Analysis of Direct Three-Dimensional Parabolic Panel Methods

Poncet, Philippe

doi:10.1137/050625849

Cited by 9 publications

(11 citation statements)

References 32 publications

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“…Vortex methods can be purely Lagrangian by using Biot-Savart laws [4,24] or grid-particles hybrid methods [32]. Moreover, fluid-solid interaction can also be managed, beside by penalization, by immersed boundaries [79] in order to enforce continuity of the normal velocity field, and by vortical flux [78] in order to enforce continuity of its tangential components.…”

Section: Lagrangian Approach and Particle Methodsmentioning

confidence: 99%

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

et al. 2020

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This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of threedimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively-based on upscaled parameters such as surface area, solid volume, and effective reaction rate-and qualitatively-based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

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Section: Lagrangian Approach and Particle Methodsmentioning

confidence: 99%

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

et al. 2020

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“…By panel methods, we mean any linear method correcting the boundary conditions by means of a flux on the boundary neighborhood, most of the time with the potential solution of an integro-differential equation (see [47,45,15] for instance). In the present situation, panel methods are not efficient since the Green's kernel support, for the Laplace equation, fills the whole domain.…”

Section: Divergence-free Projection Algorithm and Boundary Conditionsmentioning

confidence: 99%

A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

Chatelin¹,

Poncet²

2013

SIAM J. Sci. Comput.

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This article presents a new approach for the resolution of large three-dimensional Stokes equations with variable viscosity fluids, coupled with transport equations. After building the model, we will write these equations in the context of highly viscous flows and penalization, in order to consider complex geometries moving in a fluid. From a mathematical point of view, the solutions show nonlinear dynamics. Beside the use of standard tools such as finite differences and staggered grids, we have built a new methodology based on large three-dimensional simulations, including operators splitting for an efficient use of fast solvers, multi-index fixed point methods, Lagrangian methods with fast and accurate grid-particle transfers, and the multiresolution description of variables. Among the main original aspects of this method, both accurate incompressibility and variable viscosity are treated in the same fixed point. Hence the computation costs for variable and constant viscosity flows are similar. Several examples are given to validate the order of convergence and conservation rates. Such models are used, among other examples, in biological computing at the cellular scale. The present article eventually describes the ciliated epithelium cells covering a mammal's lungs, beating in a mucus film. This study of human lung diseases explores the efficiency of the mucociliary clearance, a challenging problem in health sciences, especially for the investigation of cystic fibrosis and various chronic obstructive pulmonary diseases.

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“…Basically, Chorin's algorithm consists in creating a vorticity flux at boundaries, aiming at cancelling the spurious velocity u f . Using sources of vorticity with Gaussian spreading (the heat kernel) on the surrounding environment of body has been successfully used in the 1990s for two-dimensional problems [17,18], and accurate formulae in 3D has been recently established and analyzed [28]. Indeed, x b can be written under its fundamental formulation…”

Section: Treatment Of Viscous Effects In Vorticity Formulationmentioning

confidence: 99%

Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation

Poncet

2009

Journal of Computational Physics

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a b s t r a c tThis article presents numerical analysis and practical considerations for three-dimensional flow computation using an implicit immersed boundary method. The Euler equations, or half a step of the Navier-Stokes equations when using fractional step algorithms, are investigated in their vorticity formulation. The context of flow computation around an arbitrarily shaped body is especially investigated.In conventional immersed boundary methods using vorticity, singular vortex are dispatched over the body surface. In the present study, one prefers using sources of potential velocity field, dispatched on the body, whose nature is not vorticity. Such a formulation is compatible to the Euler equations. In practice, these sources of potential flow produce a velocity through this surface, aiming in practice at cancelling a flow-through velocity.This article focuses on the use of the source-to-flow-through linear application, its properties being the key points for fast convergence. Its self-adjointness, or lack thereof, conditioning and preconditioning aspects are investigated. It follows that computing a velocity field with no-flow-through conditions in complex geometry, when using the source-toflow-through linear application, can be achieved for 4/3 of the computational cost of standard Poisson equation in a Cartesian box.The robustness of immersed boundaries is especially interesting when used together with vortex-in-cell methods, well known for their robustness in time and their ability to compute accurately convective effects. A few examples, based on real-world geometries, illustrate the method capabilities.

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Analysis of Direct Three-Dimensional Parabolic Panel Methods

Cited by 9 publications

References 32 publications

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

A Hybrid Grid-Particle Method for Moving Bodies in 3D Stokes Flow with Variable Viscosity

Analysis of an immersed boundary method for three-dimensional flows in vorticity formulation

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