An overview of projection methods for incompressible flows

Guermond, Jean‐Luc; Minev, Peter; Shen, Jie

doi:10.1016/j.cma.2005.10.010

Cited by 1,115 publications

(1,073 citation statements)

References 46 publications

(33 reference statements)

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“…The (strongly nonlinear) mathematical model is solved via a staggered grid, fractional step, projection, finite volume method [37,38]. A book-length discussion of the method is available in [39].…”

Section: Solution Methodsmentioning

confidence: 99%

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Kivotides

2018

Phys. Rev. Fluids

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The interactions between vortex tubes and magnetic-flux rings in incompressible MHD are inves- [MHD]), and, via its convection by the velocity field, becomes turbulent, developing coherent structures of its own. Thus, it is conceptually important to understand the interactions between structures in the gauge and inertial fields, and the way these can help understand (in a structural way) some of the complexity of turbulent chaos, (b) the presence of the Lorentz force in the Navier-Stokes equations enables the depiction of wave phenomena in the latter (Alfven waves), which lead to novel (in comparison with incompressible turbulence)

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Section: Solution Methodsmentioning

confidence: 99%

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Kivotides

2018

Phys. Rev. Fluids

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“…Problem (2) is discretized in time with a Chorin-Temam projection scheme (see, e.g., (Guermond et al, 2006;Chorin, 1968;Temam, 1968)) in which velocity and pressure are solved separately in two substeps. Namely, let us denote with τ the time-step size, setting t n def = nτ for 1 ≤ n ≤ N .…”

Section: Numerical Approximationmentioning

confidence: 99%

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

Guibert

McLeod

Caiazzo

et al. 2014

Medical Image Analysis

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Abstract3D computational fluid dynamics (CFD) in patient-specific geometries provides complementary insights to clinical imaging, to better understand how heart disease, and the side effects of treating heart disease, affect and are affected by hemodynamics. This information can be useful in treatment planning for designing artificial devices that are subject to stress and pressure from blood flow. Yet, these simulations remain relatively costly within a clinical context. The aim of this work is to reduce the complexity of patient-specific simulations by combining image analysis, computational fluid dynamics and model order reduction techniques. The proposed method makes use of a reference geometry estimated as an average of the population, within an efficient statistical framework based on the currents representation of shapes. Snapshots of blood flow simulations performed in the reference geometry are used to build a POD (Proper Orthogonal Decomposition) basis, which can then be mapped on new patients to perform reduced order blood flow simulations with patient specific boundary conditions. This approach is applied to a data-set of 17 tetralogy of Fallot patients to simulate blood flow through the pulmonary artery under normal (healthy or synthetic valves with almost no backflow) and pathological (leaky or absent valve with backflow) conditions to better understand the impact of regurgitated blood on pressure and velocity at the outflow tracts.The model reduction approach is further tested by performing patient simulations under exercise and varying degrees of pathophysiological conditions based on reduction of reference solutions (rest and medium backflow conditions respectively).

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“…Alternatives to the coupled scheme such as e.g. incremental pressurecorrection scheme in rotational form that provides the consistent boundary condition for the pressure [21], [35] must be investigated. Possibility of using this approach in both domains and its impact on the computational efficiency will be investigated in the future.…”

Section: Discussionmentioning

confidence: 99%

“…Interesting alternatives include the use of non-singular approximations of the Laplacian matrix in the pressure Poisson's equation or the schemes based on consistent pressure boundary condition (e.g. incremental pressure-correction scheme in rotational form, see [21]). …”

Section: Finite Element Formulation For the Liquidmentioning

confidence: 99%

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An embedded approach for immiscible multi‐fluid problems

Ryzhakov

Jarauta

2015

Numerical Methods in Fluids

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An embedded formulation for the simulation of immiscible multi-fluid problems is proposed. The method is particularly designed for handling gas-liquid systems. Gas and liquid are modeled using the Eulerian and the Lagrangian formulation, respectively. The Lagrangian domain (liquid) moves on top of the fixed Eulerian mesh. The location of the material interface is exactly defined by the position of the boundary mesh of the Lagrangian domain. The individual fluid problems are solved in a partitioned fashion and are coupled using a Dirichlet-Neumann algorithm. Representation of the pressure discontinuity across the interface does not require any additional techniques being an intrinsic feature of the method. The proposed formulation is validated and its potential applications are shown.

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An overview of projection methods for incompressible flows

Cited by 1,115 publications

References 46 publications

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Interactions between vortex tubes and magnetic-flux rings at high kinetic and magnetic Reynolds numbers

Group-wise construction of reduced models for understanding and characterization of pulmonary blood flows from medical images

An embedded approach for immiscible multi‐fluid problems

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