Summary: Numerical simulations provide a unique approach for investigating the impact of left ventricular assist devices (LVADs) on the pump function of the heart. To this end, the fictitious domain (FD) method was incorporated within a non-conforming coupled fluid-solid mechanics solver creating a model capable of capturing the full range of cardiac motion under LVAD support, including contact of the cannula with the ventricular wall. To demonstrate and verify the properties of the applied method, convergence studies were performed showing linear convergence for both a fluid only problem with an immersed rigid body, as well as a fluid - solid coupled problem with a fluid immersed rigid body interacting with the coupled elastic solid. The model was implemented on a left ventricular (LV) geometry constructed from human MRI data. Simulations were performed to compare LV function with an FD prescribed LVAD cannula and with a cannula applied as a Dirichlet boundary. Good agreement was observed between the simulations for myocardial deformation, major flow features and rates of energy transfer. Finally, an LV simulation was performed to bring the ventricular wall into contact with the cannula, demonstrating the applicability of the model to investigating LV function under LVAD support.