Bounded convection schemes for unstructured grids

Pržulj, Vlado; Basara, Branislav

doi:10.2514/6.2001-2593

Cited by 53 publications

(64 citation statements)

References 28 publications

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“…When constructing a face reconstruction scheme, in order to avoid unrealistic oscillations, especially in the volume fraction c i which is discontinuous in nature, the search for an acceptable compromise between accuracy and boundedness is a key point [17,47,72]. A practical way to introduce a new numerical implementation is to consider the Normalized Variable Diagram (NVD) analysis [16,51] and to follow the rules that enforce local monotonicity and the Convection Boundedness Criterion (CBC) [29].…”

Section: Nvd Diagram and Boundedness Considerationsmentioning

confidence: 99%

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

Wackers

Koren²,

Raven³

et al. 2011

Arch Computat Methods Eng

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The simulation of viscous free-surface water flow is a subject that has reached a certain maturity and is nowadays used in industrial applications, like the simulation of the flow around ships. While almost all methods used are based on the Navier-Stokes equations, the discretisation methods for the water surface differ widely. Many of these highly different methods are being used with success.We review three of these methods, by describing in detail their implementation in one particular code that is being used in industrial practice. The descriptions concern the principle of the method, numerical details, and the method's strengths and limitations. For each code, examples are given of its use. Finally, the methods are compared to determine the best field of application for each.The following surface descretisation methods are reviewed. First, surface fitting/mesh deformation in PARNAS-SOS, developed by MARIN; the description focuses on the efficient steady-state solution method of this code. Then surface capturing with Volume-of-Fluid in ISIS-CFD, developed by CNRS/Ecole Centrale de Nantes; the main topic of this review are the compressive flux discretisation schemes for the volume fraction that are used in this code. And finally, the Level Set method in SURF, developed by NMRI;

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Section: Nvd Diagram and Boundedness Considerationsmentioning

confidence: 99%

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

Wackers

Koren²,

Raven³

et al. 2011

Arch Computat Methods Eng

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“…Two implicit di erencing schemes can be used to evaluate the rate of change: the ÿrst-order accurate Euler and second-order accurate three time level scheme [21]. In order to calculate surface integrals over faces of arbitrary-shaped cells (see Figure 1) and account for them in Equation (22), one can choose to loop over all faces. This approach requires the face-based connectivity, i.e.…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…With that, f j = 0:5 and r j − r j is easily recalculated. For the convective transport in Equation (24), the second-order MINMOD scheme is used for the cell-face values as proposed by Przulj and Basara [22]. The simplest approach for the calculations of the cell gradients is to use the Gauss' Theorem, thus…”

Section: Numerical Proceduresmentioning

confidence: 99%

Simulation of single‐ and two‐phase flows on sliding unstructured meshes using finite volume method

Basara

Alajbegovic²,

Beader³

2004

Numerical Methods in Fluids

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SUMMARYThe paper presents an e cient ÿnite volume method for unstructured grids with rotating sliding parts composed of arbitrary polyhedral elements for both single-and two-phase ows. Mathematical model used in computations is based on the ensemble averaged conservation equations. These equations are solved for each phase and in case of single-phase ow reduce to the transient Reynolds-averaged Navier-Stokes (TRANS) equations. Transient ow induced by rotating impellers is thus resolved in time. The use of unstructured grids allows an easy and exible meshing for the entire ow domain. Polyhedral cell volumes are created on the arbitrary mesh interface placed between rotating and static parts. Cells within the rotating parts move each time step and the new faces are created on the arbitrary interfaces only, while the rest of the domain remain 'topologically' unchanged. Implicit discretization scheme allows a wide range of time-step sizes, which further reduce the computational e ort. Special attention is given to the interpolation practices used for the reconstruction of the face quantities. Mass uxes are recalculated at the beginning of each time step by using an interpolation scheme, which enhances the coupling between the pressure and velocity ÿelds. The model has been implemented into the commercially available CFD code AVL SWIFT (AVL AST, SWIFT Manual 3.1, AVL List GmbH, Graz, Austria, 2002). Single-phase ow in a mixing vessel stirred by a six-bladed Rushton-type turbine and two-phase ow in aerated stirred vessel with the four-blade Rushton impeller are simulated. The results are compared with the available experimental data, and good agreement is observed. The proposed algorithm is proved to be both stable and accurate for single-phase as well as for the two-phase ows calculations.

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“…Di usion terms arising from the Reynolds stress deÿnition and Bousinesq's formulation (u i u j k− iso ), can be discretized following the proposal of Przulj and Basara [28] (see also References [29][30][31]) by using the expression for the gradient of variable given as…”

Section: Numerical Proceduresmentioning

confidence: 99%

“…The ÿrst term (the upwind contribution) is treated implicitly, while the second, underlined term is calculated by using values from the previous iteration step and treated as an additional source. The ux limiter ' j is given by a higher order di erencing scheme used to ensure a bounded solution [28].…”

Section: Numerical Proceduresmentioning

confidence: 99%

A new hybrid turbulence modelling strategy for industrial CFD

Basara

Jakirlić

2003

Numerical Methods in Fluids

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SUMMARYThis paper presents a new strategy for turbulence model employment with emphasis on the model's applicability for industrial computational uid dynamics (CFD). In the hybrid modelling strategy proposed here, the Reynolds stress and mean rate of strain tensors are coupled via Boussinesq's formula as in the standard k-model. However, the turbulent kinetic energy is calculated as the sum of the normal Reynolds-stress components, representing the solutions of the appropriate transport equations. The equations governing the Reynolds-stress tensor and dissipation rate have been solved in the framework of a 'background' second-moment closure model. Furthermore, the structure parameter C has been re-calculated from a newly proposed functional dependency f(u i u j ; @U i =@x j ) rather than kept constant. This new deÿnition of C has been assessed by using direct numerical simulation (DNS) results of several generic ow conÿgurations featuring di erent phenomena such as separation, reattachment and rotation. Comparisons show a large departure of C from the commonly used value of 0.09. The model proposed is computationally validated in a number of well-proven uid ow benchmarks, e.g. backward-facing step, 180• turn-around duct, rotating pipe, impinging jet and three-dimensional (3D) Ahmed body. The obtained results conÿrm that the present hybrid model delivers a robust solution procedure while preserving most of the physical advantages of the Reynolds-stress model over simple kmodels. A low Reynolds number version of the hybrid model is also proposed and discussed.

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Bounded convection schemes for unstructured grids

Cited by 53 publications

References 28 publications

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

Free-Surface Viscous Flow Solution Methods for Ship Hydrodynamics

Simulation of single‐ and two‐phase flows on sliding unstructured meshes using finite volume method

A new hybrid turbulence modelling strategy for industrial CFD

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