Energy maximising controllers (EMCs), for wave energy converters (WECs), based on linear models are attractive in terms of simplicity and computation. However, such (Cummins equation) models are normally built around the still water level as an equilibrium point and assume small movement, leading to poor model validity for realistic WEC motions, especially for the large amplitude motions obtained by a well controlled WEC. The method proposed here is to use an adaptive algorithm to estimate the control model in realtime, whereby system identification techniques are employed to identify a linear model that is most representative of the actual controlled WEC behaviour. Using exponential forgetting, the linear model can be continuously adapted to remain representative in changing operational conditions. To that end, this paper presents a novel adaptive controller based on a receding horizon pseudospectral formulation. The paper also demonstrates the implementation of the adaptive controller inside a computational fluid dynamics (CFD) based numerical wave tank (NWT) simulation. The adaptive controller will create the best linear model, representative of the conditions encountered in the fully nonlinear hydrodynamic CFD simulation. Using CFD presents a method to evaluate the adaptive controller within a realistic simulation environment, allowing the convergence and adaptive properties of the present control scheme to be tested. A test case, considering a heaving point absorber, is presented and the adaptive controller is shown to perform well in irregular sea states, absorbing more power than its non-adaptive counterpart. The optimal trajectory calculated by the adaptive model is seen to have a smaller motion and power take-off (PTO) forces, compared to those calculated by the non-adaptive linear control model, due to the increased amount of hydrodynamic resistance estimated by the adaptive model, as identified from the nonlinear viscous CFD simulation.