ABSTRACT We present a high-resolution convergence study of detonation initiated by a temperature gradient in a stoichiometric hydrogen–oxygen mixture using the PENCIL CODE and compare with a code that employs a fifth order weighted essentially non-oscillating (WENO) scheme. With Mach numbers reaching 10–30, a certain amount of shock viscosity is needed in the PENCIL CODE to remove or reduce numerical pressure oscillations on the grid scale at the position of the shock. Detonation is found to occur for intermediate values of the shock viscosity parameter. At fixed values of this parameter, the numerical error associated with those small wiggles in the pressure profile is found to decrease with decreasing mesh width like down to . With the WENO scheme, solutions are smooth at , but no detonation is obtained for . This is argued to be an artifact of a decoupling between pressure and reaction fronts.

中文翻译：

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爆炸模拟的收敛特性

摘要 我们使用铅笔代码对化学计量氢氧混合物中的温度梯度引发的爆炸进行了高分辨率收敛研究，并与采用五阶加权基本非振荡 (WENO) 方案的代码进行了比较。当马赫数达到 10-30 时，PENCIL CODE 中需要一定量的激波粘度，以消除或减少激波位置网格尺度上的数值压力振荡。发现爆震发生在冲击粘度参数的中间值。在此参数的固定值下，发现与压力分布中的那些小摆动相关的数值误差随着网格宽度的减小而减小，例如下降到 。使用 WENO 方案，解在 处是平滑的，但在 处没有获得爆轰。