In this report, we develop elementary numerical schemes to simulate timedomain evolution of individual parts of a wind instrument. A one dimensional finite elements scheme for time-domain simulation of acoustic waves in a variablesection pipe is introduced, which includes viscothermal losses. Other schemes are presented for various boundary conditions, including acoustic radiation, as well as a pipe junction model useful for tone holes, and a reed model. These schemes are guaranteed to preserve energy, and can be assembled to form arbitrarily complex instruments with any number of tubes, holes, radiating parts and exciter mechanisms. Moreover, many parameters are permitted to vary continuously during the simulation without posing any stability concern. This allows to compute transient sounds from opening and closing of tone holes, or with varying reed parameters.