A new compression principle based on super multijets colliding with pulsation (Naitoh et al, 2010, 2011, 2012, 2013) has an impressive potential for engendering a new single lightweight engine capable of operating over a wide range of Mach numbers from startup to the hypersonic regime with high thermal efficiency and low noise for hypersonic aircars, while this principle can also improve traditional turbofan and ram-scram jet engines and generates small engines for automobiles and personal power generators with high efficiencies. Flow experiments using a shocktube and combustion tests of two prototype engines, computational fluid dynamics with a chemical reaction model, and theoretical fluid mechanics clarifies the potential of high thermal efficiency and stability of this engine system, although our previous computations (Naitoh et al, 2011, 2012) are very qualitative. Especially, in this report, unsteady three-dimensional computations for this engine system extended with a piston for low subsonic Mach number M< 0.3, computations for transonic operation during various continuous cycles, and computations of combustion for M>3 are shown in details. These computations will reveal the concrete specification including the number and size of nozzles of supermultijets colliding, which is necessary for achieving high thermal efficiency over 60%, even for small engines. Then, primitive testes done for two prototype engines also indicate possibility of combustion occurence.