# Houdini Micro Solvers 2

In fallowing example gas analyses micro solver is used in order to calculate curl and curvature fields for more detailed fluid shape. 1. importing points to sim.
3. normal curl and curvature fields are matched with reference “vel” field.
4. gasParticletoField, particle normals transfered to field with “normal” name.
5. gasAnalysis:  curl analyses has been applied on normal field , output is curl
6. gasAnalysis2: curvature analyses has been applie to curl field , output is curvature
7. gasFieldVop: inside vop, curl and curvature fields added to velocity field. Gas Analysis The Gas Analysis DOP computes various analytic properties of the input field to produce the output field.

• Curvature is the amount by which a geometric object such as a surface deviates from being a flat plane.
• Curl(rot)  outputs a vector that lies in the axis of rotation of the field and has magnitude proportional to the field’s rotation speed at that point.The direction of the curl is the axis of rotation. If the vector field represents the flow velocity of a moving  fluid , then the curl is the circulation density of the fluid.
• Gradient  can be used to measure how a scalar field changes in other directions. The magnitude of the gradient will determine how fast specified field will move in that direction. For example, if temperature rises faster over a shorter distance, it will create a bigger gradient.
• Laplace’s equation in fluid dynamics describes the behavior of gravitational and fluid potentials.
• Divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. As an example, consider air as it is heated or cooled. The velocity of the air at each point defines a vector field. While air is heated in a region, it expands in all directions, and thus the velocity field points outward from that region. The divergence of the velocity field in that region would thus have a positive value. While the air is cooled and thus contracting, the divergence of the velocity has a negative value.
• Normalize  destination is set to the source after normalizing the length of the source vector.
• Length the scalar field is set to the length of the vector field at each location. The length is calculated by measuring the slope of increasing values

Gas Match Field  The Gas Match Field DOP creates, resizes, and resamples as necessary to ensure the data matching the given name exists as a field of the same resolution and size as the reference field. In this example this node is used to match “curl”,”normal” and “curvature” fields  with “vel” field.

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