[mertcan]

Hi, I would like to ask : let's say that I have NO time dependent INCOMPRESSIBLE VISCOUS fluid and my reynolds number is LOW which means NO turbulence exists. I am aware that SIMPLE algorithm found by Patankar can be used and it has segregated iterative solution which includes LINEAR matrix equations in a specific sequence. BUT due to viscous, in the source term of energy equation we have DISSIPATION term which is NON-LINEAR. Therefore my question is HOW DO WE USE SIMPLE algorithm for the equations/cases that have non linear source term like dissipation function??? OR what should we do IN THAT SITUATION??

By the way even if you apply finite difference we can not convert dissipation function from non-linearity to linearity...
If you think I am not explicit please let me know I am new
Also ıf question is under wrong sub-forum again let me know or please help me to shift it to get answers

[FMDenaro]

For incompressible flows the kinetic energy equations is not coupled.
The dissipation function is relevant for sufficiently high Mach number.
Why do you want to consider such equation?

[mertcan]

Originally Posted by FMDenaro

For incompressible flows the kinetic energy equations is not coupled.
The dissipation function is relevant for sufficiently high Mach number.
Why do you want to consider such equation?

Yes you are right dissipation function has more significance in compressible flow. So please let me ask the question in that way : let's say we have average mach number for COMPRESSIBLE LAMINAR flow (thus can not convert compressible flow to incompressible flow and dissipation function must be considered). As far as I searched SIMPLE algorithm can also be used for compressible flow like in this link(https://brage.bibsys.no/xmlui/bitstr...pdf?sequence=1 and PAGE 11). But now we have to include DISSIPATION function in source term and it is non-linear. Also in SIMPLE algorithm we have segregated iterative equations which includes linear matrix equations thus using guessed initial conditions we can reach a point, but NOW we have NON LINEARITY (dissipation function), I have a conflict here : How non linear term is included in SIMPLE algorithm ??
In order to guarantee the converged point using initial guess in SIMPLE algorithm we should have diagonally dominant matrices and linear matrix equations. BUT HOW DO WE REACH CONVERGED POINT WITH INITIAL GUESSES INCLUDING NON LINEAR TERM??
Also even if we reach a point, that point CAN NOT BE UNIQUE because non linearity may require multiple solutions, for instance we can not reach unique velocity solution because dissipation function has NON LINEAR velocity terms. Am I right??

Even if we apply finite difference, still dissipation function has non linearity

[FMDenaro]

Why do you neclegt that the non linear term exists also in the convection of the momentum? How do you think to take care of that?

[mertcan]

Originally Posted by FMDenaro

Why do you neclegt that the non linear term exists also in the convection of the momentum? How do you think to take care of that?

I do not want to neglect anything I did not say like that on the contrary I would like to include dissipation term or other non linear terms. My question is about the link I shared the last time. According to the link we can use SIMPLE algorithm for compressible flow, I say that we should have linear matrix equations, diagonally dominant matrices to reach a unique point with initial guess. Also I say even if we reach a point when we apply SIMPLE algorithm to compressible flow like the link, our point will NOT BE unique. For instance, for a particular flow situation we may have 2 different velocity solutions because of the fact that when FINITE DIFFERENCE is applied to dissipation function we have second order polynomial velocities. Am I RIGHT? How do we HANDLE this situation? What can we do about BOTH MOMENTUM AND ENERGY equations?

[FMDenaro]

If I remember correctly, the dissipation in non-dimensional form has a coefficient as M^2/Re, therefore for compressible subsonic flows it can be neglected without a great lost of its contribution.
The non linearity still remains in the convective terms

[mertcan]

Originally Posted by FMDenaro

If I remember correctly, the dissipation in non-dimensional form has a coefficient as M^2/Re, therefore for compressible subsonic flows it can be neglected without a great lost of its contribution.
The non linearity still remains in the convective terms

What if we have compressible hypersonic flow?? What should we do with those non linearities?

In my opinion algorithms like SIMPLE SIMPLER do not work properly due to the fact non linearity is important in this case, then we should use beam warming or maccormack scheme and to reach the time independent solution time steps go to infinity Am I right??

If I am not right could you show me the correct path?

[FMDenaro]

Dissipation is relevant in presence of shocks

[mertcan]

Originally Posted by FMDenaro

Dissipation is relevant in presence of shocks

Initially I know dissipation is relevant for shocks which may occur when we have compressible hypersonic flow and that answer is NOT satisfactory because it is not the answer to my question.

MY QUESTION IS : HOW WE CAN HANDLE NON LINEARITIES when we have compressible hypersonic flow OR PRESENCE OF SHOCKS? What ALGORITHM should we employ to deal with those non linearities?

In my opinion algorithms like SIMPLE SIMPLER do not work properly due to the fact non linearity is important in this case, then I consider we should use BEAM WARMING or MACCORMACK scheme and to reach the time independent solution time steps go to infinity Am I RIGHT??

If I am not right could you show me the RIGHT WAY?

[mertcan]

Originally Posted by FMDenaro

Dissipation is relevant in presence of shocks

FMDenaro AM I NOT EXPLICIT ENOUGH for my last question? Why don't you give me the answer directly related to my last question at post 9?
Why can not I get answers from anybody in this forum?

