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**Harvard**

Borgqvist, J. (2015) *Curvature flows with junctions as model for capillary flows in complicated domains*. Göteborg : Chalmers University of Technology

** BibTeX **

@misc{

Borgqvist2015,

author={Borgqvist, Johannes},

title={Curvature flows with junctions as model for capillary flows in complicated domains},

abstract={The focus of the thesis is to model capillary
ow for a three phase system in complex
domains with a model involving curvature
ow in combination with triple junctions.
The first part of the report involves the implementation of a proposed solution algorithm
by Ruuth[16; 17]. The solution algorithm involves two steps, namely a diffusion step that
models the curvature
ow, and a sharpening step that corresponds to the evolution of
the three phase system at the triple junctions, that is, the points where the three phases
meet. The diffusion step involves solving the heat equation for a short period of time ,
and a finite difference approach is implemented in order to solve the heat equation. The
sharpening step is conducted by implementing a so called projection triangle algorithm,
and this step is also implemented using a finite difference approach. The accuracy of
the implementation of the diffusion step is calculated by modelling a two phase system
known as "the shrinking sphere" and the projection triangle algorithm is implemented
for two different domains. The results of the projection triangle algorithm are compared
to the results generated by Ruuth[16].
The second part of the thesis justifies the validity of the projection triangle algorithm in modelling capillary
ow. A physical condition concerning the conservation of the con-
tact angle is imposed, and a convolution thresholding calculation is presented using the
suggested condition. A numerical validation of the convolution thresholding scheme is
presented and compared to the results of the projection triangle algorithm. The convo-
lution thresholding scheme validates the result from the projection triangle algorithm.
The third part of the report includes the numerical simulations of the implemented algo-
rithm. The capillary
ow for two different liquids are simulated, and the results indicate
that a small contact angle corresponds to a faster capillary
ow. Furthermore, the capillary
ow for the faster of the two liquids is simulated in two different domain, one in
R2 and one in R3. The conclusion is that the algorithm proposed by Ruuth[16] can be
applied in order to model capillary
ow for a three phase system.},

publisher={Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,},

place={Göteborg},

year={2015},

note={178},

}

** RefWorks **

RT Generic

SR Electronic

ID 218493

A1 Borgqvist, Johannes

T1 Curvature flows with junctions as model for capillary flows in complicated domains

YR 2015

AB The focus of the thesis is to model capillary
ow for a three phase system in complex
domains with a model involving curvature
ow in combination with triple junctions.
The first part of the report involves the implementation of a proposed solution algorithm
by Ruuth[16; 17]. The solution algorithm involves two steps, namely a diffusion step that
models the curvature
ow, and a sharpening step that corresponds to the evolution of
the three phase system at the triple junctions, that is, the points where the three phases
meet. The diffusion step involves solving the heat equation for a short period of time ,
and a finite difference approach is implemented in order to solve the heat equation. The
sharpening step is conducted by implementing a so called projection triangle algorithm,
and this step is also implemented using a finite difference approach. The accuracy of
the implementation of the diffusion step is calculated by modelling a two phase system
known as "the shrinking sphere" and the projection triangle algorithm is implemented
for two different domains. The results of the projection triangle algorithm are compared
to the results generated by Ruuth[16].
The second part of the thesis justifies the validity of the projection triangle algorithm in modelling capillary
ow. A physical condition concerning the conservation of the con-
tact angle is imposed, and a convolution thresholding calculation is presented using the
suggested condition. A numerical validation of the convolution thresholding scheme is
presented and compared to the results of the projection triangle algorithm. The convo-
lution thresholding scheme validates the result from the projection triangle algorithm.
The third part of the report includes the numerical simulations of the implemented algo-
rithm. The capillary
ow for two different liquids are simulated, and the results indicate
that a small contact angle corresponds to a faster capillary
ow. Furthermore, the capillary
ow for the faster of the two liquids is simulated in two different domain, one in
R2 and one in R3. The conclusion is that the algorithm proposed by Ruuth[16] can be
applied in order to model capillary
ow for a three phase system.

PB Institutionen för matematiska vetenskaper, matematik, Chalmers tekniska högskola,

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/218493/218493.pdf

OL 30