IAP, a general technology platform for Industrial Internet, develops towards both intelligent control software for heterogeneous environments and application software for Industrial Internet. In Industrial Internet, digital twin is the key support, and its core is perception control and simulation modeling. This paper introduces the typical application of IAP in industrial internet, and the basis of IAP digital twin - IAPbox, an edge computing device with network, computing, storage and application core capabilities as a whole, and describes the IAP fusion of process-oriented and object-oriented modeling methods, then proceeds a simulation modeling with second-order systems representing numerous mechanical systems, electrical systems, fluid systems, thermodynamic systems, and so on. On the basis of introducing the simulation calculation method of IAP originated from programmable controllers, taking the first-order system as an example, assuming that the simulation system adopts the rectangular approximation solving method of the single-step method, the influence of the simulation step length on the stability of the simulation system is proved through the geometric sequence dispersion and convergence, i.e., the simulation system may be distorted if the simulation step length is too long, which may even result in the loss of stability for the stabilized system.