NeuralFlowTheory & User Reference Manual
Coordinate Systems, Body Forces and Rotating Reference Frames
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Coordinate Systems, Body Forces and Rotating Reference Frames

Formulation convention. Rotating zones use an absolute-velocity formulation. The transported velocity is the absolute velocity; grid-relative velocity is introduced only where transport crosses a moving/rotating face.

Planar and axisymmetric coordinates

NeuralFlow supports planar and two-dimensional axisymmetric problem definitions. In an axisymmetric problem, the second coordinate represents radius and finite-volume geometric measures are radius weighted. Axis faces are treated specially, and axisymmetric turbulence/strain expressions add the required radial contributions such as in the model-specific source evaluation rather than hiding them in the planar gradient tensor.

Rotating-zone grid velocity

For a rotating cell zone with angular-velocity vector and center , the face grid velocity is

The relative transport velocity used in moving-face convection is

Thus mass convection is grid relative while momentum and energy remain expressed with the absolute state.

The face-normal relative speed is

so a generic convective mass flux has the grid-relative form

Absolute-energy moving-face flux

For the compressible AUSM carrier path, the absolute total-energy flux has the formulation form

The second term is the moving-face pressure work required by the absolute-energy formulation. The artificial-compressibility face operator follows the same grid-relative transport principle.

Rotating-zone momentum source

The current absolute-velocity rotating-zone assembly adds the volumetric momentum term

Its cell contribution is assembled with the solver residual sign convention and differentiated consistently into the local block. No separate rotational total-energy volume source is added because ; moving-face pressure work is carried by the face energy flux.

The skew-symmetric cross-product operator satisfies

Its kinetic-energy contribution vanishes identically,

Gravity

When gravity is enabled, carrier momentum receives

The dilute dispersed phase receives the corresponding momentum term. In the constant-density artificial-compressibility carrier formulation, body-force work is included in the transported energy row. In the current compressible carrier formulation, gravity contributes to momentum without an additional gravity-power term in total energy. For compressible flows in which gravitational potential-energy exchange is important, include this distinction in the energy-balance qualification.

For a compressible total-energy equation, the corresponding gravitational work is

Rotating walls

A no-slip wall attached to a rotating zone uses the absolute wall velocity

so the wall-relative velocity vanishes. A wall in a stationary zone uses its prescribed absolute wall velocity.

Current compatibility limits