Loading docs/source_docs/user_guide/inputs/solids_model.rst +84 −1 Original line number Diff line number Diff line Loading @@ -230,4 +230,87 @@ when the particle density is much less than the fluid (such as bubbles). PIC model settings ------------------ .. todo:: Add PIC inputs The following inputs define the PIC solids model and its associated frictional stress parameters: .. math:: \tau_p = \frac{P_s \varepsilon_p^{\beta}}{\max \left[ (\varepsilon_{cp} - \varepsilon_p), \epsilon (1-\varepsilon_p)\right]} The following inputs are defined with the prefix ``pic``: +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | | Description | Type | Default | +====================================+=========================================================================+==========+===========+ | solve | Specified name(s) of the PIC types or None to disable the PIC solver. | Strings | "None" | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | close_pack | Solids volume fraction at close pack, :math:`\varepsilon_{cp}`. | Real | 0.55 | | | Below this threshold, the solid stress tensor has minimal impact. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | pressure_coefficient | Pressure linear scale factor in frictional stress model, :math:`P_s`. | Real | 100.0 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | beta | Volume fraction exponential scale factor in frictional stress model, | Real | 3.0 | | | :math:`\beta`. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | small_number | Non-singularity term in frictional stress model, :math:`\epsilon`. | Real | 1.0e-7 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor | An empirical dampening factor for the frictional stress model. | Real | 0.4 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor_wall_normal | Normal coefficient of restitution for parcel-wall collisions. | Real | 0.3 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor_wall_tangent | Tangential coefficient of restitution for parcel-wall collisions. | Real | 0.99 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | parcels_per_cell_at_pack | Specifies the number of particles that can occupy a regular | Real | 32.0 | | | computational cell near close packing. | | | | | | | | | | Larger values reduce sensitivity to small changes in parcel positions, | | | | | which helps stabilize the computed solids volume fraction and, by | | | | | extension, the frictional stress model. However, increasing this value | | | | | also results in simulations tracking a greater number of parcels. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | verbose | Verbosity level for PIC-related output. | Int | 0 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ The solids volume fraction is required to evaluate the frictional stress model when advancing parcels from :math:`t^n` to :math:`t^{n+1}`. Ideally, this evaluation would use either the volume fraction at the midpoint of the time step, :math:`\varepsilon_p^{n+1/2}`, or at the end of the step, :math:`\varepsilon_p^{n+1}`. However, since neither of these values is available a priori, an iterative approach is used. An initial approximation of the volume fraction is used to advance parcels to a tentative position at :math:`t^{n+1}`. These new positions are then used to compute an updated volume fraction field, which is subsequently used in the next iteration to recompute the tentative parcel positions. The following keywords control the iterative PIC algorithm and are defined with the prefix ``pic``: +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | | Description | Type | Default | +====================================+=========================================================================+==========+===========+ | initial_step_type | Specifies the initial solids volume fraction used in PIC iterations to | String | "nth_eps" | | | approximate the volume fraction at the end of the time step, | | | | | :math:t^{n+1}. | | | | | | | | | | Options (case-insensitive): | | | | | | | | | | * ``nth_eps`` - use the volume fraction from the previous time step, | | | | | :math:`t^{n}` | | | | | * ``zero_eps`` - set the initial volume fraction to zero | | | | | * ``taylor_approx`` - use a Taylor series expansion about parcel | | | | | positions to approximate the volume fraction at :math:`t^{n+1}` | | | | | | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | max_iter | Maximum number of iterations used to approximate the end state | Int | 3 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | advance_vel_p | Specifies the weighting factor used to compute the averaged particle | Real | 0.5 | | | velocity field during parcel advancement. The field-averaged velocity | | | | | is used when applying forces to parcels. | | | | | | | | | | This parameter takes values between 0 and 1, blending the particle | | | | | velocity at the beginning and end of the time step. A value of ``0.5`` | | | | | (default) yields a time-centered average. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | velocity_reference_frame | The velocity reference frame scales the field-averaged velocity | Real | 0.5 | | | used to compute the slip velocity between a parcel and the bulk when | | | | | when the parcels is moving towards an area of higher solids | | | | | concentration. This parameter takes values between 0 and 1. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ Loading
