A high‐order nodal discontinuous Galerkin method to solve preconditioned multiphase Euler/Navier‐Stokes equations for inviscid/viscous cavitating flows

Summary In this study, a high‐order accurate numerical method is applied and examined for the simulation of the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier‐Stokes equations on triangle elements. The formulation used here is based on the homogeneous equilibrium model considering the continuity and momentum equations together with the transport equation for the vapor phase with applying appropriate mass transfer terms for calculating the evaporation/condensation of the liquid/vapor phase. The spatial derivative terms in the resulting system of equations are discretized by the nodal discontinuous Galerkin method (NDGM) and an implicit dual‐time stepping method is used for the time integration. An artificial viscosity approach is implemented and assessed for capturing the steep discontinuities in the interface between the two phases. The accuracy and robustness of the proposed method in solving the preconditioned multiphase Euler/Navier‐Stokes equations are examined by the simulation of different two‐dimensional and axisymmetric cavitating flows. A sensitivity study is also performed to examine the effects of different numerical parameters on the accuracy and performance of the solution of the NDGM. Indications are that the solution methodology proposed and applied here is based on the NDGM with the implicit dual‐time stepping method and the artificial viscosity approach is accurate and robust for the simulation of the inviscid and viscous cavitating flows. A high‐order nodal discontinuous Galerkin method (NDGM) is applied and examined for computing the inviscid/viscous cavitating flows by solving the preconditioned multiphase Euler/Navier‐Stokes equations on triangle elements. An artificial viscosity approach with a suitable sensor is implemented and assessed for capturing the steep discontinuities in the interface between the two phases. The accuracy and robustness of the proposed method are demonstrated by simulating different 2D/axisymmetric inviscid/viscous cavitating flows for different conditions.