Numerical simulation of the transient flow behaviour in chemical reactors using a penalisation method

Schneider, Kai

doi:10.1016/j.compfluid.2004.09.006

Cited by 83 publications

(91 citation statements)

References 18 publications

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“…where ∆t n = t n − t n−1 [16]. For start-up a first order scheme is used, as two time steps are required to start a secondorder scheme.…”

Section: Explicit Implementation Of the Penalization Termmentioning

confidence: 99%

“…In addition to being physically motivated, this model is mathematically justified, since Angot et al [15] rigorously proved that the method converges to the Navier-Stokes equations combined with no-slip boundaries, when the porosity in the part of the domain corresponding to the boundaries is taken infinitesimally small. A first use of the method in combination with a pseudo-spectral Navier-Stokes solver was reported in [16]. An extensive validation of the method for three dimensional fixed and moving boundaries is reported in [17].…”

Section: Introductionmentioning

confidence: 99%

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Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

Moralès

Leroy

Bos

et al. 2014

Journal of Computational Physics

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A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two-and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analytical solutions. The test cases considered are two-dimensional Taylor-Couette flow, the z-pinch configuration, three dimensional Orszag-Tang flow, ohmic-decay in a periodic cylinder, three-dimensional Taylor-Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field.

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“…where ∆t n = t n − t n−1 [16]. For start-up a first order scheme is used, as two time steps are required to start a secondorder scheme.…”

Section: Explicit Implementation Of the Penalization Termmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

Moralès

Leroy

Bos

et al. 2014

Journal of Computational Physics

Self Cite

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show abstract

“…Such a simplification permits a massive reduction in solver development time, since it avoids the issues associated to the design and management of the grid, allowing for example the use of simple spectral solvers in Cartesian geometries [11,14,24]. The gain becomes even more substantial when the geometry is time-dependent, as in the case of moving obstacles [16,15], or when fluid-structure interaction is taken into account.…”

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confidence: 99%

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

2014

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Abstract. We report the results of a detailed study of the spectral properties of Laplace and Stokes operators, modified with a volume penalization term designed to approximate Dirichlet conditions in the limit when a penalization parameter, η, tends to zero. The eigenvalues and eigenfunctions are determined either analytically or numerically as functions of η, both in the continuous case and after applying Fourier or finite difference discretization schemes. For fixed η, we find that only the part of the spectrum corresponding to eigenvalues λ η −1 approaches Dirichlet boundary conditions, while the remainder of the spectrum is made of uncontrolled, spurious wall modes. The penalization error for the controlled eigenfunctions is estimated as a function of η and λ. Surprisingly, in the Stokes case, we show that the eigenfunctions approximately satisfy, with a precision O(η), Navier slip boundary conditions with slip length equal to √ η. Moreover, for a given discretization, we show that there exists a value of η, corresponding to a balance between penalization and discretization errors, below which no further gain in precision is achieved. These results shed light on the behavior of volume penalization schemes when solving the Navier-Stokes equations, outline the limitations of the method, and give indications on how to choose the penalization parameter in practical cases.

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“…The computational approach extends our previous work on the modelling of flows past rigid obstacles [2,3]. We consider either one or two flexible flat wings immersed in viscous incompressible fluid, see Fig.…”

Section: Computational Setup and Governing Equationsmentioning

confidence: 89%

“…The time integration is exact for the viscous term and an adaptive second order Adams-Bashforth scheme is used for the nonlinear term. The details of the fluid solver were reported earlier in [2,3].…”

Section: Computational Setup and Governing Equationsmentioning

confidence: 99%

Numerical Modelling of Flexible Heaving Foils

2013

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Abstract-We consider the effects of chordwise flexibility on the aerodynamic performance of flapping wings using numerical simulation. The twodimensional Navier-Stokes equations are solved using a Fourier pseudo-spectral method with no-slip boundary conditions imposed by the volume penalization method. The flexible wing is modelled with a non-linear beam equation. Our numerical simulations of heaving plates show that the maximum thrust is achieved at a stroke frequency lower than resonant, which is in agreement with experiments. The oscillatory part of the force only increases in amplitude when the frequency increases. We also consider aerodynamic interactions between two heaving foils. IndexTerms-Flapping flight, fluid-structure interaction, spectral method, volume penalization method.I.

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Numerical simulation of the transient flow behaviour in chemical reactors using a penalisation method

Abstract: ABSTRACT

Cited by 83 publications

References 18 publications

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

Approximation of the Laplace and Stokes operators with Dirichlet boundary conditions through volume penalization: a spectral viewpoint

Numerical Modelling of Flexible Heaving Foils

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