Euler calculations for flowfield of a helicopter rotor in hover

A current density conservative scheme for incompressible MHD flows at a low magnetic Reynolds number. Part II: On an arbitrary collocated mesh

“…The explicit treatment of the Coriolis force has been reported to lead to erroneous results in a rotating coordinate system [21]. Agarwal and Deese [22] cast the Coriolis force in the divergence form by noting the following formula:…”

“…(25) in a control volume when the electrical potential is obtained from the convergent solution of Eq. (22). The gradients of the electrical potential at the cell center and its neighbor center, ($u) N and ($u) P are needed to accurately calculate the current fluxes on the cell faces.…”

“…Based on this divergence form of the Coriolis force, Beddhu et al [23] have successfully formulated the Navier-Stokes equations in a fully conservative form without the traditional source terms in the case of a rotating reference frame. Using a similar idea as used in Agarwal and Desse [22], we will cast the Lorentz force in the globally and locally conservative forms. The formulation is equivalent to the original nonconservative form from a theoretical point of view, but there exist differences between these formulations from a numerical point of view.…”

“…The disadvantages of this non-conservative form of the Coriolis force on a rotating frame were reported in [21], which indicated that the explicit treatment of the Coriolis force may lead to erroneous results in a rotating frame. Agarwal and Deese [22] have absorbed half of the Coriolis force into the divergence form. Based on this divergence form of the Coriolis force, Beddhu et al [23] have successfully formulated the Navier-Stokes equations in a fully conservative form without the traditional source terms in the case of a rotating reference frame.…”

Improving Godunov-type reconstructions for simulation of vortex-dominated flows

“…The accuracy deficiency of current rotor Euler/Navier-Stokes codes for vortex preservation has led previous rotor Euler/Navier-Stokes researches to focus on coupling Euler/Navier-Stokes solutions with a separate wake model by the surface transpiration (e.g. [4][5][6][7]), field velocity (e.g. [8]), or perturbation (e.g., [9]) methods.…”