Relation between energy conservation and numerical stability

[hoomanya]

Hi,
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!

 

[Khashishi]

You can have physical laws which conserve energy, but a numerical algorithm which fails to conserve energy.

 

[Strum]

Cant you just pick any straight forward discretization of a wave equation to have a non conservative solver for a conservative system?

Some times you can show that your numerical scheme is unconditionally stable by using a free energy approach but as far as I know this uses a monotonic decrease in the specified energy not conservation.