频散可控格式的一种推广形式及其在爆轰波马赫反射中应用

频散可控格式是高精度捕捉激波的新格式.对原有频散可控格式(DCD)进行了推广,给出了适用于网格点排列不规则情况下的DCD格式,使其具有更广泛的适应性,在此基础上构造了在非结构三角形网格下的DCD格式.用一些典型算例对推广后的DCD格式进行检验,结果表明该格式是合理和可靠的,并能够较好地保留原有DCD格式的二阶精度.把推广后的DCD格式和具有8种组分和20个化学反应的基元反应模型相结合,对氢氧爆轰波在直管道中的传播问题及楔面上马赫反射问题进行计算,计算结果和实验结果比较表明,在非结构三角形网格下的DCD格式能够有效地捕捉爆轰波,在爆轰波阵面上不会产生振荡或是抹平间断现象.

A General Form of the Dispersion-controlled Dissipative Scheme and Its Application in Detonation Problems

A general form of the dispersion-controlled dissipative(DCD)scheme is proposed.An unstructured DCD is constructed and its reliability is demonstrated with numerical simulations.Comparisons of the unstructured results with the second order structured results reveal that the previous resolution is well retained.In order to simulate detonation problems,unstructured DCD is combined with detailed chemical reaction kinetics.The algorithm is used to simulate detonation propagating along a straight duct with or without a wedge.Comparison of the numerical simulations and experiments shows that the algorithm works well in capturing detonation waves.Neither numerical oscillation nor artificial viscosity occurs in practical calculations.