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Numerical simulations of complete hydraulic systems (e.g. diesel injectors) can, due to  high computational costs, currently not be done entirely in three dimensions. Our aim is  to substitute the 3D solver by a corresponding 1D method in some parts of the system and  develop a solver coupling with suitable interface models. Firstly, we investigate an  interface model for non-cavitating flow passing the interface. A flux-coupling with a thin  interface approach is considered and the jump in dimensions at the interface is  transferred to an additional variable φ, which switches between the 3D  and the 1D domain. As shown in two testcases, the error introduced in the vicinity of the  interface is quite small. Two numerical flux formulations for the flux over the 3D-1D  interface are compared and the Roe-type flux formulation is recommended. Secondly,  extending the first method to cavitating flows passing the interface, we divide the  density equation in two equations - one for liquid and one for vapor phase of the  two-phase fluid - and couple the two equations by source terms depending on the free  enthalpy. We propose two interface models for coupling 3D and 1D compressible  density-based Euler methods that have potential for considering the entire (non-)  cavitating hydraulic system behaviour by a 1D method in combination with an embedded  detailed 3D simulation at much lower computational costs than the pure 3D simulation

Evaluation of interface models for 3D-1D coupling of compressible Euler methods for the application on cavitating flows