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Consider the conservation laws for an isothermal linear incompressible flow governed by the mass and momentum equation. The kinetic energy equation is then solved to see if energy conserved. Can anyone tell me if once it is shown energy is conserved, it implies that convergence is obtained and that the numerical strategy is stable?

Are there any other cases, where some kind of an energy approach is utilised even though the governing equations are closed?

Thanks!

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# Relation between energy conservation and numerical stability

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