# Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Fundamental Equations

## 3. Similarity Transformation of Fundamental Equations

## 4. Construction of Solutions in Power Series of s

_{1}to get approximate solution as follows

_{2}to finally obtain the value of ${\lambda}_{1}$. The obtained value of ${\lambda}_{1}$ is used to get the second approximate solution. The other steps involve the repetition of the above process to get higher order approximate solutions of the problem.

## 5. The First Approximation

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Schematic of non-dimensional velocity (

**a**) ${F}^{(0)}$, (

**b**) pressure ${G}^{(0)}$, (

**c**) density ${\mathsf{\Pi}}^{(0)}$ and (

**d**) magnetic pressure ${H}^{(0)}$ for $\gamma =1.4$, ${C}_{0}=0$, $m=0$ and $\alpha =0.0,0.015,0.025,0.05$.

**Figure 2.**Schematic of non-dimensional (

**a**) velocity ${F}^{(0)}$, (

**b**) pressure ${G}^{(0)}$, (

**c**) density ${\mathsf{\Pi}}^{(0)}$ and (

**d**) magnetic pressure ${H}^{(0)}$ for $\gamma =1.4$, $\alpha =0$, $m=0$ and ${C}_{0}=0.00,0.02,0.04$.

**Figure 3.**Schematic of non-dimensional (

**a**) velocity ${F}^{(0)}$, (

**b**) pressure ${G}^{(0)}$, (

**c**) density ${\mathsf{\Pi}}^{(0)}$ and (

**d**) magnetic pressure ${H}^{(0)}$ for $\gamma =1.4$, ${C}_{0}=0$, $m=1$ and $\alpha =0.0,0.015,0.025,0.05$.

**Figure 4.**Schematic of non-dimensional (

**a**) velocity ${F}^{(0)}$, (

**b**) pressure ${G}^{(0)}$, (

**c**) density ${\mathsf{\Pi}}^{(0)}$ and (

**d**) magnetic pressure ${H}^{(0)}$ for $\gamma =1.4$, $\alpha =0$, $m=1$ and ${C}_{0}=0.00,0.02,0.04$.

**Table 1.**${F}^{(0)}$, ${\mathsf{\Pi}}^{(0)}$ and ${G}^{(0)}$ for $m=0$, $\gamma =1.4$ and ${C}_{0}=0$.

x | $\mathit{\alpha}$ | ${\mathit{F}}^{(0)}$ Sakurai [3] | ${\mathbf{\Pi}}^{(0)}$ Sakurai [3] | ${\mathit{G}}^{(0)}$ Sakurai [3] | ${\mathit{F}}^{(0)}$ | ${\mathbf{\Pi}}^{(0)}$ | ${\mathit{G}}^{(0)}$ |
---|---|---|---|---|---|---|---|

