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\section{Axisymetric geometries}
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% -----------------------------
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\cindex{axisymetric geometry}
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\cindex{polar coordinate system}
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\cindex{weighted functional space}
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\fiindex{\file{.geo} mesh}
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The coordinate system is associated to the geometry description,
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stored together with the mesh in the \file{.geo}:
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mkgeo_grid -t 10 -rz > square-rz.geo
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Note the additional line in the header:
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% The \code{geo} class also provides a way to specify the coordinates system
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% omega.set_coordinate_system ("rz");
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Here \code{"rz"} means that the coordinate system $(x_0,x_1)= (r,z)$.
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Notes that the coordinate system $(z,r)$ is also supported
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but not fully tested yet:
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it may also be implemented by a suitable coordinate swap.
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The \code{"cartesian"} argument string is also supported
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and means that the usual coordinate system may be used.
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In the \code{"rz"} case, the $L^2$ functional space is equipped with the
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following weighted scalar product
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(f,g) = \int_\Omega f(r,z) \, g(r,z) \, r \, dr dz
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and all usual bilinear forms are now implemented by using this weight.
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By this way, a program source code can handle both cartesian
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and axisymetric systems: only the input geometry makes the
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Thus, the coordinate system can be chosen at run time and
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we can expect an efficient source code reduction.
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\cindex{Poiseuille flow}
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\code{stokes-poiseuille.cc}
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\code{stokes-poiseuille-bubble.cc}
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are provided in the \code{example} directory.
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\exindex{stokes-poiseuille.cc}
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\exindex{stokes-poiseuille-bubble.cc}
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These examples are related to the Poiseuille flow
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of a fluid either between parallel planes (cartesian)
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or in a pipe (axisymetric).
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The first example implements the Taylor-Hood approximation
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while the second one uses the bubble-stabilized P1-P1 approximation.
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doc/usrman/axisymetric.tex
