Scanline VFX has created some amazing computer generated water effects with their proprietary Flowline fluid simulation software. Their website has some great videos demonstrating what they have done.
You can create similar effects with the free open-source software Blender. Of all the physical phenomena you can simulate with Blender, fluid dynamics is the easiest.
Here are the greatly simplified steps:
1. Create a starting shape for initial state the liquid will be in. In my short video I started with a sphere.
2. Create a shape to contain the water. I used a cube that was slightly larger than the sphere.
3. Tell Blender how many frames of animation to create.
4. Tell Blender to “bake” and Blender goes to work cranking out your animation.
By default the only force acting on your fluid is gravity. You can increase the complexity by adding inflows, outflows, obstacles, etc.