# A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere

## Abstract

The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.

- Authors:

- and others

- Publication Date:

- Research Org.:
- Front Range Scientific Computations, Inc., Boulder, CO (United States); USDOE, Washington, DC (United States); National Science Foundation, Washington, DC (United States)

- OSTI Identifier:
- 219592

- Report Number(s):
- CONF-9404305-Vol.2

ON: DE96005736; TRN: 96:002321-0040

- Resource Type:
- Conference

- Resource Relation:
- Conference: Colorado conference on iterative methods, Breckenridge, CO (United States), 5-9 Apr 1994; Other Information: PBD: [1994]; Related Information: Is Part Of Colorado Conference on iterative methods. Volume 2; PB: 261 p.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 54 ENVIRONMENTAL SCIENCES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; METEOROLOGY; GLOBAL ASPECTS; COMPUTERIZED SIMULATION; ITERATIVE METHODS; NONLINEAR PROBLEMS

### Citation Formats

```
Ruge, J., Li, Y., and McCormick, S.F.
```*A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere*. United States: N. p., 1994.
Web.

```
Ruge, J., Li, Y., & McCormick, S.F.
```*A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere*. United States.

```
Ruge, J., Li, Y., and McCormick, S.F. Sat .
"A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere". United States. https://www.osti.gov/servlets/purl/219592.
```

```
@article{osti_219592,
```

title = {A nonlinear multigrid solver for a semi-Lagrangian potential vorticity-based barotropic model on the sphere},

author = {Ruge, J. and Li, Y. and McCormick, S.F.},

abstractNote = {The formulation and time discretization of problems in meteorology are often tailored to the type of efficient solvers available for use on the discrete problems obtained. A common procedure is to formulate the problem so that a constant (or latitude-dependent) coefficient Poisson-like equation results at each time step, which is then solved using spectral methods. This both limits the scope of problems that can be handled and requires linearization by forward extrapolation of nonlinear terms, which, in turn, requires filtering to control noise. Multigrid methods do not suffer these limitations, and can be applied directly to systems of nonlinear equations with variable coefficients. Here, a global barotropic semi-Lagrangian model, developed by the authors, is presented which results in a system of three coupled nonlinear equations to be solved at each time step. A multigrid method for the solution of these equations is described, and results are presented.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1994},

month = {12}

}