We study the fate of internal gravity waves approaching the centre of an initially non-rotating solar-type star , by performing three-dimensional numerical simulations using a Boussinesq-type model . These waves are excited at the top of the radiation zone by the tidal forcing of a short-period planet on a circular , coplanar orbit . This extends previous work done in two dimensions by Barker & Ogilvie . We first derive a linear wave solution , which is not exact in 3D ; however , the reflection of ingoing waves from the centre is close to perfect for moderate amplitude waves . Waves with sufficient amplitude to cause isentropic overturning break , and deposit their angular momentum near the centre . This forms a critical layer , at which the angular velocity of the flow matches the orbital angular frequency of the planet . This efficiently absorbs ingoing waves , and spins up the star from the inside out , while the planet spirals into the star . We also perform numerical integrations to determine the linearised adiabatic tidal response throughout the star , in a wide range of solar-type stellar models with masses in the range 0.5 \leq m _ { \star } / M _ { \odot } \leq 1.1 , throughout their main sequence lifetimes . The aim is to study the influence of the launching region for these waves at the top of the radiation zone in more detail , and to determine the accuracy of a semi-analytic approximation for the tidal torque on the star , that was derived under the assumption that all ingoing wave angular momentum is absorbed in a critical layer . The main conclusions of this work are that this nonlinear mechanism of tidal dissipation could provide an explanation for the survival of all short-period extrasolar planets observed around FGK stars , while it predicts the destruction of more massive planets . This work provides further support for the model outlined in a previous paper by Barker & Ogilvie , and makes predictions that will be tested by ongoing observational studies , such as WASP and Kepler .