1.Non Newtonian Fluids  viscosity does not depend on on the stress state and velocity of the flow. On the other hand the viscosity of non-Newtonian fluids is dependent on shear rate or shear rate history.

In Shear thickening non-Newtonian fluid, apparent viscosity increases with increased stress. Such as,

Application in Houdini,  In example below, increased pressure make fluid more viscose after  a certain pressure threshold. Red color represents viscosity, blue color velocity.

1. import fluid source with viscosity attribute.
2. import collisions
3. gasMatchField for creating “pressureNormalised” attr. This attribute will take pressure field, manipulates with control attributes and transfer to viscosity attribute.
4. gasFieldVop,
5. import pressure field
6. ramp it for enabling threshold(very low pressures does not affect viscosity)
7. viscosity multiplier parameter
8. multiplication pressure with viscosity multiplier variable
9. viscosity min parameter for making min viscosity level even in low pressure
10. add operant
11. output pressureNormalised attr
12. gasFieldToParticle for setting particle viscosity attr by pressureNormalised

2.Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. 

Application in Houdini. System below  is based on Yancy Lindquist‘s tutorial about elasticity. In order to have elasticity effect, measure of the distortion that the fluid in the voxel has undergone(straint) is used.

1. strain field is created
2. prevStrain field is created
3. particles strain attributes is transfered to prev strain field
4. in gasCalculate microsolver previousStrain field is copied to strain field
5. gas strain integrate microsolver
6. gas strain forces microsolver
7. gas calculate microsolver for difference between strain and previous strain
8. strain field is send back to particles

Control of Elasticity can be achieved by Elasticitic modulus (in gasstrainforces microsolver),  alpha and gamma (in gasstrainintegrate microsolver.)

Elastic Modulus  provides the scale factor for how to translate a certain amount of distortion into a restorative force.  A larger value will cause the fluid to spring back faster. 

Alpha This is the rate of plastic flow. The current strain is dissipated at this rate per second.

Gamma  threshold for plastic flow. When the norm of the strain exceeds gamma, the strain is dissipated according to the alpha term. This causes the fluid to lose its history and permanently enter its new configuration.

References

https://en.wikipedia.org/wiki/Non-Newtonian_fluid
https://en.wikipedia.org/wiki/Viscoelasticity
https://cmivfx.com/products/344-houdini-frictional-viscosities

1 Bullet Altering Attributes In fallowing example deforming and in-active bullet object is transformed non-deforming active object. It is done by transferring second objects attributes (box) to bullet object in sopsolver inside dop.

• 3)object merge, merges animated box with attributes of active=1 deforming=0
• 4)attribute transfer for point attributes of active and deforming

 

2 Bullet Constraint Network In fallowing example cone twist constraint is atached pieces together until a certain angle threshold. Constraints above this threshold is removed, hence object is shattered.

 

1. sopLevel> seperated geometry’s each primative is named by assable node.
2. connect adjasent pieces sop for creating connections between primatives that will be used as cone constraint
3. attrCreate sop for creating @angleThreshold float for setting angle limit, @constraint_type string “all” for osition and rotation constraint, @constraintname string “cone”
4. assemble sop for converting packed object.
5. constraint network dop with sop path of constraints (OUT_cons).
6. coneTwitConstraint dop with data name of “cone”.
7. sop solver for removing constraints.
8. relationship geometry for importing constraints
9. delete if an angle between two piece is greater than angle threshold

 

 

 

 

 

 

 

 

1A. Cloth – Pyro Interaction 
On default, pyro interacts withj cloth(if pyro solver connected first to merge node). However in this method,  pyro  do not colide but just affect as field force(left example) . In order to have proper colision, cloth obj should be imported with sop solver as colision source. (right example)

1. importing velocity and density from source
2. cloth simulation is imported with sop solver .
3. Inside sopSolver: dop import  impors cloth object from curent dop network
4. Inside sopSolver: imported cloth object converted to colision volume
5. Source volume dop, imports cloth colision sdf

2A. RBD – Pyro Interaction 
In this example collision is introduced to sim by fluid source node in sop level. Density field is pushed by velocity of collision and all voxels inside colision is set to zero. On left version collision does not have any velocity hence density can not be pushed out but eaten by  collision. On right one colision is introduced to sim by static solver wich seems slightly faster to calculate.

1. velocity calculated for collision object via trail sop
2. sdf from geometry is built and velocity added by fluid source sop. From container settings”collision” is selected.
3. density and temperature introduce for source object by source volume dop.
4. collision is introduced by source volume dop.

2B. RBD – Pyro Mutual Relationship  In this one, two way  interaction between pyro and rbd is achieved by field force. In this method, force applied to rbd objects by generated by pyro solver. Colision is enabled by first connecting rbd than pyro solvers.

