Modelling thermal convection with large viscosity gradients in one block of the 'cubed sphere'

Research areas:

• Intérieurs planétaires (2011 - 2016)

Year:

2005

Authors:

• Gaël Choblet

Journal:

JOURNAL OF COMPUTATIONAL PHYSICS

Volume:

205

Number:

1

Pages:

269-291

Month:

MAY 1

ISSN:

0021-9991

BibTex:

@article{WOS:000228707100013, author = "Ga{\"e}l Choblet", abstract = "A numerical method solving thermal convection problems with variable viscosity in a spherical shell is presented. Several features of earlier programs solving the same problem in Cartesian geometry are adopted because of their efficiency and robustness: finite volume formulation, multigrid flow solver, parallel implementation. A recent composite mesh gridding technique for a spherical surface, termed the `cubed sphere{\&}#039;, has proven to be successful in solving other partial differential equations in geophysical problems. It is used here because of its various advantages: absence of geometrical singularities, same metric on each block, simple coupling of adjacent blocks. In addition, it is a good tool to implement grid-based methods proven efficient in the Cartesian context since it provides a mesh reasonably close to uniform. Although as in the Cartesian case, convergence rates decrease with increasing viscosity gradients, global contrasts up to 10(6) are obtained at a reasonable cost. (c) 2004 Elsevier Inc. All rights reserved.", doi = "10.1016/j.jcp.2004.11.005", extra = "PICL", issn = "0021-9991", journal = "JOURNAL OF COMPUTATIONAL PHYSICS", month = "MAY 1", number = "1", pages = "269-291", title = "{M}odelling thermal convection with large viscosity gradients in one block of the {\&}#039;cubed sphere{\&}#039;", volume = "205", year = "2005", }

Abstract:

A numerical method solving thermal convection problems with variable viscosity in a spherical shell is presented. Several features of earlier programs solving the same problem in Cartesian geometry are adopted because of their efficiency and robustness: finite volume formulation, multigrid flow solver, parallel implementation. A recent composite mesh gridding technique for a spherical surface, termed the `cubed sphere', has proven to be successful in solving other partial differential equations in geophysical problems. It is used here because of its various advantages: absence of geometrical singularities, same metric on each block, simple coupling of adjacent blocks. In addition, it is a good tool to implement grid-based methods proven efficient in the Cartesian context since it provides a mesh reasonably close to uniform. Although as in the Cartesian case, convergence rates decrease with increasing viscosity gradients, global contrasts up to 10(6) are obtained at a reasonable cost. (c) 2004 Elsevier Inc. All rights reserved.