A Finite-Element Study of Frontogenesis

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  • 1 Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015
  • | 2 Arthur D. Little, Inc., Acorn Park, Cambridge, MA 02140
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Abstract

Finite elements are used to simulate the frontogenesis in a three-dimensional model employing sigma-coordinates. The basic flow is an east-west shear layer in which the velocity increases linearly with altitude and a periodic east-west perturbation is imposed on all variables. The effects of the element order, resolution, the boundary conditions, and time advance technique on the simulation of frontal development are examined. The space discretization is achieved by the first-order and the second-order isoparametric elements and the leapfrog time integration scheme is used. A satisfactory solution is produced, even if the front is entirely between the nodes. Because the stability of the time-dependent finite element solution depends extensively on the boundary conditions, the causes of instability are examined with respect to the boundary conditions. It is concluded that finite difference techniques are at present better than finite element techniques for most meteorological problems. The situation could change if the coupling of the boundary nodes could be used to improve the numerical stability to small perturbations.

Abstract

Finite elements are used to simulate the frontogenesis in a three-dimensional model employing sigma-coordinates. The basic flow is an east-west shear layer in which the velocity increases linearly with altitude and a periodic east-west perturbation is imposed on all variables. The effects of the element order, resolution, the boundary conditions, and time advance technique on the simulation of frontal development are examined. The space discretization is achieved by the first-order and the second-order isoparametric elements and the leapfrog time integration scheme is used. A satisfactory solution is produced, even if the front is entirely between the nodes. Because the stability of the time-dependent finite element solution depends extensively on the boundary conditions, the causes of instability are examined with respect to the boundary conditions. It is concluded that finite difference techniques are at present better than finite element techniques for most meteorological problems. The situation could change if the coupling of the boundary nodes could be used to improve the numerical stability to small perturbations.

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