1. import ground static object
2. import rbd fractured objects
3. field force for importing velocity. This node is fed by fetch data for importing vel from pyro object
4. surcing fluid density and velocity

INDEX

• 1A. Cloth – Pyro Interaction
• 2A. RBD – Pyro Interaction
• 2B. RBD – Pyro Mutual Relationship

This post will continue with fallowing matrix (“pending”ones);

Top row represents effectors, leftcolumn represents affected ones. If both condition met simulation can be mutually interacted one.

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.
2. particles advected by velocity.
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.

More information about gasAnalysis microSolver, Little bit houdini help and little bit wikipedia;

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.

References:

• https://en.wikipedia.org/wiki/Gradient
• https://en.wikipedia.org/wiki/Curl_(mathematics)
• https://en.wikipedia.org/wiki/Curvature
• https://en.wikipedia.org/wiki/Laplace%27s_equation

Micro Solvers are building blocks in Houdini simulation. Mostly they are doing one task in a clean way. SideFx’ fluid solvers from scratch tutorial and  Pater  Claes’ master theses about custom fields helps a lot for learning however there are tons of them and started to a bit confusing. Hence I make little list of these nodes with some examples attasched. It is first part and I am planning to prepare 3 parts in total.

Preparation 

Lets start with multi solver as we will apply many micro solvers  fin each time step . It has two inputs,  objects(left)  solvers(right). Objects to be procesed will be as fallows:

1.EmpityObject : is a container which can have various types of data attached to it.

2.The Scalar Field DOP creates a Scalar Field data that can be attached to simulation objects and manipulated by solvers. Scalar data can be density, temperature or any  floating point number. Scalar field Visualisation is attached to this node for field visualisation.

3.The Vector Field DOP creates a Vector Field data that can be attached to simulation objects and manipulated by solvers. Same as previous one except in this node each voxel is giving a 3d vector instead float. For visualising field vectorFieldVisualization node is used.

4.Sop Geo for importing external objects in to simulation. In our case it will be particles.

5.Sop Solver to feed simulation with density in each frame. Inside this solver, density source is imported and merged with, dop geometry.

MicroSolvers

GasAdvect & GasAdvectField  Evolves fields and geometry according to a specified velocity field. The fields and geometry will be moved by the velocity field for a distance proportional to the current solver timestep. In example below  velocity drives density and particles. Velocity field needs to advect itself also, othervise velocity grid will be static(will not change through simulation).

Gas Linear Combination Combines multiple fields or geometry attributes together. In example masked force field (another sopVectorField) and velocity field added to velocity itself.

gasDisturbField Introduces small amounts of change in momentum which cancels itself out over time, preserving the simulation’s general motion. In example  velocity is disturbed according to density field

gasTurbulance Creates and applies a global turbulence field to the specified velocity field. This turbulent velocity field is modulated by the Control Field and lookup ramps provided.

gasDissipate  Performs dissipation on the specified field. This will drive the fields value to zero. An optional control field can be used to affect when the dissipation occurs.In mid Example gas dissipation is enabled by evaporation , each timestep subtraction applied to density field. In right example min clamp applied

Gas Damp The Gas Damp DOP scales the velocity field by a number between 0 and 1, thereby slowing down the motion in the simulation.

Gas Blur The Gas Blur DOP blurs fields using an optionally time dependent blur kernel. In Example density field is blurred by gaussian with radius of 0,2.

Gas BuoyancyCalculates an approximate buoyancy force dependent on the temperature field and updates a velocity field according to that force. In example gas buoyancy is driven by temperature.  While left one’s temperature is static, right one’s temperature is advected by velocity hence buoyancy force is diffused through time.

Buoyancy force = ((l * (T-Ta)) * B
Ta = Given an ambient temperature 
T= Temperature T
l = Buoyancy lift  
B = buoyancy direction

Gas Vortex Boost Applies confinement to a specific band of energy captured from the velocity field. Confinement force is applied for undoing the diffusion by amplifying existing vortices

Gas Particle to Field The Gas Particle to Field DOP copies a point attribute value from a particle system into a field. In example below, Normal attribute of points added to velocity field. “Accumulated” checkbox enables to replace or add to existing field.

Gas Field to Particle calculates the field value for each particle in the geometry. The resulting field values is then mixed with the particle’s attribute value to get the new attribute value. In example below particles stores density and velocityfield of simulation. As post solution process, low dens particles are removed and color given based on velocity.

 

Color Diffusion  In fallowing example, color  is imported as vector field to simulation and diffused togather.

1  sopScalar field for density import
2  sopVector field for velocity import
3  sopVector field for color import
4  gas resize
5  sopSolver for merging source color field for first 15 frames
6  sopSolver for merging source density field for first 15 frames
7  gas diffuse
8  gas blur
9  gas turbulance
10 gas advect nodes for velocity advect color density and itself

References

SideFx’ fluid solvers from scratch tutorial

Pater  Claes’ master theses about custom fields