Fickian Diffusivity

Fickian Diffusivity = {model_name} <species> {float_list}

Description / Usage

This card allows the user to select a Fickian diffusion mode when the model in the Diffusivity card is HYDRO. There are two {model_name} options for this mode; definitions of the input parameters are as follows:

ANISOTROPIC	an anisotropic Fickian diffusion. <species> - an integer designating the species equation. <float1> - the value of the diffusivity for the X direction, Dx. <float2> - the value of the diffusivity for the Y direction, Dy. <float3> - the value of the diffusivity for the Z direction, Dz.
EXP_DECAY	an exponential decay of flux. <species> - an integer designating the species equation. <float1> - the coefficient to the exponential decay, Do <float2> - the exponent value for exponential decay, D1

Examples

Following are two sample cards:

Fickian Diffusivity = ANISOTROPIC 0 2.e-6 2.e-6 0.

Fickian Diffusivity = EXP_DECAY 0 0.01 1.e-3

Technical Discussion

In modeling suspension flow, often a sharp concentration gradient is encountered, and the numerical convergence becomes very poor. This card should be used for numerical stability (smooth out the wiggles) and should only be introduced as a last resort. The magnitudes should remain small relative to shear rate and viscosity diffusivities.

As the name implied, anisotropic Fickian diffusivity defines an additional flux contribution much like a classic Fickian diffusion term; i.e.,

If the exponential decay option is used, the flux vector has the form,

where C and Cmax are volume fractions of suspension locally and at maximum packing.

References

No References.