Numerical Sedov-Taylor (blast-wave) solution

[jdwood983]

Homework Statement

I was asked to model the blast-wave of an explosion using Sedov's solution in MATLAB, but I'm not really sure where to begin. Most of the programming I have done has been

x=linspace(1,1000,1000);
for i=1:1000
     y(i)=x(i)^2;
end

type of code, and this one seems a lot more complex (I found a version of this code in C [sorta familiar with C, to some extent all object oriented languages are the same] which is long and has many functions in it which leads me to the 'complex' conclusion here).

Any suggestions on where to begin? If not, any suggestions on a better book than Sedov's Similarity and Dimensional Methods in Mechanics to get me started? Or maybe both?

Homework Equations

$$\frac{r}{r_2}=\left[\frac{(\nu+2)(\gamma+1)}{4}V\right]^{-2/(2+\nu)}\left[\frac{\gamma+1}{\gamma-1}\left(\frac{(\nu+2)\gamma}{2}V-1\right)\right]^{-\alpha_2}\left[\frac{(\nu+2)(\gamma+1)}{(\nu+2)(\gamma+1)-2[2+\nu(\gamma-1)]}\left(1-\frac{2+\nu(\gamma-1)}{2}V\right)\right]^{-\alpha_1}$$
and a couple others

The Attempt at a Solution

Not sure where to begin, so not much of a solution attempt can exist. I did try using the equation above and changing V from its lower bound of $2/([\nu+2]\gamma)$ to its upper bound of $4/((\nu+2)(\gamma+1))$ but that gave me bad data.

Any help would be appreciated.

 

[CFDFEAGURU]

Blandford and Thorne's free notes from CalTech discuss the blast wave. It doesn't contain any code but it might help.

See the link below

http://www.pma.caltech.edu/Courses/ph136/yr2008/0616.1.K.pdf

Thanks
Matt

 

[Mene]

my suggestion would be to first familiarize yourself with the basic concepts and principles behind Sedov's solution and the numerical methods used to solve it. This can be done by reading through textbooks or online resources, attending lectures or workshops, or consulting with colleagues who have experience in this area. It may also be helpful to start with simpler numerical problems before attempting to tackle the blast-wave solution.

In terms of resources, there are many books and online tutorials available on numerical methods and their applications, so it may be helpful to do some research and find one that suits your level of understanding and programming experience. Additionally, there are also software packages and libraries specifically designed for solving numerical problems, so you may want to explore those options as well.

When it comes to coding, it's important to start by breaking down the problem into smaller, manageable steps and then gradually building upon them. This will help you to understand the code better and make it easier to troubleshoot any issues that may arise. You may also want to consult with colleagues or online forums for guidance and support as you work through the code.

Overall, tackling a problem like the Sedov-Taylor solution takes time, patience, and a willingness to learn and try new things. Don't be discouraged if you encounter difficulties or setbacks, as these are all part of the learning process. With persistence and determination, you will eventually be able to successfully model the blast-wave using Sedov's solution in MATLAB.