Onate et al 2013a - Revision history

Cinmemj: Cinmemj moved page Draft Samper 913569722 to Onate et al 2013a

2019-05-23T12:18:25Z

Cinmemj moved page Draft Samper 913569722 to Onate et al 2013a

Cinmemj at 12:17, 23 May 2019

2019-05-23T12:17:42Z

Cinmemj at 12:14, 23 May 2019

2019-05-23T12:14:45Z

Cinmemj at 12:12, 23 May 2019

2019-05-23T12:12:46Z

Cinmemj at 12:11, 23 May 2019

2019-05-23T12:11:56Z

Cinmemj at 12:09, 23 May 2019

2019-05-23T12:09:05Z

Cinmemj at 12:07, 23 May 2019

2019-05-23T12:07:52Z

Cinmemj at 12:05, 23 May 2019

2019-05-23T12:05:52Z

Cinmemj at 12:04, 23 May 2019

2019-05-23T12:04:11Z

Cinmemj at 12:01, 23 May 2019

2019-05-23T12:01:30Z

← Older revision		Revision as of 12:17, 23 May 2019
Line 1:		Line 1:
		+	Published in ''Marine 2011, IV Int. Conference on Computational Methods in Marine Engineering. Selected papers'', L. Eça, E. Oñate, J. García-Espinosa, T. Kvamsdal and P. Bergan (Eds.), pp. 65-81, Springer, 2013<br />
	DOI: 10.1007/978-94-007-6143-8_4		DOI: 10.1007/978-94-007-6143-8_4
−
	==Abstract==		==Abstract==

@@ Line 327: / Line 327: @@
 # Compute at  the bed surface the resultant tangential stress induced by the fluid motion.
-# Compute the frictional work <math>{}^nW_f</math> originated by the tangential stresses at the bed surface.
+# Compute the frictional work <math display="inline">{}^nW_f</math> originated by the tangential stresses at the bed surface.
-# The onset of erosion at a bed point occurs when  <math>{}^nW_f</math> exceeds a critical threshold value  <math>W_c</math> .
+# The onset of erosion at a bed point occurs when  <math display="inline">{}^nW_f</math> exceeds a critical threshold value  <math display="inline">W_c</math> .
-# If  <math>{}^nW_f>W_c</math> at a bed node, then the node is detached from the bed region and it is allowed to move with the fluid. Also, the mass of the patch of bed elements surrounding the bed node is transferred to the new fluid node. This mass is subsequently transported with the fluid.
+# If  <math display="inline">{}^nW_f>W_c</math> at a bed node, then the node is detached from the bed region and it is allowed to move with the fluid. Also, the mass of the patch of bed elements surrounding the bed node is transferred to the new fluid node. This mass is subsequently transported with the fluid.
 Figure [[#img-3|3]] shows an schematic view of the bed erosion algorithm described.

@@ Line 172: / Line 172: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" |<math>{\int }_V\tau w_i\left(\frac{\partial p}{\partial x_i}+\right. </math><math>\left. {\pi }_i\right)dV=0\mbox{ }i=1,n_d\mbox{ }\mbox{ }(\mbox{no}\mbox{ }\mbox{sum}\mbox{ }\mbox{in}\mbox{ }\mbox{ }i)</math>
+| style="text-align: center;" |<math>{\int }_V\tau w_i\left(\frac{\partial p}{\partial x_i}+{\pi }_i\right)dV=0\mbox{ }i=1,n_d\mbox{ }\mbox{ }(\mbox{no}\mbox{ }\mbox{sum}\mbox{ }\mbox{in}\mbox{ }\mbox{ }i)</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (7)

@@ Line 146: / Line 146: @@
 {| style="text-align: left; margin:auto;width: 100%;"
 |-
-| style="text-align: center;" |<math>\frac{1}{K}\frac{\partial p}{\partial t}-\frac{\partial v_i}{\partial x_i}+</math><math>\sum_{i=1}^3\tau \frac{\partial q}{\partial x_i}\left[\frac{\partial p}{\partial x_i}+\right. </math><math>\left. {\pi }_i\right]=0</math>
+| style="text-align: center;" |<math>\frac{1}{K}\frac{\partial p}{\partial t}-\frac{\partial v_i}{\partial x_i}+</math><math>\sum_{i=1}^3\tau \frac{\partial q}{\partial x_i}\left[\frac{\partial p}{\partial x_i}+ {\pi }_i\right]=0</math>
 |}
 | style="width: 5px;text-align: right;white-space: nowrap;" | (5)

