A numerical study of non-linear, high amplitude standing waves in non-cylindrical circular resonators is reported here. These waves are shock-less and can generate peak acoustic overpressures that can exceed the ambient pressure by three/four times its nominal value. A high fidelity compressible computational fluid dynamic model is used to simulate the phenomena in cylindrical and arbitrarily shaped axisymmetric resonators. A right circular cylinder and frustum of cone are the two geometries studied. The model is validated using past numerical and experimental results of standing waves in cylindrical resonators. The non-linear nature of the harmonic response of the frustum of cone resonator system is investigated for two different working fluids (carbon dioxide and argon) operating at various values of piston amplitude. The high amplitude non-linear oscillations demonstrated can be used as a prime mover in a variety of applications including thermoacoustic cryocooling.