About stress in Characteristic Boundary Condition?
In Poinsot and Lele's paper<Boundary conditions for Direct Numerical Simulations of Compressible Viscous Flows>. A subsonic nonreflecting inflow impose the derivative of the stress theta(1,1) at the boundary to be zero. My question is how the stress is calculated: (1)by the formula---theta(1,1)=miu*(4/3*du/dx-2/3*dv/dy) or (2) by numerical scheme employed in the code, for example f(i)'=-2.5*f(i)+2*f(i+1)+0.5*f(i+2)=0(*),then if we know theta(1,1)at point i+1 and point i+2, we can calculate theta(1,1) at point i through equation (*). Of the two cases (1) and (2) which one is right? Thank you!