Iterative procedure

In a lot of cases the loop momentum-mass-energy-turbulence equations has only to be performed once for each increment, i.e. there is only one iteration per increment. This is for instance the case for steady state incompressible flow. For compressible flow, however, one is not only interested in the stability and the final results, also the intermediate results have to be accurate. The transient terms in the equations are modeled by a first order backward Euler scheme for compressible flow and a second order scheme for incompressible flow. Just one iteration per increment may not be sufficient to obtain a satisfactory residual for the governing equations, i.e. for accuracy reasons as many iterations per increment are performed in a transient incompressible flow calculation until the maximum residual is small enough. This roughly also applies to transient compressible flow. For steady state compressible flow the issue is rather the stability. Compressible flow is much more sensitive, since the mass, momentum and energy equation are tightly linked through the ideal gas equation. Therefore, usually more than 1 iteration is needed per increment. Furthermore, it might even be necessary to introduce subiterations iterating the mass-energy equations separately. Indeed, the solution variable of these equations are the pressure and temperature, again tightly connected through the gas equation. This is especially the case for inviscid flow, where the beneficial effects of viscosity are absent. Apart from these iterations, there are extra local iterations necessary to take the arbitrary geometry of the elements into account: this applies to the determination of the interpolated values at the faces and to the diffusion term in the conservation of mass equation.