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

¹ Robert Bosch GmbH, Wernerstraße 51, 70469 Stuttgart - Feuerbach,
e-mail: Martina.Deininger@de.bosch.com
² University of Strasbourg, 7 rue René Descartes, 67000 Strasbourg,
e-mail: jonathan.jung@unistra.fr
³ Ruhr University Bochum, Universitätstr. 150, 44801 Bochum
⁴ University of Stuttgart, Pfaffenwaldring 21, 70569 Stuttgart

Abstract

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.