A study of non-linear computational instability for a two-dimensional model
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A study of non-linear computational instability for a two-dimensional model
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  • Alternative Title:
    Non-linear computational instability for a two-dimensional model
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    "Experiments were conducted to test methods of achieving stability for three finite-difference analogues to a two-dimensional system of forecast equations. The equations described barotropic motion in an inviscid, incompressible, hydrostatic fluid with a free surface. The primary integration procedure was the leapfrog method. The measure of stability of the model was defined as a function of the available energy. No significant suppression of instability was achieved solely through manipulation of the boundary conditions of the finite-difference formulations. Increased stability was achieved for an invariant form of the forecast equations by applying initial data derived from the initialization procedure consistent with the formulation of the forecast system. A significant increase in stability was obtained by applying a space-time averaging operator to the advective coefficient of the non-linear terms of an advective form of the primitive equations. The result lends experimental support to extending a theory of non-linear computational instability in one dimension to two dimensions."
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