[RamShivam]

Hello everyone,
I have created Python program code to solve 1D Shock tube problem numerically using Smoothed Particle Hydrodynamics Meshless Approach.
Here, I use Taylor's series expansion for finding spatial derivatives(first and second derivative) occuring in one dimensional Navier Stokes equation in Lagrangian form and then by minimizing the error in the series using Weighted Least squares approximation, the spatial derivatives are found out.
Then, the results are applied in Second order Runge-Kutta method to find the properties at various points. I have used 100 points from 0 to 1 in the problem.
But my results are not in accordance with the actual solution of the shock tube problem. I could not capture the shock wave and the expansion wave in the graph obtained. It is difficult for me to find where I went wrong. Can somebody help me find out the mistake in the procedure?
Thank you

[FMDenaro]

Originally Posted by RamShivam

Hello everyone,
I have created Python program code to solve 1D Shock tube problem numerically using Smoothed Particle Hydrodynamics Meshless Approach.
Here, I use Taylor's series expansion for finding spatial derivatives(first and second derivative) occuring in one dimensional Navier Stokes equation in Lagrangian form and then by minimizing the error in the series using Weighted Least squares approximation, the spatial derivatives are found out.
Then, the results are applied in Second order Runge-Kutta method to find the properties at various points. I have used 100 points from 0 to 1 in the problem.
But my results are not in accordance with the actual solution of the shock tube problem. I could not capture the shock wave and the expansion wave in the graph obtained. It is difficult for me to find where I went wrong. Can somebody help me find out the mistake in the procedure?
Thank you

I don't know the detail in your code but you must be aware not to use Taylor expansion across the shock.

Then, you should post the plot of the results

[RamShivam]

http://shodhganga.inflibnet.ac.in/bi...hapter%207.pdf
I followed the method which is described in Pageno.203 in this pdf.
I attach my current results here.
Thank you.

[FMDenaro]

Originally Posted by RamShivam

http://shodhganga.inflibnet.ac.in/bi...hapter%207.pdf
I followed the method which is described in Pageno.203 in this pdf.
I attach my current results here.
Thank you.

I don't know the details of this method. However, derivatives are not defined across a shock but only in the regions of smooth solutions. For theis reason the weak form is adopted.

I strongly suggest to check your method before using simple test-cases, that is the scalar advection and the Burgers equation. If the results are good then you can think to solve Euler equations.