High order scheme for incompressible Navier-Stokes (N-S) equations with application to MAV (micro air vehicle)

Aim. One reason why existing schemes for the incompressible N-S equations are not satisfactory is, in our opinion, that their order is low. We now present a scheme that is relatively high in order. In the full paper, we explain our scheme in detail. In this abstract, we just add some pertinent remarks to listing the two topics of explanation. The first topic is: the calculation. In the first topic, we mention that: (1) the incompressible N-S equations are solved with the method of pseudo-compressibility, and the implicit LU-SGS method is used for time stepping; (2) the fifth-order upwind differencing method developed by Roger is employed. The second topic is: the verification of our fifth-order scheme with three instances. The three subtopics of the second topic are; the simulation of the flow field around a cylinder using Re = 200 (subtopic 2.1), the simulation with Re = 105 (subtopic 2.2), and the simulation of the flow field around E387 airfoil using Re = 100000 (subtopic 2.3). In subtopics 2.1, we present the simulation results, as shown in 4 figures in the full paper; (1) the differencing method is reliable; (2) the centered scheme with more artificial dissipation delays the periodic shedding of the vortex in the flow field around the cylinder; (3) the higher-order scheme can describe the shedding vortex more accurately, and the shedding begins earlier. In subtopic 2.2, we present a rather fine vorticity field as shown in Fig.6 in the full paper. In subtopic 2.3, our simulation results show preliminarily that; (1) in the case of low Reynold number, even a small angle of attack can make the airflow around the airfoil separate; (2) the separation on the surface of E387 airfoil causes the increase of its lift coefficient.