2019-08-26

On high Reynolds number flows, pressure-robustness and high-order methods

Dr. Alexander Linke, WIAS, Berlin

28 Aug 2019, 16:15–17:45; Location: S4|10-1

An improved understanding of the divergence-free constraint for the incompressible Navier-Stokes equations leads to the observation that a semi-norm and corresponding equivalence classes of forces are fundamental for their nonlinear dynamics. The recent concept of pressure-robustness allows to distinguish between space discretisations that discretise these equivalence classes appropriately or not. This contribution compares the accuracy of pressure-robust and non-pressure-robust 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, pressure-robust methods are shown to outperform comparable non-pressure-robust space discretisations. Indeed, pressure-robust methods of formal order kare comparably accurate than non-pressure-robust 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 non-trivial high Reynolds number flows. Connections to vortex-dominated flows are established. Thus, pressure-robustness 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 Seminar

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Technische Universität Darmstadt

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