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  • Lesson 13 – Boundedness

    Posted by MARCO on January 15, 2024 at 3:24 pm


    Sorry for disturbing you. I’ve got some doubts regarding the lesson 13. In particular, for the Gradient Schemes, I didn’t properly understand the meaning of the boundedness of the scheme, and the meaning of cellLimited option. In this last case, I don’t find so clear the motivation behind the limitation of the face values inside the values in surrounding cells and how this cannot occur.

    Thanks in advance for your time and for being patient with my english.

    Kind Regards,


    Barış Bicer replied 2 months, 1 week ago 2 Members · 3 Replies
  • 3 Replies
  • Barış Bicer

    January 23, 2024 at 10:49 pm

    Hi Marco,

    Sorry indeed for late response since I was in business trip and there were lots of other questions and I missed yours.

    Lets start first with the understanding of boundedness :

    boundness means that

    1. all properties should be bounded by its own boundary values. e.g. for pure convection problem, if the maximum and minimum T is 200 and 100, then when you do CFD, all the T value on the field should between 100 and 200(no overshoot/undershoot)

    2. all coefficients of the discretized equations should have the same sign
    e.g. if T on one cell increase, then the neighbour cells’ T should also increased.

    So this means that Physical quantities have to comply with physical conditions – kinetic energy,
    density, for example cannot become negative, or other values cannot be super high! So in same cases, especially if your mesh quality is really bad, the discretisation of specific gradient terms is then overridden to improve boundedness and stability. Therefore, cellLimited scheme is proposed that limits the gradient such that when cell values are extrapolated to faces using the calculated gradient, the face values do not fall outside the bounds of values in surrounding cells. A limiting coefficient is specified after the underlying scheme for which 1 guarantees boundedness and 0 applies no limiting; 1 is invariably used.

    I hope that it makes a clarification in your mind!



    February 5, 2024 at 10:29 pm

    Hi Dr Bicer,

    Thank you so much for your explanation and your time. It is very clear now.

    Kind regards

  • Barış Bicer

    February 7, 2024 at 9:30 pm

    You are welcome Marco.

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