Effective boundary conditions for compressible flows over rough boundaries

Deolmi, Giulia; Dahmen, Wolfgang; Müller, Siegfried

doi:10.1142/s0218202515500323

Cited by 11 publications

(3 citation statements)

References 36 publications

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“…Third, rough domains pose considerable numerical challenge. This aspect has certainly driven the development of wall laws in a model reduction perspective; see for instance [1,32]. Other approaches are being elaborated, such as Direct Numerical Simulations [21], Lattice Boltzmann Methods that are adapted to intricate geometries [79] and Large Eddy Simulations [4,16] that in this context cause important parametrization issues of the small scales.…”

Section: Introductionmentioning

confidence: 99%

Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law

Higaki

Prange

2020

Calc. Var.

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In this paper we address the large-scale regularity theory for the stationary Navier-Stokes equations in highly oscillating bumpy John domains. These domains are very rough, possibly with fractals or cusps, at the microscopic scale, but are amenable to the mathematical analysis of the Navier-Stokes equations. We prove: (i) a large-scale Calderón-Zygmund estimate, (ii) a large-scale Lipschitz estimate, (iii) large-scale higherorder regularity estimates, namely, C 1,γ and C 2,γ estimates. These nice regularity results are inherited only at mesoscopic scales, and clearly fail in general at the microscopic scales. We emphasize that the large-scale C 1,γ regularity is obtained by using first-order boundary layers constructed via a new argument. The large-scale C 2,γ regularity relies on the construction of second-order boundary layers, which allows for certain boundary data with linear growth at spatial infinity. To the best of our knowledge, our work is the first to carry out such an analysis. In the wake of many works in quantitative homogenization, our results strongly advocate in favor of considering the boundary regularity of the solutions to fluid equations as a multiscale problem, with improved regularity at or above a certain scale.

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Section: Introductionmentioning

confidence: 99%

Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law

Higaki

Prange

2020

Calc. Var.

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“…approaches to effective boundary expressions include homogenization techniques [29] or (heterogeneous) multiscale modeling [30], as well as rough reactive walls concept [31], reviewed in [32], focus on the heterogeneity of the surface structure rather than on the heterogeneity of the reactivity. Such formulation allows for a mathematically closed form and renders numerical calculations unnecessary.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

Elucidating the impact of micro-scale heterogeneous bacterial distribution on biodegradation

Schmidt

Kreft

Mackay

et al. 2018

Advances in Water Resources

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Where a licence is displayed above, please note the terms and conditions of the licence govern your use of this document. When citing, please reference the published version. Take down policy While the University of Birmingham exercises care and attention in making items available there are rare occasions when an item has been uploaded in error or has been deemed to be commercially or otherwise sensitive.

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“…Besides the works above, there are many other works focusing on the flows over rough domains, such as the wall laws for the unsteady incompressible Navier-Stokes equations [4] and for the compressible flows [8,9]. Moreover, we refer the readers to references in this paper and the references therein for more results.…”

Section: Introductionmentioning

confidence: 99%

Convergence and stability of two-level penalty mixed finite element method for stationary Navier-Stokes equations

Huang

Feng

2013

Front. Math. China

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In this paper, we consider the higher-order convergence rates for the 2D stationary and non-stationary Navier-Stokes Equations over highly oscillating periodic bumpy John domains with C 2 regularity in some neighborhood of the boundary point (0,0). For the stationary case and any γ ∈ (0, 1/2), using the variational equation satisfied by the solution and the correctors for the bumpy John domains obtained by Higaki, Prange and Zhuge [12,13] after correcting the values on the inflow/outflow boundaries ({0} ∪ {1}) × (0, 1), we can obtain an O(ε 2−γ ) approximation in L 2 for the velocity and an O(ε 2−γ ) convergence rates in L 1 approximated by the so called Navier's wall laws, which generalized the results obtained by Jäger and Mikelić [14]. Moreover, for the non-stationary case, using the energy method, we can obtain an O(ε 2−γ + exp(−Ct)) convergence rate for the velocity in L 1x .

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Effective boundary conditions for compressible flows over rough boundaries

Cited by 11 publications

References 36 publications

Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law

Regularity for the stationary Navier–Stokes equations over bumpy boundaries and a local wall law

Elucidating the impact of micro-scale heterogeneous bacterial distribution on biodegradation

Convergence and stability of two-level penalty mixed finite element method for stationary Navier-Stokes equations

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