[mertcan]

Originally Posted by mertcan

FMDenaro AM I NOT EXPLICIT ENOUGH for my last question? Why don't you give me the answer directly related to my last question at post 9?
Why can not I get answers from anybody in this forum?

I just would like to express that I do not get enough responses related to my questions and I blame myself for not being explicit (also I searched the book chung, anderson... I did my best but not get satisfied) SO LET ME SIMPLIFY my questions more and more........

1) In SUPERSONIC COMPRESSIBLE VISCOUS LAMINAR FLOW what kind of ALGORITHMS SHOULD BE EMPLOYED??

2) In SUPERSONIC COMPRESSIBLE VISCOUS TURBULENCE FLOW what kind of ALGORITHMS SHOULD BE EMPLOYED??

[beer]

Originally Posted by mertcan

I just would like to express that I do not get enough responses related to my questions and I blame myself for not being explicit (also I searched the book chung, anderson... I did my best but not get satisfied) SO LET ME SIMPLIFY my questions more and more........

1) In SUPERSONIC COMPRESSIBLE VISCOUS LAMINAR FLOW what kind of ALGORITHMS SHOULD BE EMPLOYED??

2) In SUPERSONIC COMPRESSIBLE VISCOUS TURBULENCE FLOW what kind of ALGORITHMS SHOULD BE EMPLOYED??

Use simple and iterate until convergence => problem solved.
And don't be a douche to people who are trying to help you.

[sbaffini]

Handling of non-linearity is a necessary and fundamental step in most implicit solution algorithms, and mostly has nothing to do with the algorithm in itself.

In CFD it is plenty of non-linearities. The most prominent one is in the convective term, which you can actually treat in different ways.

The viscous dissipation term has two features for which it is typically discretized explicitly. First of all, it is quite weak, so it is mostly harmless. Second, if you use a segregated approach, like in SIMPLE, you can't actually do anything else than discretize it explicitly, because the term appears in the energy equation, but it only involves the velocity variables. It is only in coupled solution methods that you can add some meaningful coefficients to the implicit matrix.

[LuckyTran]

SIMPLE segregates the solution of pressure & velocity. It has nothing to do with the energy equation. Solving the energy equation separate from the continuity and momentum equations is also segregating, but for different reasons. Yes there is a dissipation term in the energy equation but that has nothing to do with SIMPLE.

In RANS the momentum equation for laminar/turbulent flow is the same. It's just a question of what is the effective viscosity? Is it molecular viscosity only or molecular + turbulent viscosity?

Originally Posted by mertcan

MY QUESTION IS : HOW WE CAN HANDLE NON LINEARITIES..........

You are using a predictor-corrector approach. The non-linearities are handled by updating the initial guess at the next iteration. Just keep iterating until you are converged.

[mertcan]

you mean if we have non linearities then first we set initial conditions at t=0 afterwards with time marching we calculate the variables using a specific scheme??

[mertcan]

Originally Posted by LuckyTran

SIMPLE segregates the solution of pressure & velocity. It has nothing to do with the energy equation. Solving the energy equation separate from the continuity and momentum equations is also segregating, but for different reasons. Yes there is a dissipation term in the energy equation but that has nothing to do with SIMPLE.

In RANS the momentum equation for laminar/turbulent flow is the same. It's just a question of what is the effective viscosity? Is it molecular viscosity only or molecular + turbulent viscosity?



You are using a predictor-corrector approach. The non-linearities are handled by updating the initial guess at the next iteration. Just keep iterating until you are converged.

you mean if we have non linearities then first we set initial conditions at t=0 afterwards with time marching we calculate the variables using a specific scheme??

Also I consider that if we have non linearity and use initial guess then we do not have guaranteed convergence AM I RIGHT??

[LuckyTran]

Originally Posted by mertcan

you mean if we have non linearities then first we set initial conditions at t=0 afterwards with time marching we calculate the variables using a specific scheme??

Also I consider that if we have non linearity and use initial guess then we do not have guaranteed convergence AM I RIGHT??

I am not talking about time marching. I'm talking about how you solve a non-liner problem.

In general you are not guaranteed convergence for most non-linear problems. For poor initial guesses you can easily diverge (which happens frequently in this forum). Not all schemes are equal here. That convergence is not guaranteed should be quite obvious. Just try Newton-Raphson with a bad guess.

If you have a linear system then you can solve it algebraically, exactly. But you are not solving a linear system, you are solving a non-linear one (which you pointed out using CAPS). Because of non-linearities, the solution of the linearized system you solve is not necessarily the solution of the non-linear system you want to solve. Hence you (most often) iterate to get a converged solution using some scheme that we need not specify. Presumably this scheme converges to the solution, if it doesn't then it's not a very helpful scheme. If you want to dig into the mathematics of it, it belongs to a broad class of topics related to Methods of Successive Approximations.

The guaranteed existence of smooth solutions for Navier-Stokes is not even proved yet (that's one of the Millenium Prize problems), so you can forget about uniqueness. Maybe that property will come in another hundred years.