Numerical simulation plays an important role in the design of new hydraulic units. It allows to minimize the number of expensive experimental tests of products and reduces development time. The flow in pipes, valves, regulators and other hydraulic elements belongs to the internal incompressible flow. Standard numerical methods such as a finite volume method (FVM) and finite element method (FEM) are already successfully used for incompressible internal flows modeling. However, in the case of domains with moving boundaries, these methods are hard to set up and sometimes inefficient. Therefore, now, there is a necessity of search of alternative methods for such class of problems. Requirements for new methods include acceptable accuracy and high computing efficiency. The aim of this study is an overview, testing and comparison different simulation methods for simplest types of internal flow: finite volume method, particle finite volume method (PFVM) and Lattice Boltzmann method (LBM). Different shapes of circular pipes were considered: the straight pipe with the constant area, the step pipe (abruptly increase of the diameter), the backward step pipe (abruptly decrease of the diameter) and the elbow pipe. The velocities and pressure fields, accuracy and simulation time were compared. Next solvers were used in the study: pimpleFoam as the OpenFOAM implementation of FVM, XFlow as the implementation of LBM, and ParticlePimpleFoam as OpenFOAM implementation of PFVM. Four values of the non-dimensional time step (Courant numbers) for PFVM and FVM methods: 1, 2, 5 and 10 were considered.