0.0 | 0.8333 | 6.000 | 1.167 | 0.8333 | 6.000 | 1.167 | |

1.0 | 0.015 | - | - | - | 0.8208 | 5.550 | 1.167 |

0.025 | - | - | - | 0.8125 | 5.250 | 1.167 | |

0.0 | 0.7170 | 3.096 | 0.815 | 0.7251 | 3.096 | 0.815 | |

0.9 | 0.015 | - | - | - | 0.7199 | 2.899 | 0.835 |

0.025 | 0.7159 | 2.767 | 0.848 | ||||

0.0 | 0.6151 | 1.785 | 0.647 | 0.6259 | 1.785 | 0.647 | |

0.8 | 0.015 | - | - | - | 0.6251 | 1.660 | 0.664 |

0.025 | - | - | - | 0.6240 | 1.577 | 0.677 | |

0.0 | 0.5239 | 1.080 | 0.556 | 0.5341 | 1.080 | 0.556 | |

0.7 | 0.015 | - | - | - | 0.5356 | 0.990 | 0.567 |

0.025 | - | - | - | 0.5362 | 0.931 | 0.575 | |

0.0 | 0.4405 | 0.658 | 0.504 | 0.4484 | 0.658 | 0.504 | |

0.6 | 0.015 | - | - | - | 0.4507 | 0.593 | 0.508 |

0.025 | - | - | - | 0.4521 | 0.551 | 0.515 | |

0.0 | 0.3624 | 0.389 | 0.473 | 0.3676 | 0.389 | 0.473 | |

0.5 | 0.015 | - | - | - | 0.3698 | 0.345 | 0.471 |

0.025 | - | - | - | 0.3712 | 0.317 | 0.471 | |

0.0 | 0.2877 | 0.214 | 0.456 | 0.2877 | 0.214 | 0.456 | |

0.4 | 0.015 | - | - | - | 0.2921 | 0.187 | 0.450 |

0.025 | - | - | - | 0.2933 | 0.170 | 0.446 | |

0.0 | 0.2148 | 0.102 | 0.447 | 0.2160 | 0.102 | 0.447 | |

0.3 | 0.015 | - | - | - | 0.2169 | 0.088 | 0.437 |

0.025 | - | - | - | 0.2177 | 0.079 | 0.431 | |

0.0 | 0.1430 | 0.037 | 0.443 | 0.1432 | 0.037 | 0.443 | |

0.2 | 0.015 | - | - | - | 0.1436 | 0.0316 | 0.432 |

0.025 | - | - | - | 0.1439 | 0.0282 | 0.423 | |

0.0 | 0.0714 | 0.006 | 0.442 | 0.0714 | 0.006 | 0.442 | |

0.1 | 0.015 | - | - | - | 0.0715 | 0.005 | 0.429 |

0.025 | - | - | - | 0.0716 | 0.005 | 0.419 | |

0.0 | 0.0000 | 0.000 | 0.442 | 0.0000 | 0.000 | 0.442 | |

0.0 | 0.015 | - | - | - | 0.0000 | 0.000 | 0.429 |

0.025 | - | - | - | 0.0000 | 0.000 | 0.419 |

**Table 2.**${F}^{(0)}$, ${\mathsf{\Pi}}^{(0)}$ and ${G}^{(0)}$ for $m=1$, $\gamma =1.4$ and ${C}_{0}=0$.

x | $\mathit{\alpha}$ | ${\mathit{F}}^{(0)}$ Sakurai [3] | ${\mathbf{\Pi}}^{(0)}$ Sakurai [3] | ${\mathit{G}}^{(0)}$ Sakurai [3] | ${\mathit{F}}^{(0)}$ | ${\mathbf{\Pi}}^{(0)}$ | ${\mathit{G}}^{(0)}$ |
---|---|---|---|---|---|---|---|

0.0 | 0.8333 | 6.000 | 1.167 | 0.8333 | 6.000 | 1.167 | |

1.0 | 0.015 | - | - | - | 0.8208 | 5.550 | 1.167 |

0.025 | - | - | - | 0.8125 | 5.250 | 1.167 | |

0.0 | 0.7008 | 1.898 | 0.685 | 0.7072 | 1.898 | 0.684 | |

0.9 | 0.015 | - | - | - | 0.7196 | 1.767 | 0.767 |

0.025 | 0.7314 | 1.678 | 0.874 | ||||

0.0 | 0.5973 | 0.783 | 0.531 | 0.6038 | 0.783 | 0.531 | |

0.8 | 0.015 | - | - | - | 0.6246 | 0.713 | 0.577 |

0.025 | - | - | - | 0.6503 | 0.668 | 0.667 | |

0.0 | 0.5104 | 0.347 | 0.468 | 0.5141 | 0.346 | 0.468 | |

0.7 | 0.015 | - | - | - | 0.5351 | 0.309 | 0.474 |

0.025 | - | - | - | 0.5691 | 0.284 | 0.517 | |

0.0 | 0.4322 | 0.153 | 0.441 | 0.4346 | 0.150 | 0.441 | |

0.6 | 0.015 | - | - | - | 0.4503 | 0.131 | 0.414 |

0.025 | - | - | - | 0.4880 | 0.119 | 0.406 | |

0.0 | 0.3582 | 0.058 | 0.429 | 0.3592 | 0.0582 | 0.429 | |

0.5 | 0.015 | - | - | - | 0.3695 | 0.050 | 0.378 |

0.025 | - | - | - | 0.4077 | 0.045 | 0.323 | |

0.0 | 0.2859 | 0.019 | 0.425 | 0.2863 | 0.019 | 0.425 | |

0.4 | 0.015 | - | - | - | 0.2919 | 0.016 | 0.357 |

0.025 | - | - | - | 0.3255 | 0.014 | 0.260 | |

0.0 | 0.2140 | 0.005 | 0.424 | 0.2144 | 0.004 | 0.424 | |

0.3 | 0.015 | - | - | - | 0.2168 | 0.004 | 0.346 |

0.025 | - | - | - | 0.2443 | 0.003 | 0.211 | |

0.0 | 0.1429 | 0.001 | 0.424 | 0.1429 | 0.001 | 0.423 | |

0.2 | 0.015 | - | - | - | 0.1437 | 0.001 | 0.340 |

0.025 | - | - | - | 0.1630 | 0.000 | 0.173 | |

0.0 | 0.0714 | 0.000 | 0.424 | 0.0714 | 0.000 | 0.423 | |

0.1 | 0.015 | - | - | - | 0.0715 | 0.000 | 0.338 |

0.025 | - | - | - | 0.0815 | 0.000 | 0.143 | |

0.0 | 0.0000 | 0.000 | 0.424 | 0.0000 | 0.000 | 0.423 | |

0.0 | 0.015 | - | - | - | 0.0000 | 0.000 | 0.338 |

0.025 | - | - | - | 0.0000 | 0.000 | 0.118 |

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Chauhan, A.; Arora, R.; Siddiqui, M.J.
Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics. *Symmetry* **2019**, *11*, 458.
https://doi.org/10.3390/sym11040458

**AMA Style**

Chauhan A, Arora R, Siddiqui MJ.
Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics. *Symmetry*. 2019; 11(4):458.
https://doi.org/10.3390/sym11040458

**Chicago/Turabian Style**

Chauhan, Astha, Rajan Arora, and Mohd Junaid Siddiqui.
2019. "Propagation of Blast Waves in a Non-Ideal Magnetogasdynamics" *Symmetry* 11, no. 4: 458.
https://doi.org/10.3390/sym11040458