Stokes equation - Revision history

Schuetz2 at 05:39, 17 June 2025

2025-06-17T05:39:55Z

← Older revision		Revision as of 05:39, 17 June 2025
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Stokes equation'''. MORwiki - Model Order Reduction Wiki, 2018. ~~http~~://modelreduction.org/~~index.php~~/Stokes_equation		::The MORwiki Community, '''Stokes equation'''. MORwiki - Model Order Reduction Wiki, 2018. https://modelreduction.org/morwiki/Stokes_equation

	@MISC{morwiki_stokes,		@MISC{morwiki_stokes,
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	title = {Stokes equation},		title = {Stokes equation},
	howpublished = {{MORwiki} -- Model Order Reduction Wiki},		howpublished = {{MORwiki} -- Model Order Reduction Wiki},
	url = <nowiki>{~~http~~://modelreduction.org/~~index.php~~/Stokes_equation}</nowiki>,		url = <nowiki>{https://modelreduction.org/morwiki/Stokes_equation}</nowiki>,
	year = {20XX}		year = {20XX}
	}		}

Himpe: change background ref

2019-06-27T07:59:00Z

change background ref

← Older revision		Revision as of 07:59, 27 June 2019
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	* For the background on the benchmark:		* For the background on the benchmark:

	@~~ARTICLE~~{~~Sty04~~,		@PHDTHESIS{Sch07,
	author = <nowiki>{T. ~~Stykel~~}</nowiki>,		author = <nowiki>{M.Schmidt}</nowiki>,
	title = {~~Gramian-Based Model Reduction for Descriptor System},~~		title = {Systematic discretization of input/output maps and other contributions to the control of distributed parameter systems},
	~~journal = {Mathematics~~ of ~~Control, Signals,~~ and ~~Systems~~},		school = {TU Berlin},
	~~volume~~ = {~~16},~~		year = {2007},
	~~pages = {297--319~~},		doi = {10.14279/depositonce-1600}
	year = {~~2004~~},
	doi = {10.~~1007~~/~~s00498-004~~-~~014104~~}
	}		}

Himpe: add thesis ref

2019-06-26T09:26:23Z

add thesis ref

← Older revision		Revision as of 09:26, 26 June 2019
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	{{preliminary}} <!-- Do not remove -->		{{preliminary}} <!-- Do not remove -->


	[[Category:benchmark]]		[[Category:benchmark]]
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	==Description==		==Description==
	This benchmark presents the two-dimensional instationary [[wikipedia:Stokes_flow\|Stokes equation]],		This benchmark presents the two-dimensional instationary [[wikipedia:Stokes_flow\|Stokes equation]],
	which models flow of an incompressible fluid in a domain <ref name="Sty03"/>,<ref name="Sty04"/>,<ref name="MehS05"/>,<ref name="Sty06"/>.		which models flow of an incompressible fluid in a domain <ref name="Sty03"/>,<ref name="Sty04"/>,<ref name="MehS05"/>,<ref name="Sty06"/>,<ref name="Sch07"/>.
	The associated partial differential equation system is given by:		The associated partial differential equation system is given by:
	:<math>		:<math>
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	<ref name="Sty06">T. Stykel. <span class="plainlinks">[https://doi.org/10.1016/j.laa.2004.01.015 Balanced Truncation model reduction for semidiscretized Stokes equation]</span>, Linear Algebra and its Application 415(2--3): 262--289, 2006.</ref>		<ref name="Sty06">T. Stykel. <span class="plainlinks">[https://doi.org/10.1016/j.laa.2004.01.015 Balanced Truncation model reduction for semidiscretized Stokes equation]</span>, Linear Algebra and its Application 415(2--3): 262--289, 2006.</ref>

			<ref name="Sch07">M.Schmidt. <span class="plainlinks">[https://doi.org/10.14279/depositonce-1600 Systematic discretization of input/output maps and other contributions to the control of distributed parameter systems]</span>, Ph.D. thesis, TU Berlin, 2007.</ref>

	</references>		</references>


	==Contact==		==Contact==

	[[User:Himpe]]		[[User:Himpe]]

Himpe: more content

2019-06-26T09:21:05Z

more content

← Older revision		Revision as of 09:21, 26 June 2019
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	==Description==		==Description==
	This benchmark presents the two-dimensional instationary [[wikipedia:Stokes_flow\|Stokes equation]],		This benchmark presents the two-dimensional instationary [[wikipedia:Stokes_flow\|Stokes equation]],
	which models flow of an incompressible fluid in a domain.		which models flow of an incompressible fluid in a domain <ref name="Sty03"/>,<ref name="Sty04"/>,<ref name="MehS05"/>,<ref name="Sty06"/>.
	The associated partial differential equation system is given by:		The associated partial differential equation system is given by:
	:<math>		:<math>
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	The boundary conditions are no-slip.		The boundary conditions are no-slip.

