A third-order characteristic-based-split finite element scheme of Spalart–Allmaras model and its application to flow past crescent iced 4-bundled conductors

Abstract The one-equation Spalart–Allmaras (SA) model is employed to close the Reynolds averaged Navier–Stokes equations (RANS equations), and research on turbulent numerical algorithm is carried out. Using the coordinate transformation based on the characteristic line, we can obtain RANS equations without the convection terms. The intermediate velocity and correct velocity terms are introduced to split the momentum equations. The Runge–Kutta method is used to discretize it in time, and the Taylor expansion along the characteristic line is used to overcome the mesh update difficulty due to the coordinate transformation. Finally, based on the Galerkin space discretization, a third-order characteristic-based-split finite element algorithm is proposed. Numerical simulation of turbulent flow past a square cylinder is carried out to verify the effectiveness of the proposed algorithm. The prosposed algorithm is applied to simulate turbulent flow past a single conductor and 4-bundled conductors with crescent-shaped ice, the aerodynamic coefficients for different ice thicknesses and wind attack angles are obtained, and the galloping stability of crescent-shaped ice-covered conductor is discussed.