Convection Diffusion equation - Revision history

Jureslak: /* References */

2019-07-09T10:06:42Z

‎References

2018-09-24T11:50:55Z

2018-03-15T14:52:12Z

‎3D cases

2018-03-15T14:51:04Z

‎3D cases

2018-03-15T14:50:37Z

‎3D cases

2018-03-15T14:50:15Z

‎3D cases

2018-03-15T14:42:39Z

‎3D cases

2018-02-24T14:22:53Z

‎3D cases

2018-02-24T14:22:37Z

‎3D cases

2018-02-24T14:22:03Z

‎Electrostatics Poisson's equation

← Older revision		Revision as of 10:06, 9 July 2019
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	* Slak, J., Kosec, G.. Detection of heart rate variability from a wearable differential ECG device., MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938, pp 450-455.		* Slak, J., Kosec, G.. Detection of heart rate variability from a wearable differential ECG device., MIPRO 2016, 39th International Convention, 2016, Opatija, Croatia, ISSN 1847-3938, pp 450-455.

−	'''This list might be incomplete, check also reference on the [[Main Page]].'''	+	'''This list might be incomplete, check also reference on the [[Medusa \| Main Page]].'''

@@ Line 136: / Line 136: @@
 First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
 where sides with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
-is shown below.
+is shown below. Max error is taken for error measure.
 [[File:pois3d_neu_poiss.png|500px]]

@@ Line 135: / Line 135: @@
 First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
-where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
+where sides with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
 is shown below.

@@ Line 135: / Line 135: @@
 First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
-where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\dpar{u}{\vec{n}} = 0$. The convergence of MLSM in two different setups
+where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\frac{\partial u}{\partial \vec{n}} = 0$. The convergence of MLSM in two different setups
 is shown below.

← Older revision		Revision as of 14:50, 15 March 2018
Line 133:		Line 133:

	== 3D cases ==		== 3D cases ==
		+
		+	First, the behavior of the method is tested on the regular case. The equation $\nabla^2 u = -\pi^2 \sin(\pi x) \sin(\pi y) \sin(\pi z)$ is solved on domain $[0, 1/2]^3$,
		+	where sided with at least one coordinate 0 have Dirichet BCs $u = 0$ and other sides have Neumann conditions $\dpar{u}{\vec{n}} = 0$. The convergence of MLSM in two different setups
		+	is shown below.
		+
		+	[[File:pois3d_neu_poiss.png\|500px]]
		+
		+
	And few more 3D cases that are not part of any serious analysis and were made only for fun.		And few more 3D cases that are not part of any serious analysis and were made only for fun.

← Older revision	Revision as of 11:50, 24 September 2018
(No difference)

@@ Line 137: / Line 137: @@
 A 3-dimensional example, where a CAD model for aluminium heat sink is
 discretized to obtain the domain description.
-Heat equation with $\alpha = 9.7 \cdot 10^{-5}]{m^2}{s}$, with no heat generation, i.e. $q = 0 {W}{m^3}$, with Dirichlet boundary conditions
+Heat equation with $\alpha = 9.7 \cdot 10^{-5}$, with no heat generation, i.e. $q = 0$, with Dirichlet boundary conditions
-$u = \unit[100]{^\circ C}$ on the bottom surface and
+$u = 100 ^\circ C$ on the bottom surface and
-$u = \unit[20]{^\circ C}$ everywhere else.
+$u = 20 ^\circ C$ everywhere else.
 [[File:heat_sink_cad.png|440px]][[File:heat_sink_sol1.png|440px]][[File:heat_sink_sol2.png|175px]]

← Older revision		Revision as of 14:22, 24 February 2018
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	== 3D cases ==		== 3D cases ==
−
−	~~First, a 3-dimensional case on domain $[0, 1]^3$ was tested on $N = 20^3$~~
−	~~nodes, making the discretization step $\Delta x = 0.05$. Support size of~~
−	~~$n=10$ with $m=10$ Gaussian basis functions was used. Their~~
−	~~normalization parameter was $\sigma = 60\Delta x$. A time step of $\Delta~~
−	~~t = 10^{-5}$ and an explicit Euler method was used to calculate the solution~~
−	~~of to $0.01$ time units.~~
−
−
−
	And few more 3D cases that are not part of any serious analysis and were made only for fun.		And few more 3D cases that are not part of any serious analysis and were made only for fun.

@@ Line 141: / Line 141: @@
 of to $0.01$ time units.
-[[File:diffusion3d.png|300px]]
 And few more 3D cases that are not part of any serious analysis and were made only for fun.
@@ Line 159: / Line 159: @@
 [[File:beef_1.png|350px]][[File:beef_3.png|350px]][[File:beef_2.png|350px]]
-And finally, steady state temperature profile of a triceratops
+And finally, steady state temperature profile of a triceratops and ... a box.
-[[File:triceratops.jpg|400px]]
+[[File:triceratops.jpg|400px]][[File:diffusion3d.png|300px]]
 '''We will add more serious 3D results as soon as we get motivated to prepare them, hopefully with some awesome project'''