Identification

Title

Adaptively implicit MPDATA advection for arbitrary Courant numbers and meshes

Abstract

Advection schemes with time step restrictions are widely used in weather and climate models. This can lead to instability in the presence of high flow speeds (relative to mesh spacing) such as occurs in convective updraughts, regions of mesh convergence, or where the winds are unusually high. An adaptively implicit advection scheme is proposed that treats advection implicitly only where the Courant number is high. Flux correction to ensure monotonicity is adapted to work with implicit time stepping. A version of the multidimensional positive-definite advection transport algorithm MPDATA is derived with an anti-diffusive flux compensating truncation errors of off-centred implicit time stepping. The anti-diffusive flux is gradually reduced as Courant numbers increase above 2 in order to maintain stability at the expense of second-order accuracy at high Courant numbers. Results of two-dimensional advection by deformational flow are presented on various meshes of the sphere. Stability and second-order accuracy are maintained when the Courant number is over 100 in a small region, when strong wind crosses the poles of a rotated latitude-longitude mesh. Good solutions are also obtained on a skipped latitude-longitude mesh, a cubed sphere, and hexagonal meshes. Accuracy reverts to first order when Courant numbers are large over a large fraction of the domain.

Resource type

document

Resource locator

Unique resource identifier

code

http://n2t.net/ark:/85065/d7ng4vkb

codeSpace

Dataset language

eng

Spatial reference system

code identifying the spatial reference system

Classification of spatial data and services

Topic category

geoscientificInformation

Keywords

Keyword set

keyword value

Text

originating controlled vocabulary

title

Resource Type

reference date

date type

publication

effective date

2016-01-01T00:00:00Z

Geographic location

West bounding longitude

East bounding longitude

North bounding latitude

South bounding latitude

Temporal reference

Temporal extent

Begin position

End position

Dataset reference date

date type

publication

effective date

2023-01-01T00:00:00Z

Frequency of update

Quality and validity

Lineage

Conformity

Data format

name of format

version of format

Constraints related to access and use

Constraint set

Use constraints

Limitations on public access

None

Responsible organisations

Responsible party

contact position

OpenSky Support

organisation name

UCAR/NCAR - Library

full postal address

PO Box 3000

Boulder

80307-3000

email address

opensky@ucar.edu

web address

http://opensky.ucar.edu/

name: homepage

responsible party role

pointOfContact

Metadata on metadata

Metadata point of contact