MOSES Automated Mesh Refinement

Mesh quality is important because hydrodynamic results quality is dependent on the mesh quality. The automated mesh refinement feature subdivides the panel model for use as the hydrodynamic mesh. It is customary for several mesh densities to be evaluated as part of the hydrodynamic database assessment.  The ability to automatically refine a mesh is intended to allow the user to input a coarse mesh and easily produce refined mesh models.

Hydrodynamic Calculation Results and Mesh Quality

Evaluation of the hydrodynamic database is made as part of normal motions analysis procedures.  The common checks on the hydrodynamic results are an evaluation of the added mass matrix, the damping matrix, and the wave drift values. These three calculations are dependent on velocity potentials which are in turn dependent on mesh quality.  In addition, wave drift values are also dependent on the velocity gradients. 

Velocity potentials are calculated at the centroids of panels.  A good-quality mesh will have velocity potentials at evenly spaced intervals.  Velocity potentials reported at evenly spaced intervals will, in general, have potential velocity gradients that change smoothly.

Poor-quality meshes have panel centroids at varying distances. Large and sudden changes in panel geometry or panels with high aspect ratios are usually referred to as a poor-quality mesh. In a poor-quality mesh, the large variation in velocity potential between neighboring panels translates into quite significant gradients in the velocity potential and thus forms ill-conditioned matrices.  A poor-quality mesh can be evident in the added mass, damping matrix and wave drift force results.  There are exceptions to the rule, but in general added mass and damping values should be positive.  Poor-quality meshes can result in negative added mass and damping values. Meshes where panels are not evenly spaced and abrupt changes along the length of the vessel can have significant velocity potential gradients resulting in very large drift forces.

A different variety of poor-quality meshes can have panel centroids that are too dense.  In these meshes, the velocity gradient between panels is near zero.  Thus, also leading to problems with the velocity gradient and the wave drift results.

The two geometric shapes used in MOSES for panels are rectangles and triangles.  The geometric shape of the panel has a very little effect on the calculations, including second order force calculations. What matters to the computation is:

• the aspect ratio
• the normal vector and
• proximity to other panel vertices

Refinement Procedure used by MOSES

The mesh refinement feature in MOSES takes a user-defined coarse mesh and subdivides the panels automatically.  The intent of the feature is to give the user control of the mesh density. The resulting mesh can have both triangular and rectangular geometry panel shapes.  In MOSES, users can control the mesh density via the “&parameter -m_distance” command.  This command sets the maximum length of any one side of a panel.  The value set with the “&parameter -m_distance” command will be referred to as the “user length setting.”

The subdivision of the panels is done according to the logic enumerated below.  MOSES reviews each panel defined and systematically takes the following approach. 

1. Clip the panel if it is cut by the free surface.
2. Eliminate any vertices that exist on straight lines; they are surplus.
3. If the number of vertices is three, refine the panel into more triangles if needed to satisfy the user length setting.
4. If the number of vertices is four, MOSES checks to see if they are co-planar. If the vertices are not co-planar, MOSES will subdivide the panel into triangles.  The resulting size of triangles is dependent on the user length setting.
5. If the number of vertices is four and the vertices are co-planar, MOSES will refine the panel into smaller quadrilaterals to satisfy the user length setting.
6. If the number of vertices is greater than four, repeatedly refine the panel until it consists of triangles and satisfies the user length setting.
7. When the refined panels meet the user length setting, names are given to the subpanels, and it is stored in the database.

The default value MOSES is shipped with is 1e10 ft (3.048e9 meters).  For most models the default setting results in only panels that are not co-planar being changed. 

Suggested Practice for Mesh Evaluation

It is customary for several mesh densities to be evaluated as part of the hydrodynamic results assessment.  Offshore vessels vary in length, breadth, and shape. There is not one mesh size the can be recommended for all vessels.  Hydrodynamic results database is only one part of the complete motions analysis project.  Confidence in the hydrodynamic results will result in confidence in the other parts of the motions analysis project.  The approach we recommend for mesh evaluation is:

1. Start with a vessel that is good for hydrostatic computations and compute the results.
2. Review the added mass and damping matrices. 

1. 1. If there are negatives reported there should be an engineering reason.  -Call those results “A.”
   2. If there are negatives without an engineering reason, then the mesh needs to be refined.  Refine and restart the evaluation process.
   3. If all values are positive, the values can be considered for further evaluation. 

       -Call those results “A.”

1. Refine the mesh a second time and compute new results.  -Call those results “B.”
2. Compare the added mass, damping matrix results between “A” and “B.”  Plotting the added mass and damping vs. period should tend to merge within some reasonable tolerance following the same profile. 
3. Review the wave drift values; they should not be extremely large.
4. If the results between “A” and “B” stay pretty much the same, then you have converged on the mesh size.
5. If the results between “A” and “B” change, then the mesh needs to change.

The above steps include a review of the added mass and damping matrix.  Please contact the MOSES team for a sample file on how to report the added mass and damping matrices.

In the above procedure, the mesh density is changed until the hydrodynamic results are independent of the density.  Hydrodynamic results that are sensitive to the mesh density are an indication of a poor-quality mesh, and; additional time should be invested in the mesh quality. Keep in mind that too fine of a mesh can also cause results to diverge.

Suggested Practice for Modeling

In summary, you need a good panel model. Here are some scenarios that should be avoided and good working practices:

• Step 1 in the refinement procedure, clip the panel if it is cut by the free surface, can frequently be the cause of a poor-quality mesh. If the panel near the waterline already has a high aspect ratio, clipping the panel at the free surface will only worsen the situation.  It is a good idea to have panels with low aspect ratios near the waterline. An example of a panel with a high aspect ratio near the water line is shown in Figure 1 below.

• Slender panels – centroids of neighboring panels are very close in one direction and very far apart in the other direction. This can result in large gradients.
• Variable mesh – Changing suddenly from small panel size to large panel size can also have a detrimental effect on potential gradients.
• Sharp geometry changes, such as re-entry corners can cause the panel centroids to be unevenly spaced.  This can result in problems with the gradients.
• Remember that iterative solutions with various mesh densities need to be within practical limits of CPU time and available hardware.

Figure 1 High aspect ratio at the waterline