for partial differential equations , 1966 .

[11]  J. G. Charney,et al.  Integration of the primitive and balance equations. , 1962 .

[12]  H. Kreiss.  Initial boundary value problems for hyperbolic systems , 1970 .

[13]  André Robert,et al.  A SEMI-IMPLICIT SCHEME FOR GRID POINT ATMOSPHERIC MODELS OF THE PRIMITIVE EQUATIONS , 1971 .

[14]  Bertil Gustafsson,et al.  An alternating direction implicit method for solving the shallow water equations , 1971 .

[15]  H. Kreiss,et al.  Comparison of accurate methods for the integration of hyperbolic equations , 1972 .

[16]  J. Neumann,et al.  Numerical Integration of the Barotropic Vorticity Equation , 1950 .

[17]  James J. O'Brien,et al.  Boundary Conditions for Fine-Mesh Limited-Area Forecasts. , 1970 .