Segregated vs Coupled Solver
 

Hi,

If I am running a simulation should I be able to switch between these two solvers with little difference.

Currently I am trying to simulate a turbine blade and when I run the simulation in Segregated mode it runs fine (with constant density also) but when I change the solved to Coupled (with ideal gas) it no longer works and never converges and gives a really unstable solution that is continuously changing.

Does anyone know what I could be doing wrong?

Thanks

The coupled solver is generally more unstable. In terms of stability

constant density segregated > ideal gas segregated > ideal gas coupled

In general, expect a difference. Especially if you are switching between constant density and ideal gas.

When you use coupled flow, the software uses coupled equations to solve pressure and velocity. This is proper when you have high density, or high Mach. It will use more CPU and it will converge slowly but the result will be more accurate. when you use the segregated, then the segregated equations. It is proper for standard case, when there is no complicated physical conditions. It uses less CPU and it will converge faster.

Why coupled solver would converge slowly? Isn't that segregated would converge slowly due to the decoupling of pressure velocity?

Yes, you are right. The pressure-based segregated algorithm solves the momentum equation and pressure correction equations separately. This semi-implicit solution method results in slow convergence. However using the coupled approach offers some advantages over the non-coupled or segregated approach. The coupled scheme obtains a robust and efficient single phase implementation for steady-state flows, with superior performance compared to the segregated solution schemes. This pressure-based coupled algorithm offers an alternative to the density-based and pressure-based segregated algorithm with SIMPLE-type pressure-velocity coupling. For transient flows, using the coupled algorithm is necessary when the quality of the mesh is poor, or if large time steps are used.

Bascially both of them are trying to solve Saddle Point problem which is 2x2 matrix (Block matrix). This matrix has special issue that the 2,2 element is 0.

Now if you try to solve this system then it is difficult to solve as a whole. This is why coupled solver is more difficult despite of coupling. In fact that coupled version makes it difficult.

The SIMPLE is a segregated algorithm to solve the same system and has shown that it is much more effective than the coupled version. This is why it works better.

Now about velocity pressure coupling. This is basically a way of removing that 2,2 zero block by adding dissipation. Segregated pressure based uses Rhie and Chow and coupled solver uses different dissipation.

Changing from one solver to another disturbs fluxes and residual jump and many times solver can't recover. The transition from one type to another is not smooth.

There is a possibility to gradually move from 1 dissipation to another but softwares don't provide it as its not needed mostly.

Would you mind of pointing some books for paper for this material?

I thought decoupling is one operation order cheaper than the coupled solver. The decoupling partially breaks the communication between P and V, which leads to slow convergence per iteration step. For the simple problem, although the coupled solver required more RAM and have higher operation order, it will bring the solution quicker than the decoupled solver. Whereas, For the complex problem, although the decoupled solver converges "slow" per iteration, because of one order cheaper, it takes less time to converge as to the coupled solver. Meanwhile, the coupled solver may encounter convergence issue due to the nonlinear.

Above is just purely come from my intuition with some basic CFD class. Please correct me and point me to some more theoretically grounded sources. Thanks!

This whole book is pretty much about this issue https://www.amazon.com/Multilevel-Bl.../dp/0387715630

There is a beautiful summary here too http://www.mathcs.emory.edu/~benzi/Web_papers/bgl05.pdf


On the first look it looks like moving to coupled solver is way to go. But you see Fluent has both coupled solvers from year 2007 and in 11 years you can see that their main method is still segregated algorithm.

There are many numerical issues, the biggest is to have efficient solver for that coupled matrix.