An approach to fully automatic surface mesh generation used for wave resistance calculations

For many numerical calculations a given geometry is discretized using a mesh generation algorithm. In my master thesis I developed a new full or semi automatic algorithm using unstructured mesh generation techniques. Quality control functions are used to ensure high quality meshes. Please read on for more detailed information about the algorithm developed.

Mesh Generation


The complete master thesis can be found in under Publications. (in german)

Today the ship industry operates in a highly competitive market.
Besides the requirement for a high quality a short time to market and
low manufacturing costs are important assets in acquiring contracts.

In the initial design stage an emphasis is placed on precise and rapid
predictions of the capabilities of the vessel leading to an increasing
use of advanced computer techniques. These are utilized for iterative
optimization processes to test, improve and compare multiple design

In the field of fluid dynamics increasing ship speeds place an
emphasis on the reduction of wave resistance. Codes based on potential
flow theory are used to estimate and analyze the flow around the ship
hull as well as to determine the wave induced resistance by
calculating the strength of a source distribution on the ship hull and
water surface.

The distribution of the so called panels on the hull has a significant
impact on the accuracy of the wave resistance prediction. Currently
creating and placing the panels on the hull body is a labor intensive
non or semi automatic task requiring a profound experience based
knowledge. On average generating the panel meshes takes up about 60 to
80 % of the labor time needed for a potential flow calculation.


To take advantage of a significant improvement in cost and work flow
the main objective of the algorithm presented is the development of a
fully automatic mesh generation tool with automatic quality controlled
panel placement. Elements are created so that borders as well as
knuckles in the hull surface are treated correctly; controls offer the
engineer easy to use options for global and local mesh modifications.

The Algorithm


An overview of the mesh generation algorithm is shown in the following figure:

The Algorithm

In a first step the surface representation, i. e. the definition of
the surface patches, is read from the IGES file. The second step
consists of two substeps, namely creating an initial fine meshing with
an adequate approximation of the surface individually for each patch
and merging these triangular surface meshes into one consistent mesh
covering the complete hull surface. Utilizing this surface mesh the
algorithm finally performs subsequent operations reducing the number
of panels until a user controlled mesh structure and panel size is

Data Input Format

As a standardized platform and system independent input format for the
description of the hull surface the IGES standard is used. Most state
of the art initial design software used in the shipbuilding industry
is capable of exporting the surface description to this format using a
surface patch based description.

Initial Meshing

The objective of the initial meshing is to create a suitable initial
mesh on each surface patch representing the NURBS patch with a given
but small error. In the next figure examples of the initial meshing are

Initial Meshing

The initial mesh is generated using a structured approach. For a given
edge length quadrilateral elements are created which are subdivided
into two triangles. A modified butterfly subdivision method is used
for further refinement of the mesh. Criteria for refinement are
the area of the element and the distance between the midpoint of the
element edges to the NURBS surfaces.


A single consistent mesh on the complete hull surface is obtained by
merging the individual triangle surface meshes. Currently cocone, an
external surface reconstruction algorithm, reads the point set defined
by the corner points of the elements on all surface patches.
Surface reconstruction, i. e. shape, boundary and knuckle
reconstruction, is then performed on this point set resulting in one
consistent mesh. This method is used because surface reconstruction is
a robust fault tolerant method handling overlapping surface patches or
gaps between patches gracefully and does not require any further
knowledge about the topologic relations between the patches.

Experience has shown that this algorithm, albeit working perfectly for
certain meshes, doesn’t give the results expected for others.
Therefore development of a merging algorithm using advanced topology
information has started and is currently in the early stages of

Mesh Coarsening

The final step in the algorithm is a sucessive mesh coarsening
operation. Mesh coarsening, i. e. a reduction of the number of panels,
is used thereby avoiding or reducing the extensive topological
analysis as well as making the algorithm numerically more robust.

An edge collapse approach collapses an edge to a single point leading
to an area of zero for the triangular elements connected and thereby
eliminating them. The single point is selected so that
boundaries and knuckles are preserved.

Edges to collapse are selected by the following geometric quality

  • All triangular elements should be as equilateral as possible.
  • The area ratio of neighboring panels should be close to unity.
  • The area of the panels should be inverse proportional to the
    curvature of the surface.
  • A user defined definition of a source-sink distribution allows for
    local modifications of the element size.

Mesh coarsening is stopped if either a given minimum number of
elements is reached or the mean or minimum quality criteria reaches a
certain level.


Using the simple geometric properties mentioned above a homogeneous
mesh is obtained. User defined source distribution allows for control
of the element distribution and size making work in-extensive adaption
of the mesh structure to computational requirements not captured by
the geometric criteria possible. In the next figure two example meshes for
the test case DTMB 5415 are shown. It can be seen that the complex
geometry of the bow section is meshed properly; the knuckles in the
afterbody are not impaired.



A new approach to mesh generation for use in the field of wave
resistance calculation has been presented. A significant reduction in
time needed for mesh preparation as well as a reliably detection of
geometric inconsistencies like knuckles and borders have been

Further research is needed for tests clarifying whether the use of
geometric quality criteria not only leads to visually attractive but
also to meshes for highly accurate predictions.


  • G. Knieling,
    Entwicklung eines Panelgenerierungsverfahrens fuer eine
    Wellenwiderstandsberechnung von Schiffen,
    Master’s thesis, Universitaet Rostock, 2002.
  • B. Cheng and C. Plaue,
    Subdivision schemes for surfaces,
    Technical report, Georgia Institute for Technology, 2002,
  • T. Dey and S. Goswami.
    Tight cocone: a water tight surface reconstructor.
    Technical report, The Ohio State University, 2002.
  • R. Klein,
    Latest advances in multiresolution surface modeling and
    applications to visualization, reconstruction and simulation,
    Technical report, Universitaet Tuebingen, 1998.