# Conservation Vs Non-conservation Forms

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 July 9, 2013, 18:28 Conservation Vs Non-conservation Forms #1 New Member   CFDLearner Join Date: Jul 2013 Posts: 16 Rep Power: 6 Sponsored Links Hello, I understand mathematically how one can obtain the conservation equations in both the conservative and non-conservative forms. However, I am still confused, why do we call them conservative and non-conservative forms? can any one explain from a physical and mathematical point of view? Many threads deal with this question(http://www.cfd-online.com/Forums/mai...ive-forms.html, http://www.cfd-online.com/Forums/mai...tive-form.html), but none of them provides a good enough answer for me! If any one can provide some hints, I will be very grateful. Cheers.

 July 10, 2013, 03:34 #2 Senior Member     Philipp Join Date: Jun 2011 Location: Germany Posts: 1,297 Rep Power: 20 "non-conservative" form is the actual differential equation. If you integrate that equation over volume and use the divergence theorem to exchange all volume-divergence integrals by the area integral of the fluxes you get the "conservative" form. That's all. As I understand it, you call it "conservative" because it conserves the fluxes (also momentum fluxes) in your domain. Face flux of volume "a" and face flux of adjacent volume "b" are automatically the same. Edit: Also, the latter isn't always the case, when you just solve the differential equation in non-conservative form. If you have cylindrical coordinates, you will get different values for the flux from cell "a" to cell "b" in radial direction, depending on whether you calculate it in cell "a" or cell "b". However, this is not the case if you use the integral (conservative) form - also in cylindrical coordinates! FMDenaro, venkateshaero and Aeronautics El. K. like this. __________________ The skeleton ran out of shampoo in the shower.

July 10, 2013, 17:36
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 Originally Posted by RodriguezFatz "non-conservative" form is the actual differential equation. If you integrate that equation over volume and use the divergence theorem to exchange all volume-divergence integrals by the area integral of the fluxes you get the "conservative" form. That's all. As I understand it, you call it "conservative" because it conserves the fluxes (also momentum fluxes) in your domain. Face flux of volume "a" and face flux of adjacent volume "b" are automatically the same. Edit: Also, the latter isn't always the case, when you just solve the differential equation in non-conservative form. If you have cylindrical coordinates, you will get different values for the flux from cell "a" to cell "b" in radial direction, depending on whether you calculate it in cell "a" or cell "b". However, this is not the case if you use the integral (conservative) form - also in cylindrical coordinates!
Thanks RodriguezFatz for the interesting answer. For those who might be interested, I also obtained a differently explained answer at an other forum, and you can check it from the following links.
http://physics.stackexchange.com/que...direct=1#70540

Cheers.

 July 11, 2013, 05:14 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,415 Rep Power: 39 Actually, there are more concepts than a mere numeric issue... I think that that stays first of any consideration about numerics. The continuous form is conservative when it describes a balance of an estensive quantity, for example, you can see that the momentum conservative equation is d(rho*u)/dt + Div (rho*u u) = .... but the non-conservative form du/dt + u Grad u = .... expresses a balance of the accelerations, is not an evolution equation for the momentum....the same concept applies for the energy equation. Then you can talk about conservative or non-conservative discretizations ... sbaffini likes this.

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