*********************** **Fickian Diffusivity** *********************** :: Fickian Diffusivity = {model_name} {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. | | | | | | * - an integer designating the species equation. | | | * - the value of the diffusivity for the X direction, Dx. | | | * - the value of the diffusivity for the Y direction, Dy. | | | * - the value of the diffusivity for the Z direction, Dz. | +----------------------+-------------------------------------------------------------------------------------+ |**EXP_DECAY** |an exponential decay of flux. | | | | | | * - an integer designating the species equation. | | | * - the coefficient to the exponential decay, Do | | | * - 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., .. figure:: /figures/450_goma_physics.png :align: center :width: 90% If the exponential decay option is used, the flux vector has the form, .. figure:: /figures/451_goma_physics.png :align: center :width: 90% where C and Cmax are volume fractions of suspension locally and at maximum packing. -------------- **References** -------------- No References.