A Study of Frontogenesis Using Finite-Element and Finite-Difference Methods

View More View Less
  • 1 Department of Mechanical Engineering and Mechanics, Lehigh University, Bethlehem, PA 18015
  • | 2 Arthur D. Little Company, Cambridge, MA 02140
© Get Permissions
Full access

Abstract

The accuracy of finite-element and finite-difference methods used to simulate frontogenesis in a six-layer three-dimensional model employing isentropic coordinates is compared. The problem solved is that of an initial height-independent deformation velocity field with a small potential temperature perturbation. The problem has a two-dimensional analytical solution and thus the accuracy of each model is assessed with the aid of this known solution. The finite-element model required approximately half the computer time needed for the finite-difference solution. In addition, due to the strong internal coupling between elements, the finite-element method is better able to simulate the open boundary Neumann conditions which are required for the present problem. This internal coupling, together with the smoothing action of operating on an element of space rather than a point as in finite differences, provides the stibility the finite-element technique shows in this example. Both solution methods give slower wave development than the analytical solution. Without artificial viscosity and staggered grids, it has not been possible to obtain stable solutions using open-boundary Neumann conditions for more than once a day. Due to the inherent internal smoothing the finite-element method does not require these techniques.

Abstract

The accuracy of finite-element and finite-difference methods used to simulate frontogenesis in a six-layer three-dimensional model employing isentropic coordinates is compared. The problem solved is that of an initial height-independent deformation velocity field with a small potential temperature perturbation. The problem has a two-dimensional analytical solution and thus the accuracy of each model is assessed with the aid of this known solution. The finite-element model required approximately half the computer time needed for the finite-difference solution. In addition, due to the strong internal coupling between elements, the finite-element method is better able to simulate the open boundary Neumann conditions which are required for the present problem. This internal coupling, together with the smoothing action of operating on an element of space rather than a point as in finite differences, provides the stibility the finite-element technique shows in this example. Both solution methods give slower wave development than the analytical solution. Without artificial viscosity and staggered grids, it has not been possible to obtain stable solutions using open-boundary Neumann conditions for more than once a day. Due to the inherent internal smoothing the finite-element method does not require these techniques.

Save