@@ Line 425: / Line 425: @@
 Figure [[#img-9|9]] displays the impact of an overtopping wave on the same lorry placed on a road behing a breakwater.
-<div id='img-x'></div>
+<div id='img-8'></div>
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-

← Older revision	Revision as of 12:18, 23 May 2019
(No difference)

@@ Line 288: / Line 288: @@
 One of the main tasks in the PFEM is the correct definition of the boundary domain. Boundary nodes are sometimes explicitly identified. In other cases, the total set of nodes is the only information available and the algorithm must recognize the boundary nodes (Figure [[#img-2|2]]).
-In our work we use an extended Delaunay partition for recognizing boundary nodes <span id="citeF-4"></span>[[#cite-4|[4]]][4]. Considering that the nodes follow a variable <math displya="inline">h(x)</math> distribution, where <math displya="inline">h(x)</math> is typically the minimum distance between two nodes. '' All nodes on an empty sphere with a radius greater than  <math>\alpha h</math>, are considered as boundary nodes''. In practice  <math>\alpha </math> is a parameter close to, but greater than one. Values of <math>\alpha </math> ranging around 1.3 have been found to be optimal in all examples analyzed. This criterion is coincident with the Alpha Shape concept <span id="citeF-19"></span>[[#cite-19|[19]]].
+In our work we use an extended Delaunay partition for recognizing boundary nodes <span id="citeF-4"></span>[[#cite-4|[4]]]. Considering that the nodes follow a variable <math displya="inline">h(x)</math> distribution, where <math displya="inline">h(x)</math> is typically the minimum distance between two nodes. '' All nodes on an empty sphere with a radius greater than  <math>\alpha h</math>, are considered as boundary nodes''. In practice  <math>\alpha </math> is a parameter close to, but greater than one. Values of <math>\alpha </math> ranging around 1.3 have been found to be optimal in all examples analyzed. This criterion is coincident with the Alpha Shape concept <span id="citeF-19"></span>[[#cite-19|[19]]].
 Once a decision has been made concerning which nodes are on the boundaries, the boundary surface is defined by all the polyhedral surfaces (or polygons in 2D) having all their nodes on the boundary and belonging to just one polyhedron.

@@ Line 45: / Line 45: @@
 </ol>
-<div id='img-x'></div>
+<div id='img-1'></div>
 {| class="floating_imageSCP" style="text-align: center; border: 1px solid #BBB; margin: 1em auto; width: 100%;max-width: 100%;"
 |-
 | [[Image:Draft_Samper_913569722-image5.png|400px]]
 |- style="text-align: center; font-size: 75%;"
-| colspan="x" | '''Figure 1:'''Sequence of steps to update a ``cloud´´ of nodes representing a domain containing a fluid and a solid part from time  <math>n</math> ( <math>t=t_n</math> ) to time <math displya="inline">n+2</math> ( <math>t=t_n+2\Delta t</math> )
+| colspan="1" | '''Figure 1:'''Sequence of steps to update a ``cloud´´ of nodes representing a domain containing a fluid and a solid part from time  <math>n</math> ( <math>t=t_n</math> ) to time <math displya="inline">n+2</math> ( <math>t=t_n+2\Delta t</math> )
 |}

@@ Line 572: / Line 572: @@
 <div id="cite-12"></div>
-[[#citeF-11|[11]]]  Idelsohn, S.R., Marti, J., Limache, A. & Oñate, E. Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the PFEM, ''Comput Methods Appl Mech Engrg''., '''197''', pp. 1762-1776, 2008.
+[[#citeF-12|[12]]]  Idelsohn, S.R., Marti, J., Limache, A. & Oñate, E. Unified Lagrangian formulation for elastic solids and incompressible fluids: Application to fluid-structure interaction problems via the PFEM, ''Comput Methods Appl Mech Engrg''., '''197''', pp. 1762-1776, 2008.
 <div id="cite-13"></div>

@@ Line 1: / Line 1: @@
-<!-- metadata commented in wiki content
+DOI: 10.1007/978-94-007-6143-8_4
-−
-−
-==The Particle Finite Element Method (PFEM). An effective numerical technique for solving marine, naval and harbour engineering problems==
-−
-E. Oñate<sup>1</sup>, S.R. Idelsohn<sup>*</sup>, M.A. Celigueta<sup>1</sup> and B. Suárez<sup>2</sup>
-−
-''<sup>1</sup>'' ''International Center for Numerical Methods in Engineering (CIMNE), Spain''
-−
-''<sup>*</sup>'' ''ICREA Research Professor at CIMNE''
-−
-''<sup>2</sup>'' ''Universitat Politècnica de Catalunya (UPC), Spain''
--->
 ==Abstract==