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This paper presents a computational algorithm to predict highly-transient flame behavior in counterflow situations. The first objective of the paper is to extend the transient counterflow problem to incorporate some gasdynamic compressibility effects, yet retain the desirable similarity structure. By relaxing assumptions in earlier formulations, the computational algorithms can deliver high accuracy even in periods of extremely rapid transients, like combustion ignition. The algorithms aredoi:10.1080/00102200008947340 fatcat:juhcyk3yk5b5vlqdywbwtrgn74