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Magnus Svärd, University of Bergen Department of Mathematics
An alternative model for viscous and compressible flows.
It is well-known that the standard Navier-Stokes equations are mathematically very challenging and by looking closer at their derivation, it is clear that the Lagrangian frame, in which they are derived, is the cause. Mathematical difficulties aside, the Lagrangian derivation results in a number of physical inconsistencies. Therefore, I take a purely Eulerian viewpoint and derive an alternative model. It differs from the Navier-Stokes equations in the parabolic terms and includes mass diffusion.
I will present the validation cases that have been carried out for the new system to date. The results are indistinguishable from the standard Navier-Stokes equations. Moreover, codes for the new system run faster and coarser grids can often be used since they are less prone to produce spurious oscillations.
The modified set of equations has a much more tractable mathematical structure. Indeed, it is possible to demonstrate the existence of weak solutions by means of a finite volume scheme.