Blocks Library
Capacitances
Module describing capacitance blocks
- class CBlock(pressure: Quantity[float64], capacitance: Quantity[float64], time: Time)
C Block quantities and flux definitions
C Block scheme
Node 1:
\(Q = - C\dot{P}\)
Discretisation:
\[Q^{n + \frac{1}{2}} = - C\ \frac{P^{n + 1} - P^{n}}{\Delta t^n}\]- flux() Any
Compute the flux at local node 1
- Returns:
the flux
- Return type:
np.float64
- dflux_dpressure() Any
Compute the flux at local node 1 partial derivative for pressure
- Returns:
the flux derivative
- Return type:
np.float64
- class RCBlock(pressure_1: Quantity[float64], pressure_2: Quantity[float64], resistance: Quantity[float64], capacitance: Quantity[float64], time: Time)
RC Block quantities and fluxes definitions
RC Block scheme
Node 1:
\(Q_1 = \frac{P_2 - P_1}{R}\)
Node 2:
\(Q_2 = \frac{P_1 - P_2}{R} - C\dot{P_2}\)
Discretisation:
\[Q_1^{n + \frac{1}{2}} = \frac{P_2^{n + \frac{1}{2}} - P_1^{n + \frac{1}{2}}}{R}\]\[Q_2^{n + \frac{1}{2}} = \frac{P_1^{n + \frac{1}{2}} - P_2^{n + \frac{1}{2}}}{R} - C\ \frac{P_2^{n + 1} - P_2^{n}}{\Delta t^n}\]- flux_1() Any
Computes the outlet flux at local node 1.
- Returns:
the flux value for current block values
- Return type:
np.float64
- dflux_1_dpressure_1() Any
Computes the outlet flux at node 1 derivative for pressure_1.
- Returns:
the flux derivative for pressure_1
- Return type:
np.float64
- dflux_1_dpressure_2() Any
Computes the outlet flux at node 1 derivative for pressure_2.
- Returns:
the flux derivative for pressure_2
- Return type:
np.float64
- flux_2() Any
Computes the outlet flux at node 2.
- Returns:
the flux value for current block values
- Return type:
np.float64
- dflux_2_dpressure_1() Any
Computes the outlet flux at node 2 derivative for pressure_1.
- Returns:
the flux derivative for pressure_1
- Return type:
np.float64
- dflux_2_dpressure_2() Any
Computes the outlet flux at node 2 derivative for pressure_2.
- Returns:
the flux derivative for pressure_2
- Return type:
np.float64
- class RCRBlock(pressure_1: Quantity[float64], pressure_2: Quantity[float64], pressure_mid: Quantity[float64], resistance_1: Quantity[float64], capacitance: Quantity[float64], resistance_2: Quantity[float64], time: Time)
RCR Block quantities and flux definitions
Node 1:
\(Q_1 = \frac{P_{mid} - P_1}{R_1}\)
Node 2:
\(Q_2 = \frac{P_{mid} - P_2}{R_2}\)
Internal equation:
\[\frac{P_1 - P_{mid}}{R_1} + \frac{P_2 - P_{mid}}{R_2} - C\dot{P}_{mid} = 0\]Discretisation:
\[Q_1^{n + \frac{1}{2}} = \frac{P_{mid}^{n + \frac{1}{2}} - P_1^{n + \frac{1}{2}}}{R_1}\]\[Q_2^{n + \frac{1}{2}} = \frac{P_{mid}^{n + \frac{1}{2}} - P_2^{n + \frac{1}{2}}}{R_2}\]\[\frac{P_1^{n + \frac{1}{2}} - P_{mid}^{n + \frac{1}{2}}}{R_1} + \frac{P_2^{n + \frac{1}{2}} - P_{mid}^{n + \frac{1}{2}}}{R_2} - C\ \frac{P_{mid}^{n + 1} - P_{mid}^{n}}{\Delta t^n} = 0\]- flux_1() Any
Computes the outlet flux at node 1.
- Returns:
the flux value
- Return type:
np.float64
- dflux_1_dp_1() Any
Computes the outlet flux at node 1 derivative for pressure_1.
- Returns:
flux derivative for pressure_1
- Return type:
np.float64
- dflux_1_dp_mid() Any
Computes the outlet flux at node 1 derivative for pressure_mid.
- Returns:
flux derivative for pressure_2
- Return type:
np.float64
- flux_2() Any
Computes the flux at node 2.
- Returns:
the flux value
- Return type:
np.float64
- dflux_2_dp_mid() Any
Computes the outlet flux at node 2 derivative for pressure_mid.
- Returns:
flux derivative for pressure_mid
- Return type:
np.float64
- dflux_2_dp_2() Any
Computes the outlet flux at node 2 derivative for pressure_2.
