Introduction

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 alternatives.

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.

Objective

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

Overview

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

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 achieved.

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 shown.

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.

Merging

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 development.

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 criteria:

• 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.

Results

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.

Conclusion

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 achieved.

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.

Bibliography

• 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.