Viscoelastic flow around a confined cylinder using spectral/hp element methods

Claus, Susanne; Phillips, Timothy Nigel

doi:10.1016/j.jnnfm.2013.03.004

Cited by 39 publications

(52 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We implemented the method above using Camellia [3,4]; our implementation is available as part of Camellia's current stable release. The verification of our method was performed on the so-called confined cylinder problem, for which many results are available in the literature [9][10][11][12][45][46][47][48][49]. This is a simple two-dimensional problem where the fluid passes through a narrow channel with a centrally placed cylinder impeding its flow.…”

Section: Confined Cylinder Benchmarkmentioning

confidence: 99%

“…Some reasons for this could possibly include degeneration of solution regularity but-considering similar results in the literature-most likely indicates that the problem we are solving is no longer well-posed. Indeed, some researchers have indicated that the solution becomes transient in this interval [47]. Others have indicated that the problem may be entirely ill-posed in this range due to the model allowing infinite extension of the viscoelastic fluid under finite elongation rates [9,12].…”

Section: Creeping Flow With the Oldroyd-b Modelmentioning

confidence: 99%

See 1 more Smart Citation

An ultraweak DPG method for viscoelastic fluids

Keith

Knechtges

Roberts

et al. 2017

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

We explore a vexing benchmark problem for viscoelastic fluid flows with the discontinuous Petrov-Galerkin (DPG) finite element method of Demkowicz and Gopalakrishnan [1,2]. In our analysis, we develop an intrinsic a posteriori error indicator which we use for adaptive mesh generation. The DPG method is useful for the problem we consider because the method is inherently stable---requiring no stabilization of the linearized discretization in order to handle the advective terms in the model. Because stabilization is a pressing issue in these models, this happens to become a very useful property of the method which simplifies our analysis. This built-in stability at all length scales and the a posteriori error indicator additionally allows for the generation of parameter-specific meshes starting from a common coarse initial mesh. A DPG discretization always produces a symmetric positive definite stiffness matrix. This feature allows us to use the most efficient direct solvers for all of our computations. We use the Camellia finite element software package [3,4] for all of our analysis.Comment: 20 pages, 18 figures, 6 table

show abstract

Section: Confined Cylinder Benchmarkmentioning

confidence: 99%

Section: Creeping Flow With the Oldroyd-b Modelmentioning

confidence: 99%

An ultraweak DPG method for viscoelastic fluids

Keith

Knechtges

Roberts

et al. 2017

Journal of Non-Newtonian Fluid Mechanics

View full text Add to dashboard Cite

show abstract

“…The value that we use for the Newtonian case comes from an older hp finite element method[43]. At low elasticity where both[43] and[39] report results, the drag coefficients reported agree to at least two decimal places.…”

mentioning

confidence: 99%

“…This geometry is typically used to study polymeric fluids. The most accurate results currently available are from a recent high-order hp spectral element method[39], but a result for the Newtonian case is not provided in that study. The value that we use for the Newtonian case comes from an older hp finite element method[43].…”

mentioning

confidence: 99%

Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains

Stein

Guy

Thomases

2017

Journal of Computational Physics

View full text Add to dashboard Cite

The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and fails to converge pointwise for elements of the stress tensor. In a previous work we introduced the Immersed Boundary Smooth Extension (IBSE) method, a variation of the IB method that achieves high-order accuracy for elliptic PDE by smoothly extending the unknown solution of the PDE from a given smooth domain to a larger computational domain, enabling the use of simple Cartesian-grid discretizations. In this work, we extend the IBSE method to allow for the imposition of a divergence constraint, and demonstrate high-order convergence for the Stokes and incompressible Navier-Stokes equations: up to third-order pointwise convergence for the velocity field, and second-order pointwise convergence for all elements of the stress tensor. The method is flexible to the underlying discretization: we demonstrate solutions produced using both a Fourier spectral discretization and a standard second-order finite-difference discretization.

show abstract

“…Wu and Shu [7] proposed a local domain-free discretization method that is able to simulate flow around an oscillating cylinder easier due to its advantage of handling the boundary. Claus and Phillips [8] used spectral/hp element methods to study the flow around a confined cylinder. The nonconforming spectral element method and adaptive meshes method were tested by Hsu et al [9], demonstrating its feasibility on curve surfaces of cylinder.…”

Section: Introductionmentioning

confidence: 99%

Numerical Modeling of Wave-Current Flow around Cylinders Using an Enhanced Equilibrium Bhatnagar-Gross-Krook Scheme

Xing

Liu

Ding

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Flow around cylinders is a classic issue of fluid mechanics and it has great significance in engineering fields. In this study, a twodimensional hydrodynamic lattice Boltzmann numerical model is proposed, coupling wave radiation stress, bed shear stress, and wind shear stress, which is able to simulate wave propagation of flow around cylinders. It is based on shallow water equations and a weight factor is applied for the force term. An enhanced equilibrium Bhatnagar-Gross-Krook (BGK) scheme is developed to treat the wave radiation stress term in collision step. This model is tested and verified by two cases: the first case is the flow around a single circular cylinder, where the flow is driven by current, wave, or both wave and current, respectively, and the second case is the solitary waves moving around cylinders. The results illustrate the correctness of this model, which could be used to analyze the detailed flow pattern around a cylinder.

show abstract

Viscoelastic flow around a confined cylinder using spectral/hp element methods

Cited by 39 publications

References 22 publications

An ultraweak DPG method for viscoelastic fluids

An ultraweak DPG method for viscoelastic fluids

Immersed Boundary Smooth Extension (IBSE): A high-order method for solving incompressible flows in arbitrary smooth domains

Numerical Modeling of Wave-Current Flow around Cylinders Using an Enhanced Equilibrium Bhatnagar-Gross-Krook Scheme

Contact Info

Product

Resources

About