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Variable density and viscosity

Hello Users,

I am trying to model a 1D steady state gravity driven stokes flow in FLUENT. I start with a 2D geometry, where x is the direction of the flow and parameters (density and viscosity) are a function of y specified in DEFINE_PROPERTY UDF. Acceleration is applied in x direction. I have few questions about specifying physics and other parameters.

Material parameters: Density and Viscosity defined spatially varying with y only from UDF. Speed of sound not specified.

X boundaries (2D faces with normal in x dir) are made periodic since I do not want any end effects etc. Lover and upper boundaries are no-slip walls.

Solver details: No energy or viscous turned on. For flow equations, SIMPLE is used with pressure discretization as Body force weighted, Continuity and Momentum are 2nd order.

Typical order of parameters used (in SI units):
Density: MIN: 1e-10 MAX: 2000
Viscosity: MIN: 1.5e-5 MAX: 9.5e-4 AVG: 2.3e-4
Gravity in X: 1e+12
domain dimensions: 4e-9 m to 6e-9 m.

The above numbers correspond to a nano scale channel, hence there is some variation in density and viscosity spatially.

Problem with convergence are observed. The continuity residual diverges. Tried playing with some relaxation parameters but it doesn't help much. I would like to understand what am I doing incorrectly. Also, apart from playing with the source term in momentum equations, is there anything I can do to explicitly specify the equation I am going to solve (for example how to drop the intertia term completely). Please let me know your suggestions.

Sincerely,