# Steady State Discretisation and Time Step

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 August 25, 2021, 09:12 Steady State Discretisation and Time Step #1 Senior Member   Brett Join Date: May 2013 Posts: 212 Rep Power: 13 Hi everyone, So I know when solving a steady state problem we use a kind of pseudo time step to march towards convergence. What I want to know is how do we specifically discretise our equations and where is the timestep implemented in this process? If all the differentials with respect to time can be cancelled due to the problem being steady state where does the time step come in?? B

 August 25, 2021, 15:36 #2 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,664 Rep Power: 65 There are unsteady/transient solvers that use real time-stepping. If you march these in time, eventually you may arrive at a steady state solution (if it even exists). These always have temporal discretization because they are unsteady solvers and terms cancel out in the solution whenever they feel like canceling out. There are steady solvers that solve problems that don't depend on time. Steady solvers don't need pseudo time-stepping and most of them don't have any temporal discretization because the terms are cancelled out. But sometimes a steady solver will use a pseudo time-step. Are you asking how these work? The pseudo time-step is a form of implicit underrelaxation and isn't actually a form of a temporal discretization.

 August 25, 2021, 15:43 #3 Senior Member   Brett Join Date: May 2013 Posts: 212 Rep Power: 13 Hey LuckyTran. If you could explain how they work that would be cool! So theres no temporal discretisation in steady problems?

 August 25, 2021, 16:41 #4 Senior Member   Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,664 Rep Power: 65 Alright so for steady problems you have a discretized linear system that needs to be solved. You have an initial guess serving as an old solution. If you solve the linear system you get an updated solution. With implicit underrelaxation, you can inject (by adding) a certain amount of the old solution into the linear system. When you solve this modified underrelaxed system instead, the updated solution is biased and tends more towards the old solution. This is equivalent to limiting the solution change by a local time-step. You can try and figure out how the weights are related to the local time-step (hint: it's related to the flow Courant number). Or.... you can just put the time-step into the weight factor and that's pseudo transient.

 August 25, 2021, 18:40 #5 Senior Member   Brett Join Date: May 2013 Posts: 212 Rep Power: 13 care to indulge me?

 August 25, 2021, 18:46 #6 Senior Member   Brett Join Date: May 2013 Posts: 212 Rep Power: 13 For example when I set a physical timescale value in CFX, what exactly am I setting and where does it present itself in the equations (Simplified, say the Euler equations)

 Tags discretisation, numerical methods, steady, timestep