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This paper investigates the applicability of smoothed particle hydrodynamics in simulations of superfluid helium-4. We devise a new approach based on Hamiltonian mechanics suitable for simulating thermally driven and weakly compressible flows with free surfaces. The method is then tested in three cases, including a simulation of the fountain effect. We obtain remarkable agreement with referential and theoretical results. The simulations provide new physical insight, such as the pressure and temperature fields in a vessel experiencing the fountain effect.