docs/source_docs/user_guide/inputs/solids_model.rst +84 −1 Original line number Diff line number Diff line Loading @@ -230,4 +230,87 @@ when the particle density is much less than the fluid (such as bubbles). PIC model settings ------------------ .. todo:: Add PIC inputs The following inputs define the PIC solids model and its associated frictional stress parameters: .. math:: \tau_p = \frac{P_s \varepsilon_p^{\beta}}{\max \left[ (\varepsilon_{cp} - \varepsilon_p), \epsilon (1-\varepsilon_p)\right]} The following inputs are defined with the prefix ``pic``: +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | | Description | Type | Default | +====================================+=========================================================================+==========+===========+ | solve | Specified name(s) of the PIC types or None to disable the PIC solver. | Strings | "None" | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | close_pack | Solids volume fraction at close pack, :math:`\varepsilon_{cp}`. | Real | 0.55 | | | Below this threshold, the solid stress tensor has minimal impact. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | pressure_coefficient | Pressure linear scale factor in frictional stress model, :math:`P_s`. | Real | 100.0 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | beta | Volume fraction exponential scale factor in frictional stress model, | Real | 3.0 | | | :math:`\beta`. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | small_number | Non-singularity term in frictional stress model, :math:`\epsilon`. | Real | 1.0e-7 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor | An empirical dampening factor for the frictional stress model. | Real | 0.4 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor_wall_normal | Normal coefficient of restitution for parcel-wall collisions. | Real | 0.3 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | damping_factor_wall_tangent | Tangential coefficient of restitution for parcel-wall collisions. | Real | 0.99 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | parcels_per_cell_at_pack | Specifies the number of particles that can occupy a regular | Real | 32.0 | | | computational cell near close packing. | | | | | | | | | | Larger values reduce sensitivity to small changes in parcel positions, | | | | | which helps stabilize the computed solids volume fraction and, by | | | | | extension, the frictional stress model. However, increasing this value | | | | | also results in simulations tracking a greater number of parcels. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | verbose | Verbosity level for PIC-related output. | Int | 0 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ The solids volume fraction is required to evaluate the frictional stress model when advancing parcels from :math:`t^n` to :math:`t^{n+1}`. Ideally, this evaluation would use either the volume fraction at the midpoint of the time step, :math:`\varepsilon_p^{n+1/2}`, or at the end of the step, :math:`\varepsilon_p^{n+1}`. However, since neither of these values is available a priori, an iterative approach is used. An initial approximation of the volume fraction is used to advance parcels to a tentative position at :math:`t^{n+1}`. These new positions are then used to compute an updated volume fraction field, which is subsequently used in the next iteration to recompute the tentative parcel positions. The following keywords control the iterative PIC algorithm and are defined with the prefix ``pic``: +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | | Description | Type | Default | +====================================+=========================================================================+==========+===========+ | initial_step_type | Specifies the initial solids volume fraction used in PIC iterations to | String | "nth_eps" | | | approximate the volume fraction at the end of the time step, | | | | | :math:t^{n+1}. | | | | | | | | | | Options (case-insensitive): | | | | | | | | | | * ``nth_eps`` - use the volume fraction from the previous time step, | | | | | :math:`t^{n}` | | | | | * ``zero_eps`` - set the initial volume fraction to zero | | | | | * ``taylor_approx`` - use a Taylor series expansion about parcel | | | | | positions to approximate the volume fraction at :math:`t^{n+1}` | | | | | | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | max_iter | Maximum number of iterations used to approximate the end state | Int | 3 | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | advance_vel_p | Specifies the weighting factor used to compute the averaged particle | Real | 0.5 | | | velocity field during parcel advancement. The field-averaged velocity | | | | | is used when applying forces to parcels. | | | | | | | | | | This parameter takes values between 0 and 1, blending the particle | | | | | velocity at the beginning and end of the time step. A value of ``0.5`` | | | | | (default) yields a time-centered average. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+ | velocity_reference_frame | The velocity reference frame scales the field-averaged velocity | Real | 0.5 | | | used to compute the slip velocity between a parcel and the bulk when | | | | | when the parcels is moving towards an area of higher solids | | | | | concentration. This parameter takes values between 0 and 1. | | | +------------------------------------+-------------------------------------------------------------------------+----------+-----------+
