Approximation Schemes for convective term - structured grids - Summary of Discretizations Schemes and examples - Revision history

Michail: /* Example code for solving Smith-Hutton problem */

2012-04-21T05:56:18Z

Example code for solving Smith-Hutton problem

← Older revision		Revision as of 05:56, 21 April 2012
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	[[Sample code for solving Smith-Hutton test - Fortran 90]]		[[Sample code for solving Smith-Hutton test - Fortran 90]]

-	It's a results, obtained using this code ('''UDS''' and '''HLPA''' schemes)	+	It's results, obtained using this code ('''UDS''' and '''HLPA''' schemes)

2012-04-20T19:01:49Z

Pure convection of a scalar step by a rotating velocity field (Smith-Hutton problem)

← Older revision		Revision as of 19:01, 20 April 2012
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	The two parameters which define the scalar field are the Peclet number, which specifies the diffusivity of the problem, and <math>\boldsymbol{\alpha}</math> which is a parameter that defines the sharpness of the inlet profile.		The two parameters which define the scalar field are the Peclet number, which specifies the diffusivity of the problem, and <math>\boldsymbol{\alpha}</math> which is a parameter that defines the sharpness of the inlet profile.
		+
		+	Below it's cleary seen the numerical diffusion impact, comparing the contour fields obtaining using the UDS and HLPA. A bit later we shall place here a solution gained with QUICK scheme, and it will be seen the osscilations.

	[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA._probe_01.jpg]]		[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA._probe_01.jpg]]

2012-04-20T19:01:20Z

Example code for solving Smith-Hutton problem

← Older revision		Revision as of 19:01, 20 April 2012
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	It's a results, obtained using this code ('''UDS''' and '''HLPA''' schemes)		It's a results, obtained using this code ('''UDS''' and '''HLPA''' schemes)

-	Below it's cleary seen the numerical diffusion impact, comparing the contour fields obtaining using the UDS and HLPA. A bit later we shall place here a solution gained with QUICK scheme, and it will be seen the osscilations.	+

2012-04-20T18:46:57Z

Pure convection of a scalar step by a rotating velocity field (Smith-Hutton problem)

← Older revision		Revision as of 18:46, 20 April 2012
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	[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA_02_probe_03.jpg]]		[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA_02_probe_03.jpg]]

-	Below is the outlet profiles for solution of Smith-Hutton test. Clearly seen the osscilation for QUICK scheme and it can be noticed that HLPA free of its	+	Below is the outlet profiles for solution of Smith-Hutton test. Clearly seen the diffusivity of UDS, the osscilation for QUICK scheme and it can be noticed that HLPA free of its with the same accuracy.
	[[Image:Outlet_profiles.JPG]]		[[Image:Outlet_profiles.JPG]]

2012-04-20T18:45:19Z

Pure convection of a scalar step by a rotating velocity field (Smith-Hutton problem)

← Older revision		Revision as of 18:45, 20 April 2012
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	[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA_02_probe_03.jpg]]		[[Image:NM_convectionschemes_struct_grids_Smith_hutton_Countor_HLPA_02_probe_03.jpg]]
		+
		+	Below is the outlet profiles for solution of Smith-Hutton test. Clearly seen the osscilation for QUICK scheme and it can be noticed that HLPA free of its
		+	[[Image:Outlet_profiles.JPG]]

	=== Square Lid-driven cavity flow ===		=== Square Lid-driven cavity flow ===

2012-04-08T11:48:59Z

Discretizations Schemes - Estimation of order - Richardson extrapolation

2012-04-08T11:48:26Z

Discretizations Schemes - Estimation of order - Richardson extrapolation

← Older revision		Revision as of 11:48, 8 April 2012
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	</math>		</math>
	</td><td width="5%">(5)</td></tr></table>		</td><td width="5%">(5)</td></tr></table>
		+
		+	<table width="100%"><tr><td>
		+	:<math>
		+	\widetilde{p} = ln \left( \frac{\varphi_{h_{3}} - \varphi_{h_{2}}}{\varphi_{h_{2}}-\varphi_{h_{1}} } \right) / ln \left( r \right)
		+	</math>
		+	</td><td width="5%">(6)</td></tr></table>
		+
		+	<table width="100%"><tr><td>
		+	:<math>
		+	r= \left(h_{3}/h{2} \right) = \left( h_{2}/h{1} \right)
		+	</math>
		+	</td><td width="5%">(6)</td></tr></table>

	== Selection advice ==		== Selection advice ==

2012-04-08T11:42:55Z

Discretizations Schemes - Estimation of order - Richardson extrapolation

← Older revision		Revision as of 11:42, 8 April 2012
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	</math>		</math>
	</td><td width="5%">(3)</td></tr></table>		</td><td width="5%">(3)</td></tr></table>
		+


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	</math>		</math>
	</td><td width="5%">(4)</td></tr></table>		</td><td width="5%">(4)</td></tr></table>
		+
		+
		+	<table width="100%"><tr><td>
		+	:<math>
		+	\left\\| \varphi_{exact} - \varphi_{h_{1}} \right\\| \cong \left\| \left[ \frac{\varphi_{h_{2}} - \varphi_{h_{1}}}{h^{p}_{2} - h^{p}_{1}} \right]h^{p}_{1} \right\| + O \left(h^{p+1}_{1} \right) + O \left(h^{p+1}_{2} \right)
		+	</math>
		+	</td><td width="5%">(5)</td></tr></table>

	== Selection advice ==		== Selection advice ==

2012-04-08T11:06:52Z

Discretizations Schemes - Estimation of order - Richardson extrapolation

← Older revision		Revision as of 11:06, 8 April 2012
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	</math>		</math>
	</td><td width="5%">(3)</td></tr></table>		</td><td width="5%">(3)</td></tr></table>
		+
		+
		+	<table width="100%"><tr><td>
		+	:<math>
		+	\varphi_{exact} = \left[ \frac{h^{p}_{2}\varphi_{h_{1}} - h^{p}_{1}\varphi_{h_{2}} }{h^{p}_{2} - h^{p}_{1}} \right] + O \left(h^{p+1}_{1} \right) + O \left(h^{p+1}_{2} \right)
		+	</math>
		+	</td><td width="5%">(4)</td></tr></table>

	== Selection advice ==		== Selection advice ==

2012-04-08T10:57:05Z

Discretizations Schemes - Estimation of order - Richardson extrapolation

← Older revision		Revision as of 10:57, 8 April 2012
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	<table width="100%"><tr><td>		<table width="100%"><tr><td>
	:<math>		:<math>
-	\alpha = \left[ \frac{u_{h_{1}} - u_{h_{2}}}{ h^{p}_{2} - h^{p}_{1}} \right] + O \left(h^{p+1}_{1} \right) + O \left(h^{p+1}_{2} \right)	+	\alpha = \left[ \frac{\varphi_{h_{1}} - \varphi_{h_{2}}}{ h^{p}_{2} - h^{p}_{1}} \right] + O \left(h^{p+1}_{1} \right) + O \left(h^{p+1}_{2} \right)
	</math>		</math>
	</td><td width="5%">(3)</td></tr></table>		</td><td width="5%">(3)</td></tr></table>