A finite difference technique for simulating unsteady viscoelastic free surface flows

Tomé, Murilo Francisco; Mangiavacchi, Norberto; Cuminato, José Alberto; Castelo, A.; McKee, Sean

doi:10.1016/s0377-0257(02)00064-2

Cited by 139 publications

(179 citation statements)

References 33 publications

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“…The qualitative behavior described above has also been predicted using gridbased methods such as the finite difference method (FDM) of Tomé et al [15]. To evaluate the SPH method quantitatively, the results from the present work and those of Tomé et al [15] for the evolution of the width of the drop are compared in Figs.…”

Section: Comparison With the Results Of Tomé Et Al [15]mentioning

confidence: 90%

“…This effective area is called the support domain of the point x. Using the compact condition (15), integration over the entire problem domain is localized as the integration over the support domain of a given point. If the smoothing function W is an even function in x, by using the Taylor series expansion of f (x ) around x, it can be shown that, with the normalization condition (12), the integral representation of f (x) is of second order (h 2 ) accuracy.…”

Section: Sph Formulationsmentioning

confidence: 99%

“…Cormenzana et al [13] extended the CONNFESSITT idea [14] to the calculation of free surface flows. More recently Tomé et al [15] extended GENSMAC, a free surface fluid flow code based on the MAC idea, to viscoelastic flows and solved a number of viscoelastic free surface problems including impacting drops. The methods used in all the works mentioned above are loosely based upon grid-based numerical methods such as FDM and FEM and the techniques mentioned in the previous paragraph for treating moving free surfaces.…”

Section: Introductionmentioning

confidence: 99%

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A numerical study of the SPH method for simulating transient viscoelastic free surface flows

Fang

Owens

Tacher

et al. 2006

Journal of Non-Newtonian Fluid Mechanics

145

121

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The smoothed particle hydrodynamics (SPH) method is extended and tested for the numerical simulation of transient viscoelastic free surface flows. The basic equations governing the free surface flow of an Oldroyd-B fluid are considered and approximated by SPH. In particular, a drop of an Oldroyd-B fluid impacting a rigid plate is simulated. Results for a Newtonian fluid are also presented for comparison. It is found that the original SPH method, which has been successfully applied to the simulation of transient viscoelastic flows in bounded domains (such as the start-up flow between parallel plates), is unable to simulate the viscoelastic free surface flow considered here because of the so-called tensile instability. This instability leads to unrealistic fracture and particle clustering in fluid stretching and may eventually result in complete blowup of the simulation. Recent works have shown that in simulations of elastic solids the tensile instability can be removed by an artificial stress. Here we show that the same idea also works for viscoelastic fluids provided that the constant parameter entering in the definition of the artificial stress is properly chosen. Numerical results obtained are in good agreement with those simulated by a finite difference technique.

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Section: Comparison With the Results Of Tomé Et Al [15]mentioning

confidence: 90%

Section: Sph Formulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A numerical study of the SPH method for simulating transient viscoelastic free surface flows

Fang

Owens

Tacher

et al. 2006

Journal of Non-Newtonian Fluid Mechanics

145

121

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“…Several methods can be used to solve viscoelastic macroscopic constitutive equations in complex flows [4][5][6] and three-dimensional applications can be found in [7,8], but they did not take free surfaces into account. Two dimensional steady-state or transient viscoelastic flows with free surfaces have been studied for about 30 years, mainly applied to the die swell or filament stretching problems [9][10][11][12][13][14][15] and recently to extrudate swell or jet flow [16,17]. Most of the techniques are based on differential constitutive equations, since they are more efficient in CPU time and computational memory.…”

Section: Introductionmentioning

confidence: 99%

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

et al. 2011

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The original publication is available at http://www.springer.comInternational audienceTA Mixed Finite Element (MFE) method for 3D non-steady flow of a viscoelastic compressible fluid is presented. It was used to compute polymer injection flows in a complex mold cavity, which involves moving free surfaces. The flow equations were derived from the Navier-Stokes incompressible equations, and we extended a mixed finite element method for incompressible viscous flow to account for compressibility (using the Tait model) and viscoelasticity (using a Pom-Pom like model). The flow solver uses tetrahedral elements and a mixed velocity/pressure/extra-stress/density formulation, where elastic terms are solved by decoupling our system and density variation is implicitly considered. A new DEVSS-like method is also introduced naturally from the MINI-element formulation. This method has the great advantage of a low memory requirement. At each time slab, once the velocity has been calculated, all evolution equations (free surface and material evolution) are solved by a space-time finite element method. This method is a generalization of the discontinuous Galerkin method, that shows a strong robustness with respect to both re-entrant corners and flow front singularities. Validation tests of the viscoelastic and free surface models implementation are shown, using literature benchmark examples. Results obtained in industrial 3D geometries underline the robustness and the efficiency of the proposed method

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“…Reynolds são frequentes (por exemplo as aplicações em [162,161] por Prudhomme e Oden [131]. Outros estudos recentes têm sido realizados na estabilidade de esquemas implícitos aplicados às equações de Navier-Stokes: para fórmulas de diferenças atrasadas (backward dierentiation formulas) [83], para uma discretização totalmente implícita das equações de Navier-Stokes utilizando o método de Euler implícito [166], e para esquemas de Runge-Kutta [111].…”

Section: Esquemas Implícitos Na Metodologia Gensmacunclassified

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

Oishi¹

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Finalmente, e acima de tudo, a Deus pela minha vida.iii iv ResumoNo contexto do método MAC e baseado em esquemas de diferenças nitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre.Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretização explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável.Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção.Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para uidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres.Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW.A eciência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado. In the context of the MAC method and based on nite dierence schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface ows.In the stability analysis, the main result shows a precise stability restriction on the CrankNicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable.In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure elds; hence new projection methods for free surface ows need to be developed.The developed projection methods result in new methodologies for low Reynolds number free surface ows. It is also shown that the proposed methods can be applied for viscoelastic uids. New strategies are derived for obtaining second-order accurate projection methods for free surface ows.In addition to the theoretical results on the stability of numeri...

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A finite difference technique for simulating unsteady viscoelastic free surface flows

Cited by 139 publications

References 33 publications

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

A numerical study of the SPH method for simulating transient viscoelastic free surface flows

A new three-dimensional mixed finite element for direct numerical simulation of compressible viscoelastic flows with moving free surfaces

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

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