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An adaptive moving finite element method for steady low Mach number compressible combustion problems

Sun, Zhen ; Braack, Malte ; Lang, Jens (2024)
An adaptive moving finite element method for steady low Mach number compressible combustion problems.
In: International Journal for Numerical Methods in Fluids, 2020, 92 (9)
doi: 10.26083/tuprints-00015640
Article, Secondary publication, Publisher's Version

Copyright Information: CC BY 4.0 International - Creative Commons, Attribution.

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Item Type: Article
Type of entry: Secondary publication
Title: An adaptive moving finite element method for steady low Mach number compressible combustion problems
Language: English
Date: 23 January 2024
Place of Publication: Darmstadt
Year of primary publication: 2020
Place of primary publication: Chichester
Publisher: John Wiley & Sons
Journal or Publication Title: International Journal for Numerical Methods in Fluids
Volume of the journal: 92
Issue Number: 9
DOI: 10.26083/tuprints-00015640
Corresponding Links:
Origin: Secondary publication DeepGreen

This work surveys an r‐adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the computation of such a problem is often extremely time‐consuming. Importantly, to capture the significant characteristics of the flame structure when using detailed chemistry, a much more stringent requirement on the spatial resolution of the interior layers of some intermediate species is necessary. Here, we propose a moving mesh method in which the mesh is obtained from the solution of so‐called moving mesh partial differential equations. Such equations result from the variational formulation of a minimization problem for a given target functional that characterizes the inherent difficulty in the numerical approximation of the underlying physical equations. Adaptive mesh movement has emerged as an area of intense research in mesh adaptation in the last decade. With this approach, points are only allowed to be shifted in space leaving the topology of the grid unchanged. In contrast to methods with local refinement, data structure hence is unchanged and load balancing is not an issue as grid points remain on the processor where they are. We will demonstrate the high potential of moving mesh methods for effectively optimizing the distribution of grid points to reach the required resolution for chemically reacting flows with extremely thin boundary layers.

Uncontrolled Keywords: adaptive moving meshes, low Mach number combustion, Rosenbrock time integrators, stabilized finite elements
Status: Publisher's Version
URN: urn:nbn:de:tuda-tuprints-156409
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Numerical Analysis and Scientific Computing
Date Deposited: 23 Jan 2024 13:45
Last Modified: 26 Jan 2024 11:38
SWORD Depositor: Deep Green
URI: https://tuprints.ulb.tu-darmstadt.de/id/eprint/15640
PPN: 514960124
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