# Numerical Sedov-Taylor (blast-wave) solution

• jdwood983
In summary, the conversation revolves around the topic of modeling a blast-wave using Sedov's solution in MATLAB. The individual is seeking advice on how to approach the task and is also looking for recommendations on additional resources. They have attempted to use a specific equation but were unsuccessful. A helpful resource suggested is Blandford and Thorne's free notes from CalTech.
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

Code:
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.

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

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

Thanks
Matt

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.

## 1. What is the Numerical Sedov-Taylor (blast-wave) solution?

The Numerical Sedov-Taylor solution is a mathematical model used to describe the evolution of a spherically symmetric blast wave, such as a supernova explosion. It is named after two scientists, Yakov Borisovich Zel'dovich and Geoffrey Ingram Taylor, who independently derived the solution in the 1940s.

## 2. How does the solution work?

The solution is based on the conservation laws of mass, momentum, and energy. It assumes that the explosion occurs in a homogeneous medium and that the blast wave is strong enough to completely sweep up and accelerate the surrounding material. It also takes into account the effects of radiative cooling and energy loss at the blast wave front.

## 3. What are the key assumptions made in the Numerical Sedov-Taylor solution?

The solution assumes that the explosion is spherically symmetric, that the surrounding medium is homogeneous and isotropic, and that the blast wave is strong enough to completely sweep up and accelerate the surrounding material. It also assumes that the energy loss at the blast wave front is negligible compared to the total energy of the explosion.

## 4. What are the applications of the Numerical Sedov-Taylor solution?

The solution has applications in astrophysics, particularly in studying the evolution of supernova explosions. It is also used in experimental and numerical studies of shock waves in various materials, such as in high-energy density physics and detonation physics.

## 5. What are the limitations of the Numerical Sedov-Taylor solution?

The solution is limited to spherically symmetric explosions and does not take into account the effects of magnetic fields or turbulence. It also assumes a homogeneous medium, which may not be the case in some real-world scenarios. Additionally, the solution only applies to the early stages of the explosion and does not account for the later stages of evolution.

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