Controlling Fluid Simulations with Custom Fields in Houdini Master ...

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And (1) is called the momentum equation and tells us how the uid acceleratesdue to the forces acting on it and can be derived from Newton's equation−→ F = m−→ a as explained in [4]. And (2) is the incompressibility condition andstates that the divergence of the velocity must always be equal to zero. Thisconstraint ensures that the sum of all velocities entering and leaving at a pointin space is zero. When this is conserved, the total mass is conserved over theentire simulation [18].4.3.2 The steps to solve the Navier Stokes equationsThree main steps will be required to solve the Navier Stokes equations, thesesteps are very well described in [18] but will be included here again for completenessand some of the explanations of the terms summarized.1. Advection2. Diusion and External forces (Body forces)3. pressure/incompressibilityAdvection( −→ u · ∇) −→ uAdvection represents the fact that the motion of the uid causes motionof the entities within it. This can be thought of as the velocity of the uidmoving itself along, and is sometimes referred to as self-advection because ofthat property. The advection part of the equations can also be used to modelmotion of other entities inside the uid [18].Within Houdini the Gas Advect microsolver can be used for advecting one orseveral elds at the same time. For more advanced interactions between elds,other actions can be performed at this step that will update the elds. This canbe seen in the node tree for the elds_updates section inside the preset smokesolver in Figure (7). For instance:• A Gas Blur is used to diuse the temperature eld,• A Gas Calculate is used to cool the temperature eld or to copy informationfrom a source eld into a heat eld.• Fields are not the only thing that can be advected, geometry can as well,such as vorticle geometry which is explained in the external forces step.Diusion and External forces12
Figure 7: The node tree for the update elds section in the preset smoke solverin Houdini as described in (4.3.2)13
Page 1 and 2: Controlling Fluid Simulations with
Page 3 and 4: 1 AbstractThere are various dierent
Page 5 and 6: Figure 2: High resolution 2d uid co
Page 7 and 8: Figure 5: The node based operator g
Page 9 and 10: sets, which means they are built fr
Page 11: • as an axis aligned plane that s
Page 15 and 16: Figure 8: The node tree showing the
Page 17 and 18: Figure 9: The node tree in Houdini
Page 19 and 20: 4.4 Up Res techniqueIn Houdini 10 a
Page 21 and 22: • The nal option is with a Gas Fi
Page 23 and 24: Figure 12: Premultiplication proble
Page 25 and 26: Figure 14: The preset smoke solver
Page 27 and 28: Figure 16: A helix curve emitting d
Page 29 and 30: Figure 19: A few stages of the adve
Page 31 and 32: Figure 21: Top: The stages of the a
Page 33 and 34: and pyrosolver work took time. This
Page 35: [10] Christopher Horvath and Willi

Controlling Fluid Simulations with Custom Fields in Houdini Master ...

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