- Returns:
flux derivative for pressure_2
- Return type:
np.float64
- pressure_mid_residual() Any
Compute the residual representing dynamics of the mid node pressure.
- Returns:
the residual value
- Return type:
np.float64
- pressure_mid_residual_dp_1() Any
Compute the residual derivative for pressure_1
- Returns:
the residual derivative for pressure_1
- Return type:
np.float64
- pressure_mid_residual_dp_2() Any
Compute the residual derivative for pressure_2
- Returns:
the residual derivative for pressure_2
- Return type:
np.float64
- pressure_mid_residual_dp_mid() Any
Compute the residual derivative for pressure_mid
- Returns:
the residual derivative for pressure_mid
- Return type:
np.float64
- compute_volume_stored() Any
Computes volume stored in the capacitance.
- Returns:
volume stored in the capacitance
- Return type:
np.float64
Valves
Module describing Valve Blocks
- class ValveRLBlock(flux: Quantity[float64], pressure_1: Quantity[float64], pressure_2: Quantity[float64], inductance: Quantity[float64], conductance: Quantity[float64], backward_conductance: Quantity[float64], scheme_ts_flux: Quantity[float64], time: Time)
Describes valve RL block quantities and flux definitions
Valve RC Scheme
Node 1:
\(Q_1 = - Q\)
Node 2:
\(Q_2 = Q\)
Internal Equations:
\[\begin{split}L\ \dot{Q} + P_2 - P_1 + \begin{cases} RQ \text{ if Q $>$ 0 } \\ R_{\text{back}}Q \text{ else } \end{cases} = 0\end{split}\]Discretisation:
\[Q_1^{{n + \frac{1}{2}}} = - Q^{{n + \frac{1}{2}}}\]\[Q_2^{{n + \frac{1}{2}}} = Q^{{n + \frac{1}{2}}}\]\[\begin{split}L\ \frac{Q^{n + 1} - Q^{n}}{\Delta t^n} + P_2^{n + \frac{1}{2}} - P_1^{n + \frac{1}{2}} + \begin{cases} RQ^{{n + \theta}} \text{ if } Q^{{n + \theta}} > 0 \\ R_{\text{back}}Q^{{n + \theta}} \text{ else } \end{cases} = 0\end{split}\]- initialize() None
Override this method to define specific for model initialization.
- flux_residual() Any
Compute the residual giving the dynamics on the flux in the valve.
- Returns:
the residual value
- Return type:
np.float64
- flux_residual_dflux() Any
Compute the residual partial derivative for
flux- Returns:
the residual partial derivative for
flux- Return type:
np.float64
- flux_residual_dp1() Any
Compute the residual partial derivative for
pressure_1- Returns:
the residual partial derivative for
pressure_1- Return type:
np.float64
- flux_residual_dp2() Any
Compute the residual partial derivative for
pressure_2- Returns:
the residual partial derivative for
pressure_2- Return type:
np.float64
- flux_1() Any
Compute the block flux at node 1
- Returns:
the block flux at node 1
- Return type:
np.float64
- dflux_1_dflux() Any
Compute the block flux at node 1 partial derivative for
flux- Returns:
the block flux at node 1 partial derivative for
flux- Return type:
np.float64
- flux_2() Any
Compute the block flux at node 2
- Returns:
the block flux at node 2
- Return type:
np.float64
- dflux_2_dflux() Any
Compute the block flux at node 2 partial derivative for
flux- Returns:
the block flux at node 2 partial derivative for
flux- Return type:
np.float64
Cavities
Describes cavity blocks
- class SphericalCavityBlock(disp: Quantity[float64], radius: Quantity[float64], thickness: Quantity[float64], time: Time)
Spherical cavity block implementation
Spherical Cavity Scheme
Node 1:
\(Q = - \frac {dV(y)}{dt}\)
Discretised:
\(Q^{n + \frac{1}{2}} = - \frac {V(y^{n + 1}) - V(y^{n})}{\Delta t^n}\)
Note
Notice that no dynamics is given on the DOF in the block. Model components of the cavity can access the pressure and give it a dynamics.
- initialize() None
Initialize block attributes from current quantity values
- fluid_volume_current() Any
Compute the current fluid volume in the cavity.
- Returns:
the fluid volume
- Return type:
np.float64
- fluid_volume_new() Any
Compute the new fluid volume in the cavity.
- Returns:
the fluid volume
- Return type:
np.float64
- cavity_flux() Any
Compute the ventricule flux at local node 1.
- Returns:
the flux
- Return type:
np.float64
- dcavity_flux_ddisp() Any
Compute the partial derivative of the cavity flux for
disp- Returns:
the flux partial derivative
- Return type:
np.float64