Identification

Title

Adaptively implicit advection for atmospheric flows

Abstract

Implicit time‐stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time‐stepping is used for the remaining solution which is typically the majority. This adaptively implicit advection scheme facilitates efficient and robust integrations with long time‐steps while having negligible impact on the overall accuracy, and achieving monotonicity and local conservation on general meshes. A novel and important aspect for the efficiency of the approach is that only one iteration is needed each time the linear equation solver is called for solving the advection equation. The demonstration in this paper uses the second‐order Runge‐Kutta implicit/explicit time integration in combination with a second/third‐order finite‐volume spatial discretization and is tested using deformation flow tracer advection on the sphere and a fully compressible model for atmospheric flows. Tracers are advected over the poles of highly anisotropic latitude‐longitude grids with very large Courant numbers and on quasi‐uniform hexagonal and cubed‐sphere meshes with the same algorithm. Buoyant flow simulations with strong local updrafts also benefit from adaptively implicit advection. Stably stratified compressible flow simulations require a stable combination of implicit treatment of gravity and acoustic waves as well as advection in order to achieve long time‐steps.

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document

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Unique resource identifier

code

https://n2t.net/ark:/85065/d7h136b7

codeSpace

Dataset language

eng

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geoscientificInformation

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title

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publication

effective date

2016-01-01T00:00:00Z

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publication

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2024-12-01T00:00:00Z

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<span style="font-family:Arial;font-size:10pt;font-style:normal;" data-sheets-root="1">Copyright author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.</span>

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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/

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