Abstract Blast waves are produced when there is a sudden deposition of a substantial amount of energy into a confined region. It is an area of pressure moving supersonically outward from the source of the explosion. Immediately after the blast, the fore-end of the blast wave is headed by the shock waves, propagating in the outward direction. As the considered problem is highly nonlinear, to find out its solution is a tough task. However, few techniques are available in literature that may give us an approximate analytic solution. Here, the blast wave problem in magnetogasdynamics involving cylindrical shock waves of moderate strength is considered, and approximate analytic solutions with the help of the power series method (or Sakurai’s approach [1]) are found. The magnetic field is supposed to be directed orthogonally to the motion of the gas particles in an ideal medium with infinite electrical conductivity. The density is assumed to be uniform in the undisturbed medium. Using power series method, we obtain approximate analytic solutions in the form of a power series in ( a 0 / U ) 2 ${\left({a}_{0}/U\right)}^{2}$ , where a 0 and U are the velocities of sound in an undisturbed medium and shock front, respectively. We construct solutions for the first-order approximation in closed form. Numerical computations have been performed to determine the flow-field in an ideal magnetogasdynamics. The numerical results obtained in the absence of magnetic field recover the existing results in the literature. Also, these results are found to be in good agreement with those obtained by the Runge–Kutta method of fourth-order. Further, the flow variables are illustrated through figures behind the shock front under the effect of the magnetic field. The interesting fact about the present work is that the solutions to the problem are obtained in the closed form.

中文翻译：

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磁气动力学中的冲击波传播：幂级数法

摘要 当大量能量突然沉积到受限区域时，就会产生冲击波。它是从爆炸源以超音速向外移动的压力区域。紧接着爆炸后，冲击波的前端以冲击波为首，向外传播。由于所考虑的问题是高度非线性的，找出其解决方案是一项艰巨的任务。然而，文献中很少有技术可以为我们提供近似的解析解。在这里，考虑了磁气动力学中涉及中等强度圆柱冲击波的冲击波问题，并借助幂级数方法（或 Sakurai 的方法 [1]）找到了近似解析解。磁场应该垂直于气体粒子在具有无限电导率的理想介质中的运动。假设密度在未受干扰的介质中是均匀的。使用幂级数方法，我们在 ( a 0 / U ) 2 ${\left({a}_{0}/U\right)}^{2}$ 中以幂级数的形式获得近似解析解，其中a 0 和 U 分别是未受干扰的介质和激波前沿中的声速。我们以封闭形式构造一阶近似的解。已经进行了数值计算以确定理想磁气动力学中的流场。在没有磁场的情况下获得的数值结果恢复了文献中的现有结果。还，发现这些结果与通过四阶 Runge-Kutta 方法获得的结果非常吻合。此外，流动变量通过磁场作用下激波前沿后面的图形来说明。关于当前工作的有趣事实是问题的解决方案是以封闭形式获得的。