Algorithms for vector field generation in mass consistent models. (English) Zbl 1194.86014
Summary: Diagnostic models in meteorology are based on the fulfillment of some time independent physical constraints as, for instance, mass conservation. A successful method to generate an adjusted wind field, based on mass conservation equation, was proposed by Sasaki and leads to the solution of an elliptic problem for the multiplier. Here we study the problem of generating an adjusted wind field from given horizontal initial velocity data, by two ways. The first one is based on orthogonal projection in Hilbert spaces and leads to the same elliptic problem but with natural boundary conditions for the multiplier. We derive from this approach the so called E-algorithm. An innovative alternative proposal is obtained from a second approach where we consider the saddle-point formulation of the problem - avoiding boundary conditions for the multiplier - and solving this problem by iterative conjugate gradient methods. This leads to an algorithm that we call the CG-algorithm, which is inspired from Glowinsk’s approach to solve Stokes-like problems in computational fluid dynamics. Finally, the introduction of new boundary conditions for the multiplier in the elliptic problem generates better adjusted fields than those obtained with the original boundary conditions.
MSC:
| 86A10 | Meteorology and atmospheric physics |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 35Q30 | Navier-Stokes equations |
| 65N06 | Finite difference methods for boundary value problems involving PDEs |
| 35J99 | Elliptic equations and elliptic systems |
Keywords:
mass consistent model; variational formulation; finite element method; elliptic problem; saddle-point problem; conjugate gradientReferences:
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