Numerical solution of a multi-component species transport problem combining diffusion and fluid flow as engineering benchmark

Böttcher, K.

doi:10.1016/j.ijheatmasstransfer.2009.09.038

Cited by 13 publications

(15 citation statements)

References 11 publications

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“…They can be recovered from ξ using Eq. (7). This leads to a rational function for each component of J i on any element of the mesh, which can be re-interpolated by a polynomial in P 2k at the element level.…”

Section: Standard Finite Element Formulation Of Maxwell-stefan Equationsmentioning

confidence: 99%

“…There are two variants of this test case. The first is the one originally proposed in [9] where all the binary diffusion coefficients are equal and the second proposed in [7] where all three binary diffusion coefficients are different. For this test case we take our gases to be N 2 , H 2 O and H 2 .…”

Section: Mazumder Test Casementioning

confidence: 99%

“…For this test case we take our gases to be N 2 , H 2 O and H 2 . For these test cases, mixed finite element methods were applied to the mass formulation of the Maxwell-Stefan equations as in [7]. This way the mass fractions, Y i , and mass fluxes, j i , could be computed directly.…”

Section: Mazumder Test Casementioning

confidence: 99%

“…The authors invert the Maxwell-Stefan equations to express the fluxes in terms of gradients of mass fractions before applying a finite element method using the software Femlab. In [7] a benchmark for diffusion and fluid flow is introduced. The model used relies on an inversion of the Maxwell-Stefan equations before applying a finite element method to find the solution.…”

Section: Introductionmentioning

confidence: 99%

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Mixed finite element methods for addressing multi-species diffusion using the Maxwell–Stefan equations

McLeod

Bourgault

2014

Computer Methods in Applied Mechanics and Engineering

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Section: Standard Finite Element Formulation Of Maxwell-stefan Equationsmentioning

confidence: 99%

Section: Mazumder Test Casementioning

confidence: 99%

Section: Mazumder Test Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mixed finite element methods for addressing multi-species diffusion using the Maxwell–Stefan equations

McLeod

Bourgault

2014

Computer Methods in Applied Mechanics and Engineering

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“…3 or 4 species, we could also reformulate the problem into an equation system of 2 or 3 species. Here, we apply the condition of the summation of the mole fractions n i=1 ξ i = 1 to the equation system and reformulate into a smaller system of (n − 1)-species without the constraints, see also [81].For the numerical schemes, we deal with such a reformulation in a lower dimensional coupled nonlinear equation system and apply the discretization and linearisation schemes.In the following, we discuss a complicate plasma model, which can be applied for plasma mixture problems. …”

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confidence: 99%

Engineering Applications

Geiser

2015

Multicomponent and Multiscale Systems

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In this chapter, we discuss the different engineering applications related to multicomponent and multiscale models, that occur in different categories (microscopic, mesoscopic and macroscopic). As we have described in the Introduction on p. xxv. That such models can be used as basic model to couple to more complicate models, describing materials, interfaces, etc., see Rosso and de Baas (Review of materials modelling: what makes a material function? Let me compute the ways, 2014, [1]).We deal with the following engineering applications with the two classified multiscaling approaches, see also the Introduction on p. xxv and in Fig. 5.1:• Different time-or spatial scales of same model (mono model or basic model).• Linking of different models (different models or multimodel).One of the main contributions to link the different scales and models together are the coupling techniques. In our motivation, such coupling of different time-and spatial scales or coupling of different models, need the suggested methods, e.g. multiscale methods, multicomponent methods, that allow a data transfer between the different scales and models. Such methods, we have introduced in the previous sections and now, we will close the gap between the theoretical discussions of methods and their applications to engineering problems. In such a stage, we have to adapt the numerical schemes with respect to the real-life properties and we obtain truly working multiscale approaches, that we solve the engineering complexities, see [1].Based on the real-life applications, we could study such helpful coupling of different scales or different models. Therefore, we overcome the gap of the recent problem in linking different scales of complicated engineering models in the industrial applications. Multiscale Methods for Langevin-Like EquationsAbstract In this section, we discuss multiscale methods, that solve Langevin-like equations, see [2]. The underlying ideas are to split into a deterministic and stochastic part of the Langevin equation, see [3]. The splitting methods are based on additive and iterative schemes, which are discussed with respect of their benefits and drawbacks, see [4]. We are motivated to reduce computational time for Coulomb collisions in plasma done in particle simulations. We extend splitting schemes, which are well-known in deterministic applications, to stochastic applications and modify the methods with respect to the stochastic terms. Such an idea allows to solve the multiscale behaviour of the coarse deterministic and fine stochastic timescales in an adequate computational time. Introduction of the ProblemIn the underlying problem, we are motivated to develop fast algorithms to solve the Coulomb collisions in plasma simulations, see [5].Recently in the literature, we can find two main ideas to deal with the Coulomb collisions in particle simulations. Here we have the following two ideas:• Binary algorithm: Particles in a finite cell selected into binary pairs. The collision is computed by the scattered velocities by an ...

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Applicability of the linearized theory of the Maxwell–Stefan equations

Weber

Bothe

2016

AIChE Journal

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The present article aims for a better understanding of the applicability of the linearized theory of the Maxwell-Stefan equations for multi-component diffusion. An analysis of the theory's accuracy is performed with respect to the classical two-bulb diffusion experiments by Duncan and Toor, from which the results are transferred to more general scenarios. It is shown that for an accurate linearized theory it is essential to have a quasi-stationary and quasi-one-dimensional flux, and also a so-called reference point. Two examples illustrating the theory's failure in case of unmet prerequisites are presented: a three-bulb configuration and a two-dimensional diffusion case. For the first setup the linearized theory results in negative concentrations, for the second it requires influxes at openings that are actually outlets.

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Numerical solution of a multi-component species transport problem combining diffusion and fluid flow as engineering benchmark

Cited by 13 publications

References 11 publications

Mixed finite element methods for addressing multi-species diffusion using the Maxwell–Stefan equations

Mixed finite element methods for addressing multi-species diffusion using the Maxwell–Stefan equations

Engineering Applications

Applicability of the linearized theory of the Maxwell–Stefan equations

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