To render your simulation with Motion Blur, you need to enable Velocity channel export from the Output rollout of your simulator.
When rendering liquids, the Motion blur of the mesh is obtained by shifting each vertex along the velocity by the shutter time. If rendering a Liquid simulation with secondary particle effects such as Foam, Splashes or Mist, you would also have to enable Velocity export for each particle system under the Output rollout → Output Particles section.
Multiplier | mbmult – Specifies a multiplier that affects the strength of the motion blur. This value can be a negative number.
Prevent Self Intersection | mbself – In all Mesh modes, some motion blurred vertices might penetrate the opposite side of the geometry. When enabled, this option prevents such situations. The self-intersection analysis is expensive, so enable this parameter only when an intersection is obvious.
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Phoenix meshes are motion blurred in a different way than regular transforming and deforming geometries. When rendering regular meshes with motion blur, the entire mesh is moved along its transformation path back and forward in time, and so each individual vertex of the mesh follows this path. However, for each rendered frame, a new Phoenix mesh must be built from the voxel grid, and so it usually has a different number of vertices than the previous and the next frame. Because of this, individual vertices can not be traced back or forward in time between frames. Instead, motion blur of fluid meshes uses the velocity of vertices which is recorded by the simulation, and moves each vertex back and forward in time along the vertex velocity. This is why the generated liquid mesh does not support frame sub-sampling for motion blur. This may cause a mismatch between the liquid and transforming/deforming objects in your scene that interact with it. The fluid mesh is generated from data at the exact rendered frame and fluid data for the preceding or following frames is not used, unlike regular deforming meshes. As a consequence, the liquid and the objects in your scene would synchronize best if those objects do not use additional geometry samples for motion blur.
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The Grid Channel Smoothing controls allow you to smooth the Grid Channels loaded from cache files for preview and rendering.
You can smooth the Velocity Grid Channel stored in the simulated caches in case the motion blurred edges are looking jagged.
The recommended values for the smoothest result are all zeroes for the Threshold, Similarity and Random Variation options - this will produce strongest smoothing, evenly applied over the entire Grid, without adding any random variation.