PGE/Euler - Revision history

Jet53man: /* Eulerian Representation */

2024-04-14T22:11:09Z

Eulerian Representation

← Older revision		Revision as of 18:11, 14 April 2024
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	<span id="ConservingMomentum:Eulerian"><font color="#770000">'''Eulerian Representation'''</font></span><br />		<span id="ConservingMomentum:Eulerian"><font color="#770000">'''Eulerian Representation'''</font></span><br />
	of the Euler Equation,		of the (inertial-frame) Euler Equation,

	{{Template:Math/EQ_Euler02}}		{{Template:Math/EQ_Euler02}}

Jet53man: /* in terms of velocity: */

2024-04-14T22:09:52Z

in terms of velocity:

← Older revision		Revision as of 18:09, 14 April 2024
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	<span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br />		<span id="ConservingMomentum:Lagrangian"><font color="#770000">'''Lagrangian Representation'''</font></span><br />
	of the Euler Equation,		of the (inertial-frame) Euler Equation,

	{{Template:Math/EQ_Euler01}}		{{Template:Math/EQ_Euler01}}

Jet53man: /* in terms of velocity: */

2024-04-14T22:07:04Z

in terms of velocity:

← Older revision		Revision as of 18:07, 14 April 2024
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	{{Template:Math/EQ_Euler02}}		{{Template:Math/EQ_Euler02}}

			[<b>[[Appendix/References#BT87\|<font color="red">BT87</font>]]</b>], p. 672, Appendix Eq. (1E-8)

	</div>		</div>

Jet53man: /* in terms of velocity: */

2024-04-14T22:05:40Z

in terms of velocity:

← Older revision		Revision as of 18:05, 14 April 2024
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	{{Template:Math/EQ_Euler01}}		{{Template:Math/EQ_Euler01}}

			[<b>[[Appendix/References#BT87\|<font color="red">BT87</font>]]</b>], p. 671, Appendix Eq. (1E-6)<br />
	[<b>[[Appendix/References#BLRY07\|<font color="red">BLRY07</font>]]</b>], p. 13, Eq. (1.55)		[<b>[[Appendix/References#BLRY07\|<font color="red">BLRY07</font>]]</b>], p. 13, Eq. (1.55)
	</div>		</div>

Jet53man: /* Related Discussions */

2024-04-14T17:57:28Z

Related Discussions

← Older revision		Revision as of 13:57, 14 April 2024
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	=Related Discussions=		=Related Discussions=
	* Euler equation viewed from a [[PGE/RotatingFrame\|rotating frame of reference]].
	* An [[PGE/ConservingMomentum#Euler_Equation\|earlier draft of this "Euler equation" presentation]].		* An [[PGE/ConservingMomentum#Euler_Equation\|earlier draft of this "Euler equation" presentation]].
			* [[PGE/RotatingFrame\|Rotating Frame]].
			* [[Appendix/Ramblings/HybridSchemeOld\|Hybrid Scheme]].


	{{ SGFfooter }}		{{ SGFfooter }}

Jet53man: /* Euler Equation */

2021-07-28T03:16:22Z

Euler Equation

← Older revision		Revision as of 23:16, 27 July 2021
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	==Lagrangian Representation==		==Lagrangian Representation==
	~~ <br />~~
	~~ <br />~~
	~~ <br />~~
	~~ <br />~~

	===in terms of velocity:===		===in terms of velocity:===
	Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the		Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the
			<br />
			<br />

	<div align="center">		<div align="center">

Jet53man: /* Euler Equation */

2021-07-28T03:14:51Z

Euler Equation

← Older revision		Revision as of 23:14, 27 July 2021
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	<font size="-1">[[H_BookTiledMenu#Context\|<b>Euler</b>]]</font>		<font size="-1">[[H_BookTiledMenu#Context\|<b>Euler</b>]]</font>
	\|}		\|}
	~~There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].~~

	==Lagrangian Representation==		==Lagrangian Representation==
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	<br />		<br />
	<br />		<br />
			<br />

	===in terms of velocity:===		===in terms of velocity:===
	Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the		Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the
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	==Double Check Vector Identities==		==Double Check Vector Identities==

	In a subsection of an accompanying chapter titled, [[~~User:Tohline/~~AxisymmetricConfigurations/SolutionStrategies#Double_Check_Vector_Identities\|''Double Check Vector Identities,'']] we explicitly demonstrate for four separate "simple rotation profiles" that these two separate terms involving a nonlinear velocity expression do indeed generate identical mathematical relations, namely,		In a subsection of an accompanying chapter titled, [[AxisymmetricConfigurations/SolutionStrategies#Double_Check_Vector_Identities\|''Double Check Vector Identities,'']] we explicitly demonstrate for four separate "simple rotation profiles" that these two separate terms involving a nonlinear velocity expression do indeed generate identical mathematical relations, namely,
	<table border="0" cellpadding="5" align="center">		<table border="0" cellpadding="5" align="center">

Jet53man: /* Euler Equation */

2021-07-28T03:12:19Z

Euler Equation

← Older revision		Revision as of 23:12, 27 July 2021
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	=Euler Equation=		=Euler Equation=

			{\| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
			\|-
			! style="height: 125px; width: 125px; background-color:white;" \|
			<font size="-1">[[H_BookTiledMenu#Context\|<b>Euler</b>]]</font>
			\|}
	There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].		There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].

	==Lagrangian Representation==		==Lagrangian Representation==
			<br />
			<br />
			<br />
	===in terms of velocity:===		===in terms of velocity:===
	Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the		Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the

Jet53man: /* Euler Equation */

2021-07-26T21:35:17Z

Euler Equation

← Older revision		Revision as of 17:35, 26 July 2021
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	=Euler Equation=		=Euler Equation=
			There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].

	==Lagrangian Representation==		==Lagrangian Representation==
	~~There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].~~
	===in terms of velocity:===		===in terms of velocity:===
	Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the		Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the

Jet53man: /* Euler Equation */

2021-07-26T21:33:42Z

Euler Equation

← Older revision		Revision as of 17:33, 26 July 2021
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	==Lagrangian Representation==		==Lagrangian Representation==
			There is an earlier version of this chapter whose title emphasizes [[PGE/ConservingMomentum\|conservation of momentum]].
	===in terms of velocity:===		===in terms of velocity:===
	Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the		Among the [[PGE#Principal_Governing_Equations\|principal governing equations]] we have included the