A new package of strategies for the modelling of fluid-solid interactions is presented. The fluid and structure formulations are derived from the generic transport equations described in a moving framework, providing a direct route to numerical methods. The use of discontinuous elements along with Galerkin weightings provides a finite volume like structure to the system of fluid and solid equations. A homogenised formulation is obtained throughout by treating the fluids and solid terms alike. The principle differences arise from the constitutive laws that account for the nature of the material. A new method based on the mechanical parts of the energy equation is derived and introduced to enforce the constitutive laws. The fluid and solid equations are formed into a system of governing equations coupled through their boundaries. A monolithic strategy is used to solve the complete system of equations. Initially, the developed strategies are tested on a series of one dimensional test cases. This way the predictive capabilities of the methods are established. In particular, the energy approach shows encouraging results in terms of enhancing energy conservation and computational efficiency. The methods are tested further in the fluid-solid interaction context via their application to the classical piston problem. The ability of the method to capture the coupled frequencies of the system is established whilst stability issues are identified. The source of the problem is established to be the approach used to linearly interpolate the convective fluxes at element boundaries. Suggestions are made on how to improve the problem. It is shown that for less strongly coupled cases, relatively stable solutions are possible using the current methods.