A high-order nodal discontinuous Galerkin method for simulation of three-dimensional non-cavitating/cavitating flows

Abstract

In this study, the nodal discontinuous Galerkin method is formulated in three-dimensions and applied to simulate three-dimensional non-cavitating/cavitating flows. For this aim, the three-dimensional preconditioned Navier-Stokes equations based on the artificial compressibility approach considering appropriate source terms to model cavitating phenomena are used. The spatial derivative terms in the resulting equations are discretized by utilizing the nodal discontinuous Galerkin method on tetrahedral elements and the derivative of the solution vector with respect to the artificial time is discretized by applying an explicit time integration method. An artificial viscosity method is formulated in three-dimensions and applied to properly capture the discontinuities in the cavitating flow-field. Here, different non-cavitating/cavitating flow problems including non-cavitating flow in a 3:1:1 driven cavity, non-cavitating flow between two concentric rotating spheres, cavitating flow over a sphere and cavitating flow over a wavy cylinder are solved to examine the accuracy and robustness of the proposed solution method. These flow problems are selected to properly assess the numerical method in the presence of straight and curved boundaries and for different Reynolds and cavitation numbers. From linear to cubic polynomial degrees are used in the simulations and the numerical results are compared with the available analytical and numerical results. Indications are that the present numerical method based on the NDGM formulated in three-dimensions can accurately simulate the three-dimensional non-cavitating/cavitating flows. • Formulating a nodal discontinuous Galerkin method (NDGM) in 3D to simulate noncavitating/cavitating flows. • Implementing an artificial viscosity approach in 3D for capturing the steep discontinuities in the cavity interface. • Examining the accuracy and robustness of the solution method by computing different 3D noncavitating/cavitating flow problems. • Considering the 3D NDGM proposed to assess other solution methods for computing noncavitating/cavitating flows.