Taylor Maccoll Eq. with Runge Kutta

yow · November 21, 2015, 23:31

Before I go use CFD, I wanted to approximate the supersonic flow field after a shock in front of a cone (0 deg. angle of attack). I used 4th order Runge Kutta with Taylor Maccoll eq. and am getting Vtheta = 0 at 31 deg cone half angle when I assume my shock beta = 34 deg. I've stared at my code for 20 h and have manually coded the Runge Kutta eq. as well as using ode45 function and get the same results. My step size is - .001. Can anyone please help? Maybe I'm just braindead...

Apologies if this is the wrong place to ask.

yow · December 6, 2015, 12:22

Nevermind, I found the answer after contemplating for a while... The initial Vtheta used for the Taylor-Maccoll equations must be negative to account for the decreasing Vr due to the flow relieving effect of the 3D cone surface.

psakkos · April 29, 2021, 15:12

I am having a similar issue. My RK4 is approximating a very high cone angle that is very close to the shock. What did you code your program in? I’m using Matlab. My initial conditions are right, though, so I don’t know what the issue is

November 21, 2015, 23:31	Taylor Maccoll Eq. with Runge Kutta	#1
yow New Member Yang Join Date: Jun 2015 Posts: 25 Rep Power: 11	Before I go use CFD, I wanted to approximate the supersonic flow field after a shock in front of a cone (0 deg. angle of attack). I used 4th order Runge Kutta with Taylor Maccoll eq. and am getting Vtheta = 0 at 31 deg cone half angle when I assume my shock beta = 34 deg. I've stared at my code for 20 h and have manually coded the Runge Kutta eq. as well as using ode45 function and get the same results. My step size is - .001. Can anyone please help? Maybe I'm just braindead... Apologies if this is the wrong place to ask.

April 29, 2021, 15:12	Similar Issue	#3
psakkos New Member Join Date: Apr 2021 Posts: 1 Rep Power: 0	I am having a similar issue. My RK4 is approximating a very high cone angle that is very close to the shock. What did you code your program in? I’m using Matlab. My initial conditions are right, though, so I don’t know what the issue is

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December 6, 2015, 12:22		#2
yow New Member Yang Join Date: Jun 2015 Posts: 25 Rep Power: 11	Nevermind, I found the answer after contemplating for a while... The initial Vtheta used for the Taylor-Maccoll equations must be negative to account for the decreasing Vr due to the flow relieving effect of the 3D cone surface.