[robyTKD]

Hi Foamers,

How can I calculate the curvature of a patch?

For example I want to know the curvature of an airfoil at each point of the surface. I know it is possible to do this using faMesh class, but in version 2.1.1 this class is no more available.

Thank you,
Roberto

[kmooney]

Hi Roberto,

I've dealt extensively with patch curvature in the past and its not very easy to implement if you're starting from scratch. A good resource to use would be Zeljko Tukovic's finiteArea library which is distributed with OpenFOAM-1.6-ext. There curvature is calculated on pseudo-2D finite area meshes as opposed to the fvPatchs but the idea should be pretty similar. If you search around google for his dissertation you can get the mathematical background on it.

I have done something like this in the past and I believe I did this type of procedure:

1. create a new volScalarField K to store curvatures for later and post processing
2. construct a finiteArea mesh from my patch of interest
3. Use the finiteArea lib to calculate K on the patch
4. Copy the K values from the finiteArea mesh to the FV volScalarField K patch
5. Write out the K field for post processing.

I'll hunt around for the code I wrote but no promises.

Cheers,

Kyle

[ngj]

Hi Roberto,

I might add that Zeljko's thesis is written in Croatian (found here: http://powerlab.fsb.hr/ped/kturbo/Op...vicPhD2005.pdf), though a recent paper does describe the mathematical background with the text in between given in English. Here is the bib-file:

@article{ tukovicJasak2012,
Author = {Tukovi\'{c}, {\v{Z}}. and Jasak, H.},
Title = {{A moving mesh finite volume interface tracking method for surface
   tension dominated interfacial fluid flow}},
Journal = {{Computers \& Fluids}},
Year = {{2012}},
Volume = {{55}},
Pages = {{70-84}},
Abstract = {{This paper describes a moving mesh interface tracking method implemented
   in OpenFOAM for simulating three-dimensional (3-D) incompressible and
   immiscible two-phase interfacial fluid flows with dominant surface
   tension forces. Collocated finite volume (FV) method is used for spatial
   discretisation of Navier-Stokes equations on moving polyhedral mesh. The
   mesh consists of two parts separated on interface. Fluid flow is solved
   on each mesh separately and coupling is accomplished in an iterative
   manner by enforcing the kinematic and dynamic condition at the
   interface. Surface tension force is calculated on arbitrary polygonal
   surface mesh with second order accuracy using a ``force-conservative{''}
   approach. Arbitrary polyhedral mesh adapts to the time-varying shape of
   the interface using vertex-based automatic mesh motion solver which
   calculates the motion of internal points based on the prescribed motion
   of interface points by solving the variable diffusivity Laplace equation
   discretised using the finite element method. The overall solution
   procedure based on iterative PISO algorithm with modified Rhie-Chow
   interpolation is second-order accurate in space and time, as is
   confirmed by numerical experiments on small amplitude sloshing in a
   two-dimensional (2-D) tank, 3-D droplet oscillation and buoyant rise of
   a 3-D air bubble in water. Numerical results are found to be in
   excellent agreement with available theoretical and experimental results.
   (C) 2011 Elsevier Ltd. All rights reserved.}},
Publisher = {{PERGAMON-ELSEVIER SCIENCE LTD}},
Address = {{THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND}},
Type = {{Article}},
Language = {{English}},
Affiliation = {{Tukovic, Z (Reprint Author), Univ Zagreb, Fac Mech Engn \& Naval Architecture, Ivana Lucica 5, Zagreb 41000, Croatia.
   Tukovic, Z.; Jasak, H., Univ Zagreb, Fac Mech Engn \& Naval Architecture, Zagreb 41000, Croatia.
   Jasak, H., Wikki Ltd, London W8 7PU, England.}},
DOI = {{10.1016/j.compfluid.2011.11.003}},
ISSN = {{0045-7930}},
Keywords = {{Collocated finite volume method; Moving polyhedral mesh; Interface
   tracking; Surface tension; Multiphase fluid flow; PISO algorithm;
   Rhie-Chow interpolation; OpenFOAM}},
Keywords-Plus = {{MOMENTUM INTERPOLATION METHOD; FREE-BOUNDARY PROBLEMS; LEVEL SET
   METHODS; INCOMPRESSIBLE-FLOW; NUMERICAL-SOLUTION; UNSTRUCTURED MESHES;
   CONSERVATION LAW; PURE WATER; GAS BUBBLE; COMPUTATIONS}},
Subject-Category = {{Computer Science; Mechanics}},
Web-of-Science-Category  = {{Computer Science, Interdisciplinary Applications; Mechanics}},
Author-Email = {{Zeljko.Tukovic@fsb.hr
   h.jasak@wikki.co.uk}},
Number-of-Cited-References = {{55}},
Times-Cited = {{1}},
Journal-ISO = {{Comput. Fluids}},
Doc-Delivery-Number = {{888AC}},
Unique-ID = {{ISI:000299975200008}},
}

If it is not possible to copy and compile the entire finiteArea library to 2.1.1 due to cross-version discrepancies, at least you can be inspired by looking into the source code as Kyle suggestion. If I do recall correctly, then it is the file faMeshDemandDrivenData.[C,H], which will be a good place to begin.

Good luck,

Niels

P.S. The foamToVTK in 1.6-ext does have an option to cast the finiteArea meshes into VTK format, which can then be visualised in ParaView without wasting memory on an entire volField to store boundary field data.

[robyTKD]

Thank you very much Niels and Kyle for the replies.
Unfortunately I am very busy in this period, but as soon as possible I will give you feedback regarding your advises.

Cheers,
Roberto