  We derive new boundary conditions and implementation procedures for nonlinear
initial boundary value problems (IBVPs) with non-zero boundary data that lead
to bounded solutions. The new boundary procedure is applied to nonlinear IBVPs
in skew-symmetric form, including dissipative terms. The complete procedure has
two main ingredients. In the first part (published in [1, 2]), the energy and
entropy rate in terms of a surface integral with boundary terms was produced
for problems with first derivatives. In this second part we complement it by
adding second derivative terms and new nonlinear boundary procedures leading
for boundary conditions with non-zero data. The new nonlinear boundary
procedure generalise the well known characteristic boundary procedure for
linear problems to the nonlinear setting. To introduce the procedure, a
skew-symmetric scalar IBVP encompassing the linear advection equation and
Burgers equation is analysed. Once the continuous analysis is done, we show
that energy stable nonlinear discrete approximations follow by using
summation-by-parts operators combined with weak boundary conditions. The scalar
analysis is subsequently repeated for general nonlinear systems of equations.
Finally, the new boundary procedure is applied to four important IBVPs in
computational fluid dynamics: the incompressible Euler and Navier-Stokes, the
shallow water and the compressible Euler equations.
