On the efficiency of finite volume method, particle finite element method, vortex method and immersed boundary method for 2D incompressible flow simulation around airfoils

The design of the structural elements of the technical systems, which interact with the fluid or gas flow, is a complicated multidisciplinary problem. The accuracy of mathematical modelling and numerical simulation in the corresponding hydrodynamic and/or coupled hydroelastic problems plays an essential role in the estimation of hydrodynamic loads acting on the structure. Therefore the technical characteristics of the developing structures strongly depend on the quality of the solution of this problem. The experiment scheduling requires preliminary careful estimation of flow parameters in order to avoid damage of the investigated structure. The calculation of the aerodynamic and hydrodynamic loads is the most complicated part of the problem, especially if the construction is movable or deformable, i.e. when coupled fluid structure interaction (FSI) problem is considered. Some of the existing engineering methods are based on the usage of steady-state averaged aerohydrodynamic coefficients; these methods are applicable for calculation of quasi-steady aerohydrodynamic loads, but they are not suitable for the simulation of high-speed and transient regimes. This leads to the necessity of introducing an additional ultimate load safety factor that reduces the technical and economic properties of the designed structures. The aim of the present research is to analyse and compare the efficiency of four numerical methods for 2D incompressible flow simulation around the airfoils: finite volume method implementer in OpenFOAM, finite element method with particles (PFEM) implemented in Kratos software, meshless Lagrangian vortex methods and eulerian immersed boundary methods, implemented in in-house numerical codes.