Optimal Inclusion of Transverse Effects in NonReflecting Outflow Boundary Condition

The inclusion of transverse effects in designing characteristic boundary conditions for the Euler and Navier-Stokes equations was discussed by different authors and has proved to give some improvement in the perspective of reducing numerical perturbations generated at open boundaries. Based on the most general characteristic formulation using nonorthogonal and rotated reference frames, an analysis of the different terms involved in such an approach is carried out in the present work. To achieve the best performance for the numerical behavior of the boundary condition, it is then shown that different transverse terms need to be treated differently when included in the definition of the incoming wave amplitude variations. The analysis is supported by a series of numerical tests involving an inviscid vortex convected at an angle or a purely acoustic wave propagating radially. It is concluded that the optimal behavior in terms of acoustic reflection by outgoing vorticity can be achieved by minimizing the contribution of the transverse terms related to the material derivatives along the bicharacteristics, either by properly relaxing them or by selecting a characteristic direction which is not necessarily orthogonal to the boundary.