ALE/finite element modeling of an unconfined bubble plume in periodic domain: bubble shape and oscillation analysis

Oliveira, Gustavo P.; Anjos, Gustavo Rabello dos; Pontes, J.; Mangiavacchi, Norberto; Thome, John R.

doi:10.1007/s40430-015-0320-x

Cited by 1 publication

(2 citation statements)

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“…In the last step,

ℱ_{1} (t^{n}, A r, E o, f, g)

is only a generic functional form that embeds all the terms resulting from the uncoupled solution of Equation (1a) by a projection method 24,41 . This way, the update step becomes similar to the classical Euler's method for initial value problems.…”

Section: Methodsmentioning

confidence: 99%

“…The authors have been reaching considerable outcomes with moving mesh SL/FEM techniques based on a front-tracking arbitrary Lagrangian-Eulerian (ALE) approach to simulate the dynamics of multiple continuous and dispersed two-phase flow patterns with first-order SL integration. [23][24][25][26] This ensemble SL/ALE/FEM has advantages that come across many challenges faced in two-phase flow modeling. 27 A series of arguments support this assertion.…”

Section: Introductionmentioning

confidence: 99%

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One‐ and two‐step semi‐Lagrangian integrators for arbitrary Lagrangian–Eulerian‐finite element two‐phase flow simulations

Anjos

Oliveira

Mangiavacchi

et al. 2022

Numerical Methods in Fluids

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Semi‐Lagrangian (SL) schemes are of utmost relevance to simulate two‐phase flows where advection dominates. The combination of SL schemes with the finite element (FE) method and arbitrary Lagrangian–Eulerian (ALE) dynamic meshes yields a strong ingredient to deal with applications in Earth sciences, environmental engineering, and oil and gas industry whose numerical background is incipient. This article is intended to propose a second‐order time multistep SL/ALE/FE scheme to track particle trajectories traveling amidst single‐ or two‐phase incompressible flows both in fixed and moving mesh situations. The novel scheme is a BDF2‐like implementation that considers the mesh velocity as part of its backward‐in‐time integration. Trajectory departure points are searched through extrapolation and followed by a multistep interpolation corrector that works both for constant and varying time steps. A series of two‐phase benchmark flow simulations are carried out by using the cubic element to compare the performance of the new integrator against single‐step approximations as well as to analyze enhancements in representing the two‐phase flow dynamics. We use the 2D axisymmetric Navier–Stokes equations as underlying model. Error analyses, convergence tests, quantitative, and qualitative comparisons are presented and discussed to highlight the superior conservative feature of the novel scheme.

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“…In the last step,