20190826
An improved understanding of the divergencefree constraint for the incompressible NavierStokes equations leads to the observation that a seminorm and corresponding equivalence classes of forces are fundamental for their nonlinear dynamics. The recent concept of pressurerobustness allows to distinguish between space discretisations that discretise these equivalence classes appropriately or not. This contribution compares the accuracy of pressurerobust and nonpressurerobust space discretisations for transient high Reynolds number flows, starting from the observation that in generalised Beltrami flows the nonlinear convection term is balanced by a strong pressure gradient. Then, pressurerobust methods are shown to outperform comparable nonpressurerobust space discretisations. Indeed, pressurerobust methods of formal order kare comparably accurate than nonpressurerobust methods of formal order 2kon coarse meshes. Investigating the material derivative of incompressible Euler flows, it is conjectured that strong pressure gradients are typical for nontrivial high Reynolds number flows. Connections to vortexdominated flows are established. Thus, pressurerobustness appears to be a prerequisite for accurate incompressible flow solvers at high Reynolds numbers. The arguments are supported by numerical analysis and numerical experiments.
Category: CE SeminarTechnische Universität Darmstadt
Graduate School CE
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D64293 Darmstadt

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