	A finite ~~difference~~ discretization yields the descriptor system:		A finite volume discretization on a uniform, staggered grid yields the descriptor system:
	:<math>		:<math>
	\begin{align}		\begin{align}
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	</math>		</math>

	==~~Origin~~==		==Data==

			This is a procedural benchmark.
			A MATLAB m-file to generate <math>E, A, B, C</math> matrices can be found as part of the [https://www.mpi-magdeburg.mpg.de/projects/mess M.E.S.S] project,
			under:

			DEMOS/models/stokes/stokes_ind2.m

	==~~Data~~==		==Dimensions==

			System structure:

			:<math>
			\begin{align}
			E \dot{x}(t) &= Ax(t) + Bu(t) \\
			y(t) &= Cx(t)
			\end{align}
			</math>

			System dimensions:

			<math>E \in \mathbb{R}^{N \times N}</math>,
			<math>A \in \mathbb{R}^{N \times N}</math>,
			<math>B \in \mathbb{R}^{N \times 1}</math>,
			<math>C \in \mathbb{R}^{1 \times N}</math>.

	==~~Dimensions~~==		==Citation==

			To cite this benchmark, use the following references:

			* For the benchmark itself and its data:
			::The MORwiki Community, '''Stokes equation'''. MORwiki - Model Order Reduction Wiki, 2018. http://modelreduction.org/index.php/Stokes_equation

	==~~Citation~~==		@MISC{morwiki_stokes,
			author = <nowiki>{{The MORwiki Community}}</nowiki>,
			title = {Stokes equation},
			howpublished = {{MORwiki} -- Model Order Reduction Wiki},
			url = <nowiki>{http://modelreduction.org/index.php/Stokes_equation}</nowiki>,
			year = {20XX}
			}

			* For the background on the benchmark:

			@ARTICLE{Sty04,
			author = <nowiki>{T. Stykel}</nowiki>,
			title = {Gramian-Based Model Reduction for Descriptor System},
			journal = {Mathematics of Control, Signals, and Systems},
			volume = {16},
			pages = {297--319},
			year = {2004},
			doi = {10.1007/s00498-004-014104}
			}

	==References==		==References==

			<references>

			<ref name="Sty03">T. Stykel. <span class="plainlinks">[https://doi.org/10.1002/pamm.200310302 Balanced truncation model reduction for descriptor systems]</span>, Proceedings in Applied Mathematics and Mechanics 3: 5--8, 2003.</ref>

			<ref name="Sty04">T. Stykel. <span class="plainlinks">[https://doi.org/10.1007/s00498-004-0141-4 Gramian-Based Model Reduction for Descriptor System]</span>, Mathematics of Control, Signals, and Systems 16(4): 297--319, 2004.</ref>

			<ref name="MehS05">V. Mehrmann, T. Stykel. <span class="plainlinks">[https://doi.org/10.1007/3-540-27909-1_3 Balanced Truncation Model Reduction for Large-Scale Systems in Descriptor Form]</span>, Dimension Reduction of Large-Scale Systems, Lecture Notes in Computational Science and Engineering, vol 45: 83--115, 2005.</ref>

			<ref name="Sty06">T. Stykel. <span class="plainlinks">[https://doi.org/10.1016/j.laa.2004.01.015 Balanced Truncation model reduction for semidiscretized Stokes equation]</span>, Linear Algebra and its Application 415(2--3): 262--289, 2006.</ref>

			</references>

Himpe: Stokes description init

2019-06-26T08:08:42Z

Stokes description init

@@ Line 1: / Line 1: @@
 {{preliminary}} <!-- Do not remove -->
 [[Category:linear]]
 ==Description==
+A finite difference discretization yields the descriptor system:
 ==Origin==

Himpe: init Stokes

2019-06-26T07:24:09Z

init Stokes

New page

{{preliminary}} 

[[Category:linear]]

==Description==

==Origin==

==Data==

==Dimensions==

==Citation==

==References==

==Contact==

[[User:Himpe]]