THE PRESSURE TERM IN THE ANELASTIC MODEL - A SYMMETRICAL ELLIPTIC SOLVER FOR AN ARAKAWA-C GRID IN GENERALIZED COORDINATES

For the anelastic or pseudoincompressible system, the diagnostic conti nuity equation is the constraint filtering sound waves. Hamiltonian fl uid dynamics considers the pressure force as the reaction force to thi s constraint. The author emphasizes the notion of an adjoint operator, as it provides the link between the constraint and the reaction. The elliptic equation for pressure is self-adjoint. Applied to a discretiz ed model, the author discusses the possibility to maintain this symmet ry in the pressure equation. Its discretization is deduced from one of the anelastic constraints. The author takes the example of a 2D model with orography, discretized on an Arakawa C grid in generalized coord inates. A specific treatment of boundaries is necessary to prevent Gib bs-like errors in the pressure term. It is possible to solve the press ure equation by a plain conjugate gradient method. Preconditioning is achieved by the Laplacian with no orography solved by a fast direct me thod. Criteria for efficiency depending upon the domain geometry are g iven.