Loading docs/source_docs/user_guide/inputs/solids_model.rst +38 −0 Original line number Diff line number Diff line Loading @@ -87,6 +87,10 @@ Enabling the DEM solver and specifying model options. | dem.damping_tang_fac.pw | Factor relating the tangential damping coefficient to the normal | Real | 0.5 | | | damping coefficient :: particle to wall collisions | | | +-------------------------+-------------------------------------------------------------------------+----------+-----------+ | dem.implicit_drag | Apply fluid-particle drag force by | int | 0 | | | :ref:`implicit velocity update<InputsDEMImplicitDrag>`. | | | +-------------------------+-------------------------------------------------------------------------+----------+-----------+ The following inputs use the DEM type names specified using the `dem.solve` input to define restitution coefficients and are proceeded with `dem.restitution_coeff`. These must be defined for all solid-solid and solid-wall combinations. Loading Loading @@ -126,6 +130,40 @@ Below is an example for specifying the inputs for two DEM solids. dem.restitution_coeff.sand.wall = 0.85 dem.restitution_coeff.char.wall = 0.89 .. _InputsDEMImplicitDrag: Implicit drag ~~~~~~~~~~~~~ By default, the fluid-particle drag force is applied explicitly to particles, .. math:: u_p^{n^{\prime}+1} = u_p^{n^\prime} + dt_{\mathrm{DEM}}\left(\beta^n (u_f^{n+1} - u_p^{n}) + \mathcal{F}_p^{n^\prime}\right)/m_p where :math:`u_p` is the `p`-th particle velocity at the indicated time level, :math:`\beta^n` is the drag coefficient, :math:`u_f^{n+1}` is the fluid velocity, :math:`\mathcal{F}_p` are all non-drag forces (e.g., gravitational, buoyancy, collision etc.), and :math:`m_p` is particle mass. Terms exist at different time levels due in part to how the fluid and particle models are coupled and partly because particles typically sub-step in time. Specifically, a time step advances the fluid from :math:`t^n` to :math:`t^{n+1}`, then particles take multiple smaller time steps to traverse the same total time. In the above equation, prime markers differentiate quantities updated at each DEM sub-step. The updated particle velocity, :math:`u_p^{n^{\prime}+1}`, is substituted into the drag expression when `implicit drag` is enabled. .. math:: u_p^{n^{\prime}+1} = \frac{u_p^{n^\prime} + dt_{\mathrm{DEM}}\left( \beta^n u_f^{n+1} + \mathcal{F}_p^{n^\prime} \right)/m_p}{1 + dt_{\mathrm{DEM}} \beta^n / m_p} By using the updated velocity, the drag force computed for the fluid and particles is inconsistent, and interphase momentum is not conserved. However, implicit drag may be needed for numerical stability when the particle density is much less than the fluid (such as bubbles). PIC model settings ------------------ Loading Loading
docs/source_docs/user_guide/inputs/solids_model.rst +38 −0 Original line number Diff line number Diff line Loading @@ -87,6 +87,10 @@ Enabling the DEM solver and specifying model options. | dem.damping_tang_fac.pw | Factor relating the tangential damping coefficient to the normal | Real | 0.5 | | | damping coefficient :: particle to wall collisions | | | +-------------------------+-------------------------------------------------------------------------+----------+-----------+ | dem.implicit_drag | Apply fluid-particle drag force by | int | 0 | | | :ref:`implicit velocity update<InputsDEMImplicitDrag>`. | | | +-------------------------+-------------------------------------------------------------------------+----------+-----------+ The following inputs use the DEM type names specified using the `dem.solve` input to define restitution coefficients and are proceeded with `dem.restitution_coeff`. These must be defined for all solid-solid and solid-wall combinations. Loading Loading @@ -126,6 +130,40 @@ Below is an example for specifying the inputs for two DEM solids. dem.restitution_coeff.sand.wall = 0.85 dem.restitution_coeff.char.wall = 0.89 .. _InputsDEMImplicitDrag: Implicit drag ~~~~~~~~~~~~~ By default, the fluid-particle drag force is applied explicitly to particles, .. math:: u_p^{n^{\prime}+1} = u_p^{n^\prime} + dt_{\mathrm{DEM}}\left(\beta^n (u_f^{n+1} - u_p^{n}) + \mathcal{F}_p^{n^\prime}\right)/m_p where :math:`u_p` is the `p`-th particle velocity at the indicated time level, :math:`\beta^n` is the drag coefficient, :math:`u_f^{n+1}` is the fluid velocity, :math:`\mathcal{F}_p` are all non-drag forces (e.g., gravitational, buoyancy, collision etc.), and :math:`m_p` is particle mass. Terms exist at different time levels due in part to how the fluid and particle models are coupled and partly because particles typically sub-step in time. Specifically, a time step advances the fluid from :math:`t^n` to :math:`t^{n+1}`, then particles take multiple smaller time steps to traverse the same total time. In the above equation, prime markers differentiate quantities updated at each DEM sub-step. The updated particle velocity, :math:`u_p^{n^{\prime}+1}`, is substituted into the drag expression when `implicit drag` is enabled. .. math:: u_p^{n^{\prime}+1} = \frac{u_p^{n^\prime} + dt_{\mathrm{DEM}}\left( \beta^n u_f^{n+1} + \mathcal{F}_p^{n^\prime} \right)/m_p}{1 + dt_{\mathrm{DEM}} \beta^n / m_p} By using the updated velocity, the drag force computed for the fluid and particles is inconsistent, and interphase momentum is not conserved. However, implicit drag may be needed for numerical stability when the particle density is much less than the fluid (such as bubbles). PIC model settings ------------------ Loading
