# non-linear terms in conservative or non-conservative form

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 May 24, 2012, 06:56 non-linear terms in conservative or non-conservative form #1 Senior Member   Join Date: Jun 2010 Posts: 111 Rep Power: 9 Hi, When solving an equation that involves non-linear terms such as in Burger's equations. Will the results be different if the conservative form of the term was used instead. Does it result in differences in terms of accuracy and stability. Thanks!

May 24, 2012, 11:28
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Filippo Maria Denaro
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 Originally Posted by Hooman Hi, When solving an equation that involves non-linear terms such as in Burger's equations. Will the results be different if the conservative form of the term was used instead. Does it result in differences in terms of accuracy and stability. Thanks!
yes, the discrete equations can drive to very different results (e.g. different wave propagation), as advice you must use always the conservative form!

 May 24, 2012, 11:39 #3 Senior Member   Join Date: Jun 2010 Posts: 111 Rep Power: 9 Thanks very much. On a slightly different note, if the non-lineaity was in an unsteady term for instance , how would one go about discretizing with respect to time? Say, Explicit Euler was being used, would it be possible to just find at the next time step and take the square root of that or is there more to it due to the non-linearity? I think this would reduce the accuracy but I am not really sure. Thanks again!

May 24, 2012, 11:46
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Filippo Maria Denaro
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Quote:
 Originally Posted by Hooman Thanks very much. On a slightly different note, if the non-lineaity was in an unsteady term for instance , how would one go about discretizing with respect to time? Say, Explicit Euler was being used, would it be possible to just find at the next time step and take the square root of that or is there more to it due to the non-linearity? I think this would reduce the accuracy but I am not really sure. Thanks again!
The equation for the kinetic energy equation has such a term and the equation is solved in time for the variable k=u^2 ....

 May 24, 2012, 13:51 #5 Senior Member   cfdnewbie Join Date: Mar 2010 Posts: 557 Rep Power: 13 Just as a quick addition to this: There's something called the "skew symmetric form" that avoids aliasing errors and consists of a combination of both formulations. In that sense, it might not always be advisable to use the conservative form alone, but on general, yes, use it rather than the non-con form! Hooman likes this.

 May 31, 2012, 12:37 #6 Senior Member   Join Date: Jun 2010 Posts: 111 Rep Power: 9 Thanks! Can I just ask more specifically why the conservative form is preferred. If you know any good reading material on this specific topic , please let me know.

May 31, 2012, 12:59
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Filippo Maria Denaro
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 Originally Posted by Hooman Thanks! Can I just ask more specifically why the conservative form is preferred. If you know any good reading material on this specific topic , please let me know.
any CFD book treating the FV approach is good for you, e.g. LeVeque, Ferziger & Peric, etc ...
then, many papers in journals are more specific in analyzing the properties of the conservative (divetgence) form in terms of accuracy and stability

 June 1, 2012, 00:20 #8 Super Moderator     Praveen. C Join Date: Mar 2009 Location: Bangalore Posts: 271 Blog Entries: 6 Rep Power: 11 If solutions are discontinuous, then conservative form should be used. For smooth solutions, the skew symmetric form can be used; it conserves energy and thats one of the reasons it is used. Hooman likes this.

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