An Approximate Projection Scheme for Incompressible Flow Using Spectral Elements

Timmermans, Ljp Luc; Minev, Peter; Vosse, van de Fn Frans

doi:10.1002/(sici)1097-0363(19960415)22:7<673::aid-fld373>3.0.co;2-o

Cited by 245 publications

(202 citation statements)

References 20 publications

(2 reference 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%

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Lift-up process in a heated-cylinder wake flow

2006

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A three-dimensional flow transition behind a heated cylinder is analyzed at low Reynolds numbers: Re=O(100). Both visualizations and numerical simulations show that the transition manifests itself in the form of mushroom-type structures in the far wake and Λ-shaped structures in the near wake. The legs of the Λ-shaped structures coincide with streamwise vorticity regions. An intermediate stage is observed between the Λ-shaped structures and the escaping mushroom-type structures. This intermediate step is characterized by a lift-up process, which takes place in the center region between the legs and head of the Λ-shaped structures. As a result, hot fluid is being pulled out of the upper vortex core. Due to this lift-up process, mushroom-type structures are generated in the form of escaping vortex rings in the far wake.

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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%

Lift-up process in a heated-cylinder wake flow

2006

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“…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%

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

2014

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The flow behavior of many multiphase flow applications is greatly influenced by wetting properties and the presence of surfactants. We present a numerical method for two-phase flow with insoluble surfactants and contact line dynamics in two dimensions. The method is based on decomposing the interface between two fluids into segments, which are explicitly represented on a local Eulerian grid. It provides a natural framework for treating the surfactant concentration equation, which is solved locally on each segment. An accurate numerical method for the coupled interface/surfactant system is given. The system is coupled to the Navier-Stokes equations through the Immersed Boundary Method, and we discuss the issue of force regularization in wetting problems, when the interface touches the boundary of the domain. We use the method to illustrate how the presence of surfactants influences the behavior of free and wetting drops.

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“…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%

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

Wan

Aliabadi

Bigler

2009

Numerical Methods in Fluids

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SUMMARYWe have successfully extended our implicit hybrid finite element/volume (FE/FV) solver to flows involving two immiscible fluids. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centered FV method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. This updating strategy can be rigorously proven to be able to eliminate the unphysical pressure boundary layer and is crucial for the correct temporal convergence rate. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centers and the auxiliary variable at vertices. The fluid interface is captured by solving an advection equation for the volume fraction of one of the fluids. The same matrix-free FV method, as the one used for momentum equations, is used to solve the advection equation. We will focus on the interface sharpening strategy to minimize the smearing of the interface over time. We have developed and implemented a global mass conservation algorithm that enforces the conservation of the mass for each fluid.

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An Approximate Projection Scheme for Incompressible Flow Using Spectral Elements

Cited by 245 publications

References 20 publications

Lift-up process in a heated-cylinder wake flow

Lift-up process in a heated-cylinder wake flow

An explicit Eulerian method for multiphase flow with contact line dynamics and insoluble surfactant

A hybrid scheme based on finite element/volume methods for two immiscible fluid flows

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