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We numerically model key building blocks of a phononic integrated circuit that enable phonon routing in high-acoustic-index waveguides. Our particular focus is on the gallium nitride-on-sapphire phononic platform which has recently demonstrated high acoustic confinement in its top layer without the use of suspended structures. We start with the systematic simulation of various transverse phonon modes supported in strip waveguides and ring resonators with sub-wavelength cross section. Mode confinement and quality factors of phonon modes are numerically investigated with respect to geometric parameters. A quality factor of up to 10 8 is predicted in optimized ring resonators. Next, we study the design of the phononic directional couplers and present key design parameters for achieving strong evanescent couplings between modes propagating in parallel waveguides. Last, interdigitated transducer electrodes …