A flux-corrected transport algorithm for handling the close-packing limit in dense suspensions

Kuzmin, Dmitri; Gorb, Yuliya

doi:10.1016/j.cam.2011.10.019

Cited by 17 publications

(23 citation statements)

References 14 publications

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“…In order to enforce the physical maximum principle α ≤ α M , the convective flux must be set to zero in regions where the maximum concentration is attained. In this paper, we achieve this effect using the 3D version of the flux-corrected transport algorithm developed in [10].…”

Section: Overshoot Limitermentioning

confidence: 99%

“…The continuity equation (3) is discretized using Q 1 elements. The maximum principle for volume fractions is enforced using algebraic flux correction [9,10]. The coupling with the Navier-Stokes solver is accomplished using outer iterations.…”

Section: Finite Element Discretizationmentioning

confidence: 99%

“…Given the maximum-packing bound α M , we eliminate nonphysical maxima using the following flux-based representation of the discrete problem [10] …”

Section: Overshoot Limitermentioning

confidence: 99%

“…The flux-corrected transport (FCT) algorithm proposed in [10] combines the idea of Leiderman and Fogelson [15] with algebraic flux correction [9]. Instead of modifying the convective flux at the continuous level, we decompose the discretized convective term into numerical fluxes and limit the magnitude of these fluxes so as to get rid of unrealistic maxima.…”

Section: Introductionmentioning

confidence: 99%

“…In the original publication [10], we applied the overshoot limiter to a 2D implosion problem with a prescribed velocity field. In the present paper, we use the same strategy to enforce the maximum principle for volume fractions in 3D mixture models of particulate flows.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Finite element simulation of three-dimensional particulate flows using mixture models

Gorb

Mierka

Rivkind

et al. 2014

Journal of Computational and Applied Mathematics

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In this paper, we discuss the numerical treatment of three-dimensional mixture models for (semi-)dilute and concentrated suspensions of particles in incompressible fluids. The generalized Navier-Stokes system and the continuity equation for the volume fraction of the disperse phase are discretized using an implicit high-resolution finite element scheme, and maximum principles are enforced using algebraic flux correction. To prevent the volume fractions from exceeding the maximum packing limit, a conservative overshoot limiter is applied to the converged convective fluxes at the end of each time step. A numerical study of the proposed approach is performed for 3D particulate flows over a backward-facing step and in a lid-driven cavity.

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Section: Overshoot Limitermentioning

confidence: 99%

Section: Finite Element Discretizationmentioning

confidence: 99%

“…Given the maximum-packing bound α M , we eliminate nonphysical maxima using the following flux-based representation of the discrete problem [10] …”

Section: Overshoot Limitermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite element simulation of three-dimensional particulate flows using mixture models

Gorb

Mierka

Rivkind

et al. 2014

Journal of Computational and Applied Mathematics

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A density‐dependent FEM‐FCT algorithm with application to modeling platelet aggregation

Danes

Leiderman

2019

Numer Methods Biomed Eng

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Upon injury to a blood vessel, flowing platelets will aggregate at the injury site, forming a plug to prevent blood loss. Through a complex system of biochemical reactions, a stabilizing mesh forms around the platelet aggregate forming a blood clot that further seals the injury. Computational models of clot formation have been developed to a study intravascular thrombosis, where a vessel injury does not cause blood leakage outside the blood vessel but blocks blood flow. To model scenarios in which blood leaks from a main vessel out into the extravascular space, new computational tools need to be developed to handle the complex geometries that represent the injury. We have previously modeled intravascular clot formation under flow using a continuum approach wherein the transport of platelet densities into some spatial location is limited by the platelet fraction that already reside in that location, i.e., the densities satisfy a maximum packing constraint through the use of a hindered transport coefficient. To extend this notion to extravascular injury geometries, we have modified a finite element method flux‐corrected transport (FEM‐FCT) scheme by prelimiting antidiffusive nodal fluxes. We show that our modified scheme, under a variety of test problems, including mesh refinement, structured vs unstructured meshes, and for a range of reaction rates, produces numerical results that satisfy a maximum platelet‐density packing constraint.

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Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

Sarraf Joshaghani,

Riviere

2023

Numerical Meth Engineering

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This paper presents a numerical study of immiscible, compressible two‐phase flows in porous media, that takes into account heterogeneity, gravity, anisotropy and injection/production wells. We formulate a fully implicit stable discontinuous Galerkin solver for this system that is accurate, that respects maximum principle for the approximation of saturation, and that is locally mass conservative. To completely eliminate the overshoot and undershoot phenomena, we construct a flux limiter that produces bound‐preserving elementwise average of the saturation. The addition of a slope limiter allows to recover a pointwise bound‐preserving discrete saturation. Numerical results show that both maximum principle and monotonicity of the solution are satisfied. The proposed flux limiter does not impact the local mass error and the number of nonlinear solver iterations.

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A flux-corrected transport algorithm for handling the close-packing limit in dense suspensions

Cited by 17 publications

References 14 publications

Finite element simulation of three-dimensional particulate flows using mixture models

Finite element simulation of three-dimensional particulate flows using mixture models

A density‐dependent FEM‐FCT algorithm with application to modeling platelet aggregation

Bound‐preserving discontinuous Galerkin methods for compressible two‐phase flows in porous media

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