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- Chiara Sorgentone, Cristina La Cognata, Jan Nordström
- J. Comput. Physics
- 2015

A new high order Arakawa-like method for the incompressible vorticity equation in two-dimensions has been developed. Mimetic properties such as skewsymmetry, energy and enstrophy conservations for the semi-discretization are proved for periodic problems using arbitrary high order summation-by-parts operators. Numerical simulations corroborate the… (More)

The nonlinear incompressible Navier-Stokes equations with boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the energy method. Both formulations are implemented in both strong and weak form and lead to an estimate of the velocity field. Equipped with energy bounding boundary… (More)

The advection equation is studied in a completely general two domain setting with different wave-speeds and a time-independent jump-condition at the interface separating the domains. Well-posedness and conservation criteria are derived for the initial-boundary-value problem. The equations are semidiscretized using a finite difference method on… (More)

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 inand outgoing variables on the convergence to the steady state is… (More)

v Sammanfattning p̊a svenska vii List of Papers ix Acknowledgements xi

A robust interface treatment for the discontinuous coefficient advection equation satisfying time-independent jump conditions is presented. The aim of the investigation is to show how the different concepts like well-posedness, conservation and stability are related. The equations are discretized using high order finite difference methods on Summation By… (More)

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