Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

Peerenboom, Kim; Dijk, Jan van; Boonkkamp, J. H. M. ten Thije; Liu, L.; Goedheer, W. J.; Mullen, J.J.A.M. van der

doi:10.1016/j.jcp.2011.02.001

Cited by 19 publications

(25 citation statements)

References 20 publications

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“…, u m ) is the advection matrix, E = (ε ij ) the diffusion matrix and s the source term vector. This system is a model problem that can be derived from the continuity equations for a mixture combined with the Stefan-Maxwell equations for multi-species diffusion; see [13]. The vector of unknowns ϕ contains, e.g., the species mass fractions of a reacting flow or a plasma.…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

“…The derivation of the complete flux scheme in the next sections can be easily extended to nonuniform grids. In fact, we have already employed the homogeneous flux scheme on nonuniform grids to simulate multi-species diffusion [13].…”

Section: Finite Volume Discretizationmentioning

confidence: 99%

“…The governing equations for the mass fractions y i of the constituent species can be written as [13] …”

Section: Example 3 (Dissociation Of H 2 )mentioning

confidence: 99%

“…This means that the continuity equations for multi-component mixtures are coupled with the Stefan-Maxwell equations [7]. Peerenboom et al [13] derive from the continuity equations and the Stefan-Maxwell equations a system of conservation laws of advection-diffusion-reaction type, coupled through the diffusion term. The advection/drift velocities of the species in a mixture are often not the same, due to, e.g., different mobilities [15].…”

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confidence: 99%

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Extension of the Complete Flux Scheme to Systems of Conservation Laws

et al. 2012

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We present the extension of the complete flux scheme to advection-diffusionreaction systems. For stationary problems, the flux approximation is derived from a local system boundary value problem for the entire system, including the source term vector. Therefore, the numerical flux vector consists of a homogeneous and an inhomogeneous component, corresponding to the advection-diffusion operator and the source term, respectively. For time-dependent systems, the numerical flux is determined from a quasi-stationary boundary value problem containing the time-derivative in the source term. Consequently, the complete flux scheme results in an implicit semidiscretization. The complete flux scheme is validated for several test problems.

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Section: Finite Volume Discretizationmentioning

confidence: 99%

Section: Finite Volume Discretizationmentioning

confidence: 99%

“…The governing equations for the mass fractions y i of the constituent species can be written as [13] …”

Section: Example 3 (Dissociation Of H 2 )mentioning

confidence: 99%

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confidence: 99%

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Extension of the Complete Flux Scheme to Systems of Conservation Laws

et al. 2012

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“…We also allow the diffusion matrix to be discontinuous. The second problem is typical for multi-species diffusion in mixtures or plasmas; see for example [3] for a detailed account. Due to the nonlinear dependency of the diffusion process on pressure, temperature and plasma composition, diffusion matrices can vary rapidly in space.…”

Section: Introductionmentioning

confidence: 99%

Harmonic Complete Flux Schemes for Conservation Laws with Discontinuous Coefficients

Boonkkamp

Liu

Dijk

et al. 2014

Lecture Notes in Computational Science and Engineering

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Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems

Jüngel

Leingang

2019

Adv Comput Math

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A fully discrete Galerkin scheme for a thermodynamically consistent transient Maxwell-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the diffusive dynamics of an isothermal ionized fluid mixture with vanishing barycentric velocity. The equations are studied in a bounded domain, and different molar masses are allowed. The Galerkin scheme preserves the total mass, the nonnegativity of the particle densities, their boundedness, and satisfies the second law of thermodynamics in the sense that the discrete entropy production is nonnegative. The existence of solutions to the Galerkin scheme and the convergence of a subsequence to a solution to the continuous system is proved. Compared to previous works, the novelty consists in the treatment of the drift terms involving the electric field. Numerical experiments show the sensitive dependence of the particle densities and the equilibration rate on the molar masses.

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Mass conservative finite volume discretization of the continuity equations in multi-component mixtures

Cited by 19 publications

References 20 publications

Extension of the Complete Flux Scheme to Systems of Conservation Laws

Extension of the Complete Flux Scheme to Systems of Conservation Laws

Harmonic Complete Flux Schemes for Conservation Laws with Discontinuous Coefficients

Convergence of an implicit Euler Galerkin scheme for Poisson–Maxwell–Stefan systems

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