Spectral analysis of the incompressible Navier-Stokes equations with different boundary conditions

• The influence of boundary conditions on the spectrum of the incompressible Navier-Stokes equations is studied. The spectra associated to different types of boundary conditions are derived using the Fourier-Laplace technique. In particular, the effect of various combinations of generalized in- and outgoing variables on the convergence to the steady state is investigated. The boundary conditions are analysed in both the continuous and semi-discrete problems. In the latter, high-order schemes in summation-by-parts form with weakly imposed boundary conditions are used to approximate the equations. Numerical calculations are performed and show that the discrete behaviour agrees with the theoretical analysis.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Incompressible flows

Navier-Stokes

Fourier-Laplace technique

summation-by-parts

weak boundary conditions

Publikations- och innehållstyp

vet (ämneskategori)

rap (ämneskategori)