Title of article :
Energy inconsistency of Galerkin approximationsfor plane Couette flow
Author/Authors :
Rauh، نويسنده , , Alexander and Page، نويسنده , , Steffen and Spille، نويسنده , , Andreas، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2004
Abstract :
For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow.
Keywords :
Galerkin approximation , Energy balance , Navier-Stokes equations
Journal title :
Reports on Mathematical Physics
Journal title :
Reports on Mathematical Physics