Windtunnel/Boundary Conditions

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in pluto.ini

• ObjectType_int: 0=nothing, 1=cylinder/sphere, 2=square/cube of size ObjectDiameter_cm
• WindPressure_Pa, WindPressure_mbar (mutually exclusive): pressure at entry (left)
• PressureGradient_mbar_per_cm positive (even though pressure drops from left to right)
• Wind velocity is ramped up to WindVelocity_m_per_s over time InjectionTime_s
• WindTemperature_C
• KinematicViscosity_m2_per_s, DynamicViscosity_Pa_s,
• Wall_BoundaryCondition for tangential walls, value from {0,1,2,3}

(ignored if given values <0)

in init.c

• macro SOLID to enable an object
• array solid containing value 1 or 0 for object matter being present/absent

Walls

tangential

Boundary condition for the wall
	vx1	vx2
no-shear	zero-gradient	reflective
no-slip	reflective	reflective
no-wall	zero-gradient	zero-gradient
one-way wall	zero-gradient	zero-gradient & no-inflow

entry/exit

prescribe pressure drop (left to right)

• current simulation result: $v_x$-profile slightly asymmetric and $v_x<0$ at one wall

Object

• Strong asymmetry when driven by pressure gradient. Bug!

$v_y$ is not symmetric to the $x$-axis.

• At the boundary of a region which has FLAG_INTERNAL_BOUNDARY set, no boundary conditions are specified. Ghostcells are frozen.

Open Questions

Reflective cells

Setting the vector ${\overrightarrow{v}}_g$ in a ghost cell as ${\overrightarrow{v}}_g=-\overrightarrow{v}$, with $\overrightarrow{v}$ being the value in the adjacent real cell, yields $\overrightarrow{0}$ as interpolation right at the boundary. This works for plane walls. What to do in cases where a ghost cell has more than one real cell as nearest neighbor? This calls for discussion!

Analytical Solutions

empty 2D channel

$$v_x(y)=\frac{\mathrm{\Delta }p}{L}\frac{D^2/4-y^2}{2\mu }$$

empty circular tube

$$v_z(r)=\frac{\mathrm{\Delta }p}{L}\frac{R^2-r^2}{4\mu }$$

with $\mu$=dynamical viscosity