What does M.O.C. mean in boundary condition treatment?

Thank you in advance

Hi there,

I am not sure if it refers to a specific method or just it might be an abbreviation for

Method Of Characteristics

which is how to treat boundary conditions in order to avoid reflection of waves and instabilities at the boundaries. See for example:

Abarbanel et al. 1991, J. Fluid Mech., 225, 557

Gottlieb, Gunzburger and Turkel, 1982, SIAM J. Numer. Anal. 19, 671

Or see the Review paper of Givoli on non-reflective boundary conditions:

Givoli, 1991, J. Comput. Phys. 94, page 1.

I Hope this helps,

Patrick

(1). In the inviscid, compressible flow system, whether steady supersonic or transient, the method of characteristics can be used to obtain the exact solution. The method of characteristics is not applicable for the subsonic compressible steady-state flows. (2). The idea behind the method is that the wave ( or the small distrubance in the flow field) tends to move along certain path in time or space. This disturbance can be originated from the small change of the wall curvature. In this case, it will move away from the wall point outward along a particular path (depending upon whether it is a compression wave or an expansion wave). This particular path is the so-called characteristic direction. (3). So, instead of looking everywhere for solutions, it is easier to propagate the solution (say from a wall point) away into the flow field and predict the answer. So, the method of characteristics will cover the supersonic compressible flow region with a network of solutions. (4). In applying the MOC to the boundary conditions, it is assumed that the disturbance generated at the interior point next to the boundary will also propagate in the similar way, even though in reality the flow is turbulent and viscous. (5). So, why do we have the disturbances in the boundary region in the first place? This is because the transient solution normally contain disturbances generated from the initial flow field, or during the iteration process. An even if the exit boundary region is smooth, parallel, the disturbances generated from the wall ahead of the exit can still move along the characteristic direction and intersect the exit plane. ( the same is true for the outer boundary.) (6). The use of MOC is critical for supersonic flows. It is also important for the density-based transient compressible flow formulations, because such methods actually follow the wave motion in the flow field. You can easily see this wave following behavior of the density-based method by watching the transient contour plots of the pressure field. (7). But, for steady-state subsonic problems, the characteristics of the system do not exist for the equivalent inviscid equations, and hence it can not be used. So, if the equation is steady state, and the exit is subsonic, one can not use the MOC there because it is not applicable.