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Interface Discontinuities in Spectral-Element Simulations with Adaptive Mesh Refinement

2022; Springer Nature; Linguagem: Inglês

10.1007/978-3-031-20432-6_24

2197-7100

Daniele Massaro, Adam Peplinski, Philipp Schlatter,

Fluid Dynamics and Turbulent Flows

We investigate the discontinuities arising at non-conforming (or non-conformal) interfaces in spectral element method (SEM) simulations. The derivate terms are by definition discontinuous and interface instabilities are usually not visible with a conformal mesh and sufficient resolution. Using the adaptive mesh refinement (AMR) technique the initial coarse mesh is progressively refined according to an error indicator or estimator. In our case, the spectral error indicator (SEI) is adopted. This leads to non-conformal interfaces, where hanging nodes are introduced through h-refinement implemented in the SEM code Nek5000. We consider the flow in a three-dimensional periodic straight pipe and use the turbulent kinetic energy budget as an indicator for assessing discontinuities (wiggles). They involve first and second-order derivatives and represent a fixed point in the statistical analysis of this canonical flow. Looking at the results, we observe that our AMR implementation does not affect the interface discontinuities. The jumps in derivatives are uniquely related to an inadequately resolved mesh. Relying on an error-driven approach, the SEI produces a mesh that allows computing the TKE budgets in excellent agreement with the literature and ensures saving in grid points by a factor of 2.