International audienceA graph-based modelling approach for wind instruments with tone holes has been recently proposed by the author. This preliminary work remained at a rather theoretical level with high degree of generality, focussing nevertheless on musical acoustics applications while laying foundations for concrete applications. The purpose of the present work is to present concrete computation methods and numerical results in order to validate these theoretical results. For this task, elementary resonators are investigated, for which great knowledge has been accumulated for a long time through the impedance, transfer matrix and modal decomposition approaches, which can thus serve for checking. The resonator profiles focussed on belong to a musically useful class : cylinders and stepped cones, as studied by Dalmont and Kergomard 20 years ago. The case of a cylindrical resonator with one tonehole is also presented. One important feature of the approach is that mode matching is automatically satisfied, natural frequencies and eigenmodes being computed at once by the method, even for geometries with discontinuities. Also, perspectives are opened for exhibiting a very wide class of resonators with harmonically related natural frequencies, which is the subject of an another paper
