SmoothingLength

In MESHFREE, the smoothing length is the parameter for the spatial discretization in MESHFREE. For each point within the pointcloud it defines the radius of point interaction.

All points within a radius of the local smoothing length around a point are called neighbors of the point. The stencils for setting up the discretization are based on these neighbor relations.

Based on the definition of the smoothing length MESHFREE will automatically fill the simulation domain with a pointcloud corresponding to the choice of the smoothing length.

Choosing smaller smoothing length yields finer discretizations. The smoothing length should locally be at maximum a little smaller than the size of the effect that should be resolved - let it be a thin geometry part or a boundary layer.

Strategies for defining the smoothing length

MESHFREE offers different strategies for specifying the discretization - steered by the compulsory parameter USER_h_funct.

Constant smoothing length

CONS: Constant smoothing length provides a constant discretization in the simulation domain. It is specified by A constant coarse smoothing length is the preferred mode for the first setup.

Discrete smoothing length

DSCR: variable smoothing length allows user defined refinements on location and physical quantities. Good to know:

• For example, this is useful if you want to refine locally around thin geometry parts. (see SMOOTH_LENGTH)
• If a small smoothing length is attached to a large geometry part, many reference points for the determination of the smoothing length are created on the geometry. If there are too many, then the computation becomes inefficient and will abort if this upper bound is met.

Adaptive smoothing length

ADTV: There are also automatic approaches to adapt the smoothing length to the transient simulation. The idea is to see the smoothing length as function on the pointcloud. The user can assign values to Y%ind_h_adaptive% and the pointcloud is organized with respect to this proposal of the smoothing length, see ADTV for a more detailed description

Adaptive plus discrete smoothing length

ADDS allows for combining the two previous approaches:

Miscellaneous

Checking the smoothing length

The local smoothing length on the pointcloud can be visualized by saving the index Y%ind_h% :

Quality of the smoothing length function

A transition from a fine to a coarse smoothing length should always be smooth and not abrupt - otherwise small effects due to approximation or discretization can build up and lead to instabilities.