1996
DOI: 10.1002/(sici)1097-0363(19960415)22:7<673::aid-fld373>3.0.co;2-o
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An Approximate Projection Scheme for Incompressible Flow Using Spectral Elements

Abstract: An approximate projection scheme based on the pressure correction method is proposed to solve the Navier–Stokes equations for incompressible flow. The algorithm is applied to the continuous equations; however, there are no problems concerning the choice of boundary conditions of the pressure step. The resulting velocity and pressure are consistent with the original system. For the spatial discretization a high‐order spectral element method is chosen. The high‐order accuracy allows the use of a diagonal mass ma… Show more

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Cited by 248 publications
(202 citation statements)
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“…The pressure term is treated by a projection method. 18 Due to the limitation of memory storage, an iterative technique is used and the linear system is solved based on a preconditioning conjugate gradient method. The energy equation is solved in a similar way.…”
Section: D Spectral Element Methodsmentioning
confidence: 96%
See 1 more Smart Citation
“…The pressure term is treated by a projection method. 18 Due to the limitation of memory storage, an iterative technique is used and the linear system is solved based on a preconditioning conjugate gradient method. The energy equation is solved in a similar way.…”
Section: D Spectral Element Methodsmentioning
confidence: 96%
“…This implicitly states that the pressure is near zero at the outflow boundary. 18 It should be noticed that the vortices leaving the computational domain will be influenced by the applied boundary condition at the outflow boundary. However, van de Vosse et al 20 showed that this influence is hardly noticeable.…”
Section: -3mentioning
confidence: 99%
“…Here we use the incremental pressure-correction method in rotational form, due to Timmermans et al [63], discussed also in [26,Sec. 3.3].…”
Section: Interface Forces and Equations Of Statementioning
confidence: 99%
“…We have introduced all the components of the mathematical model for the two-phase NavierStokes system involving surfactants and contact point dynamics, summarized as follows: a) Interface tracking using the domain-decomposition method in Section 2, involving the evolution equation (6) on each segment; b) Surfactant dynamics, which are governed by an advection-diffusion equation (10) in the local coordinates of each segment, as discussed in Section 3; c) Navier-Stokes equations (16, 17) using the pressure-correction method of Timmermans et al [63], given in Section 4; d) Contact-point boundary conditions (30) following Ren and E [49], to account for the contact point dynamics; e) Flow-interface coupling using an immersed boundary method [47], which amounts to computing (15), (22) and (23).…”
Section: Treating the Full Systemmentioning
confidence: 99%
“…The momentum equation in the form of Equation (9) is more commonly used in non-FE-based flow solvers [2,3]. Our experience shows that Equations (6) and (9) yield almost identical results using our current solver.…”
Section: Governing Equationsmentioning
confidence: 99%