Schröder, Philipp W.

[["dc.bibliographiccitation.firstpage","533"],["dc.bibliographiccitation.issue","11"],["dc.bibliographiccitation.journal","International Journal for Numerical Methods in Fluids"],["dc.bibliographiccitation.lastpage","556"],["dc.bibliographiccitation.volume","91"],["dc.contributor.author","Fehn, Niklas"],["dc.contributor.author","Kronbichler, Martin"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schröder, Philipp W."],["dc.date.accessioned","2020-03-02T16:00:09Z"],["dc.date.available","2020-03-02T16:00:09Z"],["dc.date.issued","2019"],["dc.description.abstract","The accurate numerical simulation of turbulent incompressible flows is a challenging topic in computational fluid dynamics. For discretisation methods to be robust in the under-resolved regime, mass conservation as well as energy stability are key ingredients to obtain robust and accurate discretisations. Recently, two approaches have been proposed in the context of high-order discontinuous Galerkin (DG) discretisations that address these aspects differently. On the one hand, standard ^2ehBbased DG discretisations enforce mass conservation and energy stability weakly by the use of additional stabilisation terms. On the other hand, pointwise divergence-free (\\operatorname{div})ehBconforming approaches ensure exact mass conservation and energy stability by the use of tailored finite element function spaces. The present work raises the question whether and to which extent these two approaches are equivalent when applied to under-resolved turbulent flows. This comparative study highlights similarities and differences of these two approaches. The numerical results emphasise that both discretisation strategies are promising for under-resolved simulations of turbulent flows due to their inherent dissipation mechanisms."],["dc.identifier.arxiv","1905.00142v1"],["dc.identifier.doi","10.1002/fld.4763"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63042"],["dc.language.iso","en"],["dc.notes.intern","DeepGreen Import"],["dc.relation.issn","0271-2091"],["dc.relation.issn","1097-0363"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","High-order DG solvers for under-resolved turbulent incompressible flows: A comparison of $L^2$ and $H(div)$ methods"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","629"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","SeMA Journal"],["dc.bibliographiccitation.lastpage","653"],["dc.bibliographiccitation.volume","75"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Linke, Alexander"],["dc.contributor.author","Lube, Gert"],["dc.date.accessioned","2020-03-02T16:11:38Z"],["dc.date.available","2020-03-02T16:11:38Z"],["dc.date.issued","2018"],["dc.description.abstract","Inf-sup stable FEM applied to time-dependent incompressible Navier–Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure–robustness ensures the fulfilment of a fundamental invariance principle and velocity error estimates are not corrupted by the pressure approximability. Secondly, Re-semi-robustness means that constants appearing on the right-hand side of kinetic and dissipation energy error estimates (including Gronwall constants) do not explicitly depend on the Reynolds number. Such estimates rely on the essential regularity assumption ∇u∈L1(0,T;L∞(Ω)) which is discussed in detail. In the sense of best practice, we review and establish pressure- and Re-semi-robust estimates for pointwise divergence-free H1-conforming FEM (like Scott–Vogelius pairs or certain isogeometric based FEM) and pointwise divergence-free H(div)-conforming discontinuous Galerkin FEM. For convection-dominated problems, the latter naturally includes an upwind stabilisation for the velocity which is not gradient-based."],["dc.identifier.doi","10.1007/s40324-018-0157-1"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63048"],["dc.language.iso","en"],["dc.relation.issn","2254-3902"],["dc.relation.issn","2281-7875"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Towards computable flows and robust estimates for inf-sup stable FEM applied to the time-dependent incompressible Navier–Stokes equations"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.firstpage","1010"],["dc.bibliographiccitation.issue","4"],["dc.bibliographiccitation.journal","Computers & Mathematics with Applications"],["dc.bibliographiccitation.lastpage","1028"],["dc.bibliographiccitation.volume","77"],["dc.contributor.author","Schröder, Philipp W."],["dc.contributor.author","John, Volker"],["dc.contributor.author","Lederer, Philip L."],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schöberl, Joachim"],["dc.date.accessioned","2020-11-18T15:42:55Z"],["dc.date.available","2020-11-18T15:42:55Z"],["dc.date.issued","2018-03-19"],["dc.description.abstract","Two-dimensional Kelvin-Helmholtz instability problems are popular examples for assessing discretizations for incompressible flows at high Reynolds number. Unfortunately, the results in the literature differ considerably. This paper presents computational studies of a Kelvin-Helmholtz instability problem with high order divergence-free finite element methods. Reference results in several quantities of interest are obtained for three different Reynolds numbers up to the beginning of the final vortex pairing. A mesh-independent prediction of the final pairing is not achieved due to the sensitivity of the considered problem with respect to small perturbations. A theoretical explanation of this sensitivity to small perturbations is provided based on the theory of self-organization of 2D turbulence. Possible sources of perturbations that arise in almost any numerical simulation are discussed."],["dc.identifier.arxiv","1803.06893v4"],["dc.identifier.doi","10.1016/j.camwa.2018.10.030"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/68807"],["dc.relation.issn","0898-1221"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dc.type.subtype","original_ja"],["dspace.entity.type","Publication"]]

[["dc.bibliographiccitation.issue","1"],["dc.bibliographiccitation.journal","Proceedings in Applied Mathematics and Mechanics"],["dc.bibliographiccitation.volume","19"],["dc.contributor.author","Lehrenfeld, Christoph"],["dc.contributor.author","Lube, Gert"],["dc.contributor.author","Schröder, Philipp W."],["dc.date.accessioned","2020-03-02T16:35:32Z"],["dc.date.available","2020-03-02T16:35:32Z"],["dc.date.issued","2019"],["dc.description.abstract","Nowadays, (high‐order) DG methods, or hybridised variants thereof, are widely used in the simulation of turbulent incompressible flow problems. For turbulence simulations, and especially in the practically relevant situation of strong under‐resolution, it is important to distinguish between the resolved physical dissipation rate and the contribution of numerical dissipation originating from the underlying method. In this note, a certain ambiguity related to such a decomposition for the viscous effects in a DG‐discretised fluid flow problem, which is due to the discontinuity of the approximate solution, is addressed. A novel but rather natural decomposition into ‘physical’ and ‘numerical’ viscous dissipation is proposed for a class of DG methods. Based on a typical 3D benchmark problem for decaying turbulence, its meaningfulness is confirmed numerically. In order to justify the term ‘dissipation’, both the physical and the numerical contributions for the proposed additive decomposition are provably non‐negative (possibly zero)."],["dc.identifier.doi","10.1002/pamm.201900049"],["dc.identifier.uri","https://resolver.sub.uni-goettingen.de/purl?gro-2/63061"],["dc.language.iso","en"],["dc.relation.issn","1617-7061"],["dc.relation.issn","1617-7061"],["dc.relation.orgunit","Institut für Numerische und Angewandte Mathematik"],["dc.relation.workinggroup","RG Lehrenfeld (Computational PDEs)"],["dc.title","Viscous dissipation in DG methods for turbulent incompressible flows"],["dc.type","journal_article"],["dc.type.internalPublication","yes"],["dspace.entity.type","Publication"]]