A physically consistent weakly compressible high-resolution approach to underresolved simulations of incompressible flows

Schranner, Felix S.; Hu, Xiangyu; Adams, Nikolaus A.

doi:10.1016/j.compfluid.2013.06.034

Cited by 19 publications

(4 citation statements)

References 42 publications

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“…Following the naming used in Ghia et al [1982], we consider the primary vortex, the top-left vortex (TL), the bottom-left vortex region (BL), and the bottom-right vortex region (BR). Although the methods and equations solved differ considerably (the authors use finite differences with multigrid and they solve a vorticity-stream function formulation) we find an overall good agreement with the reference Ghia et al [1982] and with other incompressible NSE solvers Schranner et al [2013], with an absolute difference less than 5 × 10 −2 in all quantities except for the vorticity in the highest Reynolds number case because of the under-resolution. In very small vortices (e.g.…”

Section: Lid Driven Cavitysupporting

confidence: 52%

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A high–order discontinuous Galerkin multiphase flow solver for industrial applications

Torrico¹

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This thesis investigates models and simulation techniques to solve multiphase flows. Applications for multiphase flows encompasses chemical and process technology, power generation, nuclear reactor safety, or oil and gas. We concentrate on developing models that allow for varying flow morphologies (e.g. both a polydisperse bubbly flow and a fully separated flow) as those present in crude oil transport in pipes. Additionally, we want to retain most chemical phenomena as the phase separation of immiscible fluids, i.e., the coalescence and growth of stable separated phases from an initially mixed state, as well as other fundamental properties such as phases (mass) conservation.We model multiphase phenomena using phase field methods. Phase field (or diffuse interface) methods, as opposed to the sharp interface methods, consider a finite, yet thin, thickness of the interface that separates the two fluids. Therefore, the thermodynamic properties (e.g. the density) vary smoothly across the interface. From the available phase field methods, we solve the Cahn-Hilliard equation, which naturally retains the phase separation phenomena from the minimization of a free-energy, and additionally is phase-conserving.The Cahn-Hilliard equation is coupled with the incompressible Navier-Stokes equations. This is a two-way coupling, since the Cahn-Hilliard governs the density of the Navier-Stokes flow, and also introduces capillary forces at the interfaces. Then, the Navier-Stokes equations modify the Cahn-Hilliard equation to transport the phases with its velocity field. To obtain an efficient model, we relax the incompressibility constraint with an artificial compressibility model, that hyperbolizes the system providing an evolution equation for the pressure. In this thesis, we construct the approximation of two multiphase models: an provably stable two-phase NS/CH system, and a (non provably stable) three-phase NS/CH system.We approximate the models with the high-order Discontinuous Galerkin Spectral Element Method (DGSEM). The DGSEM is chosen since the schemes are arbitrarily high-order accurate, they handle unstructured curvilinear meshes, and they have been widely used to solve hyperbolic/parabolic systems. From the different DGSEM variants, we use the DGSEM with Gauss-Lobatto points, since it allows us to construct schemes that are provably stable. The parabolic systems studied in this thesis involve non-linear terms that can easily make the scheme unstable. We include a thourough vii viii study of the errors incurred to construct schemes that are provably stable.To study the stability of the proposed schemes, we first study two simplified cases: provably stable approximations of the incompressible Navier-Stokes equations with variable density and artificial compressibility, and the standalone version (i.e. without fluid motion) of the Cahn-Hilliard equations. Then, we combine the findings to construct a provably stable approximation of the two-phases incompressible Navier-Stokes/Cahn-Hilliard system. Finally, we also construct...

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Section: Lid Driven Cavitysupporting

confidence: 52%

“…We discretize the domain Ω = [0, 1] 2 into a 20×20 Cartesian grid, and we use a polynomial order N = 10. This produces a total of 220 2 degrees of freedom, which are fewer than the 257 2 points used in the DNS Ghia et al [1982]; Schranner et al [2013]. We apply no-slip 4.…”

Section: Lid Driven Cavitymentioning

confidence: 99%

A high–order discontinuous Galerkin multiphase flow solver for industrial applications

Torrico¹

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“…in smoothed particle hydrodynamics (SPH) [35,21] and the lattice Boltzmann method [9]. Moreover, the weakly compressible model has been applied recently to study a range of turbulent and non-turbulent incompressible flows [46]. From the original method for compressible multi-phase flow the present method inherits the property of mass conservation and the ability of handling large density ratios.…”

Section: Introductionmentioning

confidence: 98%

A conservative sharp interface method for incompressible multiphase flows

Luo

Adams

2015

Journal of Computational Physics

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“…The development of the Kelvin-Helmholtz instability and generation of two-dimensional turbulence are used in [23] for LES modeling by LBM. In [24], LES is used to refine the simulations done by Brown and Minion [3] for a layer at Reynolds number of Re = 10 000, while Schranner et al [25] investigated a high-order precision WENO scheme in which a truncation error is used as an implicit subgrid scale model (SGS).…”

Section: Introductionmentioning

confidence: 99%

Double shear layer evolution on the non-uniform computational mesh

Kulikov¹,

Son²

2021

Phys. Scr.

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This paper considers the problem of a thin shear layer evolution at Reynolds number rmRe = 400000 using the novel Compact Accurately Boundary Adjusting high-Resolution Technique (CABARET). The study is focused on the effect of the specific mesh refinement in the high shear rate areas on the flow properties under the influence of the developing instability. The original sequence of computational meshes (2562, 5122, 10242, 20482 cells) is modified using an iterative refinement algorithm based on the hyperbolic tangent. The properties of the solutions obtained are discussed in terms of the initial momentum thickness and the initial vorticity thickness, viscous and dilatational dissipation rates and also integral enstrophy. The growth rate for the most unstable mode depending on the mesh resolution is considered. In conclusion the accuracy of calculated mesh functions is estimated via L 1, L 2, L ∞ norms.

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A physically consistent weakly compressible high-resolution approach to underresolved simulations of incompressible flows

Cited by 19 publications

References 42 publications

A high–order discontinuous Galerkin multiphase flow solver for industrial applications

A high–order discontinuous Galerkin multiphase flow solver for industrial applications

A conservative sharp interface method for incompressible multiphase flows

Double shear layer evolution on the non-uniform computational mesh

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