# Elementary dispersion analysis of some mimetic discretizations on triangular C-grids

## Abstract

Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noise in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriatelymore »

- Authors:

- Max Planck Institute for Meteorology, Hamburg (Germany)
- Alfred Wegener Institute for Polar and Marine Research, Bremerhaven (Germany)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22622244

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 330; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; ATMOSPHERES; COMPUTERIZED SIMULATION; CONTINUITY EQUATIONS; FILTERS; GRIDS; MASS; MATHEMATICAL SOLUTIONS; NOISE; VELOCITY; VISCOSITY; WAVE PROPAGATION

### Citation Formats

```
Korn, P., E-mail: peter.korn@mpimet.mpg.de, Danilov, S., and A.M. Obukhov Institute of Atmospheric Physics, Moscow.
```*Elementary dispersion analysis of some mimetic discretizations on triangular C-grids*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2016.10.059.

```
Korn, P., E-mail: peter.korn@mpimet.mpg.de, Danilov, S., & A.M. Obukhov Institute of Atmospheric Physics, Moscow.
```*Elementary dispersion analysis of some mimetic discretizations on triangular C-grids*. United States. doi:10.1016/J.JCP.2016.10.059.

```
Korn, P., E-mail: peter.korn@mpimet.mpg.de, Danilov, S., and A.M. Obukhov Institute of Atmospheric Physics, Moscow. Wed .
"Elementary dispersion analysis of some mimetic discretizations on triangular C-grids". United States.
doi:10.1016/J.JCP.2016.10.059.
```

```
@article{osti_22622244,
```

title = {Elementary dispersion analysis of some mimetic discretizations on triangular C-grids},

author = {Korn, P., E-mail: peter.korn@mpimet.mpg.de and Danilov, S. and A.M. Obukhov Institute of Atmospheric Physics, Moscow},

abstractNote = {Spurious modes supported by triangular C-grids limit their application for modeling large-scale atmospheric and oceanic flows. Their behavior can be modified within a mimetic approach that generalizes the scalar product underlying the triangular C-grid discretization. The mimetic approach provides a discrete continuity equation which operates on an averaged combination of normal edge velocities instead of normal edge velocities proper. An elementary analysis of the wave dispersion of the new discretization for Poincaré, Rossby and Kelvin waves shows that, although spurious Poincaré modes are preserved, their frequency tends to zero in the limit of small wavenumbers, which removes the divergence noise in this limit. However, the frequencies of spurious and physical modes become close on shorter scales indicating that spurious modes can be excited unless high-frequency short-scale motions are effectively filtered in numerical codes. We argue that filtering by viscous dissipation is more efficient in the mimetic approach than in the standard C-grid discretization. Lumping of mass matrices appearing with the velocity time derivative in the mimetic discretization only slightly reduces the accuracy of the wave dispersion and can be used in practice. Thus, the mimetic approach cures some difficulties of the traditional triangular C-grid discretization but may still need appropriately tuned viscosity to filter small scales and high frequencies in solutions of full primitive equations when these are excited by nonlinear dynamics.},

doi = {10.1016/J.JCP.2016.10.059},

journal = {Journal of Computational Physics},

number = ,

volume = 330,

place = {United States},

year = {Wed Feb 01 00:00:00 EST 2017},

month = {Wed Feb 01 00:00:00 EST 2017}

}