[wm2300]

Dear all,

I am trying to implement the SIMPLE scheme for steady state incompressible flow simulations.

I use a false transient approach in order to linearize the convective term (I use convective fluxes from previous timesteps). This can also be regarded as a relaxation which I add to the updates of the momentum equations in subsequent timesteps.

Now, one of the major ambiguities which I seem to find in literature is the definition of inner and outer iterations in the simple scheme (i.e. from Ferziger).

I have one iteration loop for my false transient, which I would assume to be my outer loop. Now, from literature I seem to understand that, in every timestep, I first calculate the estimates u* and v* based on the pressure of previous timestep; then proceed in calculating the pressure correction p'; correcting the velocities and the pressure and again perform a new calculation to achieve new u* and v*, based on p + p', until my p' becomes smaller than a chosen tolerance (these would be the inner iterations); as mentioned in Patankar's book on Numerical Heat Transfer in Section 6.7-1 (point 7)

I would not however update my coefficient matrix in the inner iterations, which would render my velocity update useless actually (unless I take the tolerance on p' to be rather loose).

Now my question is, is this the correct approach for the simple scheme? Or do you need to update the coefficients for the convective terms in the matrices also in these inner iterations?

Literature does not seem to be giving me a closing answer due to a vague representation of what is done to the non-linear terms. Also, I've studied some implementations online and they seem to be doing different things as well.

I appreciate any feedback.