A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures

Wang, Yongqi; Hutter, Kolumban

doi:10.1007/s100350050023

Cited by 58 publications

(27 citation statements)

References 20 publications

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“…Based on drag relations proposed in the literature for multiphase granular materials, e.g. [55,56] and reviews [32,51], here we consider functions D in the following quasi-linear form in |v f − v s |:…”

Section: Drag Source Termsmentioning

confidence: 99%

A Roe-type scheme for two-phase shallow granular flows over variable topography

Pelanti¹,

Bouchut²,

2008

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Abstract.We study a depth-averaged model of gravity-driven flows made of solid grains and fluid, moving over variable basal surface. In particular, we are interested in applications to geophysical flows such as avalanches and debris flows, which typically contain both solid material and interstitial fluid. The model system consists of mass and momentum balance equations for the solid and fluid components, coupled together by both conservative and non-conservative terms involving the derivatives of the unknowns, and by interphase drag source terms. The system is hyperbolic at least when the difference between solid and fluid velocities is sufficiently small. We solve numerically the one-dimensional model equations by a high-resolution finite volume scheme based on a Roe-type Riemann solver. Wellbalancing of topography source terms is obtained via a technique that includes these contributions into the wave structure of the Riemann solution. We present and discuss several numerical experiments, including problems of perturbed steady flows over non-flat bottom surface that show the efficient modeling of disturbances of equilibrium conditions. Mathematics Subject Classification. 65M99, 76T25.

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Section: Drag Source Termsmentioning

confidence: 99%

A Roe-type scheme for two-phase shallow granular flows over variable topography

Pelanti¹,

Bouchut²,

2008

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“…Finally, we wish to reiterate that, although our analysis has been restricted to the continuum model of Goodman and Cowin, it carries over to other continuum models for both dry and fluid-saturated granular materials [3][4][5][6][7][8], in view of their similarities in structure.…”

Section: Discussionmentioning

confidence: 99%

“…Nevertheless, the two governing systems are completely equivalent, and thus, they share the same integrability condition. The particular form of the model of Goodman and Cowin employed herein has been favored over its original one because it allows for straightforward comparisons with other models for either dry or fluid-saturated granular materials; see, for example, [3][4][5][6][7][8].…”

Section: The Continuum Model For Dry Granular Flows Of Goodman and Cowinmentioning

confidence: 99%

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Gibbs free energy and integrability of continuum models for granular media at equilibrium

Varsakelis

2014

Continuum Mech. Thermodyn.

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In this letter, we address the problem of the integrability of a continuum model for granular media at equilibrium. By the means of a formal integrability analysis, we show that the equilibrium limit of such models can be cast into a gradient equation with zero right-hand side. In turn, this implies that the model of interest is inherently Frobenius integrable, in the absence of additional compatibility conditions. Moreover, the quantity inside the gradient is identified with the granular material's Gibbs free energy. Consequently, the integrability for the model at hand is equivalent to setting the Gibbs free energy of the granular material constant throughout the domain. In other words, integrability is equivalent to the definition of equilibrium employed in statistical physics.

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“…This will be done by application of a similar procedure to that used in phenomenological thermodynamics, based on the entropy inequality and the concept of Lagrange multipliers [45,52,71,72].…”

Section: Constitutive Equationsmentioning

confidence: 99%

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

Cieszko

2016

Meccanica

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A new macroscopic description of capillary transport of liquid and gas in porous materials is presented within the framework of multiphase continuum mechanics. It is assumed that unsaturated porous material form a macroscopic continuum composed of three constituents: gas, mobile liquid and capillary liquid, while the skeleton is rigid with an isotropic pore space structure. The capillary liquid forms a thin layer on the internal contact surface with the skeleton, is immoveable and contains the whole capillary energy. The remaining part of the liquid, surrounded by the layer of the capillary liquid and menisci, forms the constituent called mobile liquid. Both liquids exchange mass, momentum and energy in the vicinity of menisci surfaces during their motion, which is described by an additional macroscopic velocity field. A macroscopic scalar quantity is introduced, parametrizing changes of saturations, which for quasi static and stationary processes is equal to the capillary pressure. This quantity extends the dimensionality of the description of mechanical processes taking place in unsaturated porous materials. For the three fluid constituents of the medium, balance equations of mass and linear momentum and evolution equations for saturations are formulated. The constitutive relations for quantities describing mechanical processes in such a medium are proposed based on the dissipation inequality of mechanical energy for the whole system. A new approach is proposed, similar to that used in rational thermodynamics, based on entropy inequality analysis and the Lagrange multipliers method.

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A constitutive model of multiphase mixtures and its application in shearing flows of saturated solid-fluid mixtures

Cited by 58 publications

References 20 publications

A Roe-type scheme for two-phase shallow granular flows over variable topography

A Roe-type scheme for two-phase shallow granular flows over variable topography

Gibbs free energy and integrability of continuum models for granular media at equilibrium

Macroscopic description of capillary transport of liquid and gas in unsaturated porous materials

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