Computational Aerodynamics Assignment 5 — Boundary Conditions
 Question #1
Consider the following domain:
The freestream properties correspond to $M_\infty=2$, $T_\infty=300$ K, $P_\infty=1$ atm, $\theta=30^\circ$ and the properties on the nodes at the iteration $n$ are as follows:
 Node $P^n$, atm $T^n$, K $u^n$, m/s $v^n$, m/s 1 1.0 300 400 -400 2 1.1 310 300 -300 3 1.1 310 300 -300 4 1.2 320 200 -300 5 1.2 330 200 -200 6 1.3 340 100 -200 7 1.3 340 100 -100 8 1.4 350 100 -100 9 1.4 360 100 -100
Knowing that the node spacing is constant, do the following:
 (a) Find the properties at iteration $n+1$ at node 1 using a 2nd degree polynomial to extrapolate the properties. (b) Find the properties at iteration $n+1$ at node 9 using a 2nd degree polynomial to extrapolate the properties.
Outline clearly what kind of boundary condition (subsonic inflow/outflow, supersonic inflow/outflow) you are choosing and why.
 04.28.17
 Question #2
Consider the following domain:
The freestream properties correspond to $M_\infty=0.7$, $T_\infty=300$ K, $P_\infty=1$ atm, $\theta=70^\circ$ and the properties on the nodes at the iteration $n$ are as follows:
 Node $P^n$, atm $T^n$, K $u^n$, m/s $v^n$, m/s 1 1.0 300 100 -80 2 1.1 330 130 -100 3 1.1 350 150 -130 4 1.2 380 170 -160
Knowing that the node spacing is constant, do the following:
 (a) Find the properties at iteration $n+1$ at node 1 using a 1st degree polynomial to extrapolate the properties.
Outline clearly what kind of boundary condition (subsonic inflow/outflow, supersonic inflow/outflow) you are choosing and why.
 Question #3
Consider a computational domain as follows:
with the gas constant $R=286~$J/kgK, the ratio of specific heats $\gamma=1.4$, $P_\infty=2~$atm, $T_\infty=300~$K, and $M_\infty=0.8$. Knowing the properties at nodes 1, 2, 3, and 4 at time level $n$:
 Node $x$, m $y$, m $P^n$, Pa $T^n$, K $u^n$, m/s $v^n$, m/s 1 1.00 1.00 90000 310 400 30 2 0.99293 1.00707 90000 310 380 20 3 0.97879 1.02121 90000 350 350 10 4 0.96464 1.03535 90000 330 340 0
Do the following:
 (a) Determine what kind of boundary condition node 1 is. (b) Find the pressure and temperature at time level $n+1$ at node 1 using a 2nd degree polynomial to extrapolate the properties from the inner nodes 2, 3 and 4.
Hint: the spacing between the nodes 4, 3, 2, and 1 can not be assumed constant.
 05.01.18
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