The Navier-Stokes equations formulated in a rotating coordinate system read (Ref. 1 and Ref. 2)

where v is the velocity vector in the rotating coordinate system, r is the position vector, and Ω is the angular velocity vector. The relation between v and the velocity vector in the stationary coordinate system is

The Rotating Machinery, Fluid Flow interfaces solve Equation 3-143 and Equation 3-144, but reformulated in terms of a non-rotating coordinate system; that is, they solve for u. This is achieved by invoking the Arbitrary Lagrangian-Eulerian Formulation (ALE) machinery. In rotating domains, x = x(Ω, t) as prescribed in the Rotating Domain features. The Navier-Stokes equations on rotating domains then read

The derivative operator is the mesh time derivative of the density and appears in the equation view as d(rmspf.rho,TIME). Analogously, is the mesh time derivative of the velocity. The variable TIME replaces t as the variable for time.

The user input for a rotating domain prescribes the angular frequency, w. To calculate Ω, the physics interfaces set up an ODE variable for the angular displacement ω. The equation for ω is

Ω, is defined as w times the normalized axis of rotation. In 2D, the axis of rotation is the z direction while it in 3D is specified in the Rotating Domain features. If the model contains several rotating domains, each domain has its own angular displacement ODE variable.

Boundary conditions in the rotating parts must be specified correctly. For example, walls that rotate must be prescribed as rotating walls. Walls in rotating domains can also be prescribed as non-rotating, but in that case, , where n is the wall normal, must be tangential to the wall.