### PAR, DYNAMIC, $\tau ,{n}_{\mathrm{t1}},{n}_{\mathrm{t2}},\gamma$

Defines the material density and runs the dynamical calculations including the structure inertial effects. It can be combined with the FSI command.

Parameter Description
$\tau$ Time step for the structure solver (equals to the FSI time step). Time step for the fluid solver can be set by the PAR, FLUID command.
${n}_{\mathrm{t1}},{n}_{\mathrm{t2}}$ Number of time steps equals to ${n}_{\mathrm{t1}}×{n}_{\mathrm{t2}}$. Results are saved after each ${n}_{\mathrm{t2}}$ time step. Usual setting is ${n}_{\mathrm{t2}}=1$, then results are saved after each time step. If ${n}_{\mathrm{t2}}>1$ then the command SAVEALLLS is ignored.
$\gamma$ The artificial viscosity parameter of the HHT method. If $\gamma =0$ then the Newmark method is used.

### PAR, FLUID, ${\tau }_{\mathrm{fluid}}$, parametr not used, ${\epsilon }_{S},{l}_{0},{p}_{S},{p}_{\mathrm{out}},{R}_{u},{R}_{d},$

Sets parameters describing the fluid medium.

Parameter Typical value Description
${\tau }_{\mathrm{fluid}}$ ${10}^{-6}\mathrm{s}$ time step for the fluid solver
${\epsilon }_{S}$ $0$ fourth derivative stabilization term
${l}_{0}$ $0.15\mathrm{s}$ rigid tube length
${p}_{S}$ $4000\mathrm{Pa}$ fluid pressure in reservoir
${p}_{\mathrm{out}}$ $0\mathrm{Pa}$ pressure behind the downstream restrictor
${R}_{u}$ $5·{10}^{8}\mathrm{Pa}{\mathrm{s}}^{2}{\mathrm{m}}^{-2}$ upstream resistor resistance
${R}_{d}$ $5·{10}^{11}\mathrm{Pa}{\mathrm{s}}^{2}{\mathrm{m}}^{-2}$ downstream resistor resistance

### PAR, FLUID2, ${\mathrm{Re}}_{C},c,\rho ,\nu ,{A}_{0}$, parameter not used, $f$, ic

Sets parameters describing the fluid medium.

Parameter Typical value Description
${\mathrm{Re}}_{C}$ $1067$ critical Reynolds number
$c$ $\mathrm{1494}\mathrm{m}{\mathrm{s}}^{-2}$ sound velocity in fluid
$\rho$ $\mathrm{997.05}\mathrm{kg}{\mathrm{m}}^{-3}$ fluid density
$\nu$ $0.8937·{10}^{-6}{\mathrm{m}}^{2}{\mathrm{s}}^{-1}$ kinematic fluid viscosity
${A}_{0}$ $0.00049087385{\mathrm{m}}^{2}$ undeformed cross-section
Parameter Possible values Description
$f$ LAMINAR Only laminar friction is applied to the fluid.
TURBULENT Only turbulent friction is applied to the fluid.
NORMAL Both laminar and turbulent friction are applied to the fluid.
ic IC_FILE Initial conditions for the fluid are taken from the last time position in the file IC.xml. The file is expected to be found in the same folder as the script. This file should be result of the simulation on the rigid tube of the same geometry.
IC_COMMAND Initial conditions for the fluid are given by the IC command.
AUTO Initial conditions for the fluid are determined via the formulae given below.

If ic = AUTO, the following initial conditions are used:

$Q=\frac{-\frac{8\pi {\mu }_{d}\left(l+2{l}_{0}\right)}{{A}_{0}^{2}}+\sqrt{{\left(\frac{8\pi {\mu }_{d}\left(l+2{l}_{0}\right)}{{A}_{0}^{2}}\right)}^{2}+4\left({R}_{u}+{R}_{d}+\frac{\rho }{2{A}_{0}^{2}}\right)\left({p}_{S}-{p}_{\mathrm{out}}\right)}}{2\left({R}_{u}+{R}_{d}+\frac{\rho }{2{A}_{0}^{2}}\right)}$
${p}_{1}={p}_{S}-\left({R}_{u}+\frac{\rho }{2{A}_{0}^{2}}\right){Q}^{2}-\frac{8\pi {\mu }_{d}{l}_{0}}{{A}_{0}^{2}}Q$
${p}_{2}={p}_{S}-\left({R}_{u}+\frac{\rho }{2{A}_{0}^{2}}\right){Q}^{2}-\frac{8\pi {\mu }_{d}\left(l+{l}_{0}\right)}{{A}_{0}^{2}}Q$

However, the best choice with respect to the quality of initial conditions can be achieved by the following procedure:

1. Precompute the initial condition by setting PAR, FSI, ... , rigid=TRUE,
2. Rename the result to IC.xml,
3. Set PAR, FSI, ... , rigid=FALSE and PAR, FLUID2, ... , IC COMMAND=IC FILE,
4. Run the main FSI simulation.

### PAR, FSI, $d{p}_{\mathrm{MIN}},d{p}_{\mathrm{MAX}},{N}_{\mathrm{SCI}},{N}_{\mathrm{SCI0}}$, rigid

Sets the fluid-structure interaction parameters.

Parameter Typical value Description
$d{p}_{\mathrm{MIN}}$ $\mathrm{0.5}\mathrm{Pa}$ If the pressure increment, transferred from the fluid solver to the structural solver, is less then $d{p}_{\mathrm{MIN}}$, the subiteration process is supposed to converge successfully.
$d{p}_{\mathrm{MAX}}$ $\mathrm{1000}\mathrm{Pa}$ Upper limit for the amount of the transferred pressure from the fluid to the structural solver.
${N}_{\mathrm{SCI}}$ $4$ Number of coupling iterations per time step.
${N}_{\mathrm{SCI0}}$ $4$ Index from which the strong coupling starts.
rigid TRUE The tube is supposed to be rigid.
FALSE The tube is supposed to be elastic (default setting).