Lagrangian differencing dynamics for incompressible flows

Bašić, Josip; Degiuli, Nastia; Blagojević, Branko; Ban, Dario

doi:10.1016/j.jcp.2022.111198

Cited by 11 publications

(10 citation statements)

References 66 publications

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“…The factor

\alpha \ge 0

in (20) can be interpreted as a penalizing term for large velocity divergences and can greatly improve mass conservation 26 . Different expressions have been proposed for this parameter, 25,26,45 and here we consider simply

α = 𝒪 false(normalΔ t^{prefix- 1}

). An essential feature of consistent splitting methods is that no velocity projections are needed.…”

Section: Fractional‐step Methodsmentioning

confidence: 99%

“…Although the analysis of consistent splitting methods is not as developed as in other classical approaches, there is significant numerical evidence of their stability, robustness and accuracy. 22 Extensions have been recently proposed for more complex flow scenarios, such as with generalized Newtonian fluids, 23,24 free-surface 25 or two-phase 26 flows, and fluid-structure interaction. 27 In this article, we present the first formulation for viscoelastic fluids.…”

Section: Introductionmentioning

confidence: 99%

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Consistent splitting schemes for incompressible viscoelastic flow problems

Pacheco

Castillo

2023

Numerical Meth Engineering

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Viscoelastic fluids are highly challenging from the rheological standpoint, and their discretization demands robust, efficient numerical solvers. Simulating viscoelastic flows requires combining the Navier–Stokes system with a dynamic tensorial equation, increasing mathematical and computational demands. Hence, fractional‐step methods decoupling the calculation of the flow quantities are an attractive option. In consistent fractional‐step schemes, the splitting of the equations is derived from the continuous level, so that neither mass nor momentum balance is sacrificed. Thus, no corrections or velocity projections are needed, resulting in fewer algorithmic steps than other classical approaches. Moreover, consistency guarantees the absence of both numerical boundary layers and splitting errors, enabling high‐order accuracy in space and time. This article introduces the first consistent splitting methods for incompressible flows of viscoelastic fluids, for which arbitrary constitutive laws are allowed. We present the formulation and the algorithm, along with various numerical examples testing their accuracy. First‐, second‐ and third‐order backward‐differentiation schemes are numerically tested, and optimal convergence is confirmed for several spatial and temporal discretizations. Furthermore, good numerical stability is verified in challenging benchmark problems, including steady and time‐dependent solutions.

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“…The factor

\alpha \ge 0

α = 𝒪 false(normalΔ t^{prefix- 1}

). An essential feature of consistent splitting methods is that no velocity projections are needed.…”

Section: Fractional‐step Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Consistent splitting schemes for incompressible viscoelastic flow problems

Pacheco

Castillo

2023

Numerical Meth Engineering

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“…In contrast, the present work deals with volume conservation defects from other sources of the numerical scheme, and aims to perform an artificial point shifting to correct that. Another approach for volume conservation considered in the context of meshfree collocation methods is the so-called Position-Based Dynamics [2,3,4], which aims to keep the volume of each point constant as points move in a Lagrangian fashion. In contrast, here we aim to keep the global fluid volume constant.…”

Section: Types Of Meshfree Methodsmentioning

confidence: 99%

Volume and Mass Conservation in Lagrangian Meshfree Methods

Suchde¹,

Leithäuser²,

Kuhnert³

et al. 2023

Preprint

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Meshfree Lagrangian frameworks for free surface flow simulations do not conserve fluid volume. Meshfree particle methods like SPH are not mimetic, in the sense that discrete mass conservation does not imply discrete volume conservation. On the other hand, meshfree collocation methods typically do not use any notion of mass. As a result, they are neither mass conservative nor volume conservative at the discrete level. In this paper, we give an overview of various sources of conservation errors across different meshfree methods. The present work focuses on one specific issue: unreliable volume and mass definitions. We introduce the concept of representative masses and densities, which are essential for accurate post-processing especially in meshfree collocation methods. Using these, we introduce an artificial compression or expansion in the fluid to rectify errors in volume conservation. Numerical experiments show that the introduced frameworks significantly improve volume conservation behaviour, even for complex industrial test cases such as automotive water crossing.

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“…We now consider another 1-D dam-break test case that is a classical problem for benchmarking free-surface and thin-film flows, motivated by [47][48][49]. Here, the DDM is tested for an initial condition with a discontinuous height function.…”

Section: -D Dam-break Problemmentioning

confidence: 99%

A Discrete Droplet Method for Modelling Thin Film Flows

Bharadwaj,

Kuhnert,

Bordas

et al. 2022

Preprint

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In this paper, we present a new model to simulate the formation, evolution, and break-up of a thin film of fluid flowing over a curved surface. Referred to as the discrete droplet method (DDM), the model captures the evolution of thin fluid films by tracking individual moving fluid droplets. In contrast to existing thin-film models that solve a PDE to determine the film height, here, we compute the film height by numerical integration based on the aggregation of droplets. The novelty of this approach in using droplets makes it suitable for simulating the formation of fluid films, and modelling thin film flows on partially wetted surfaces. The DDM is a Lagrangian approach, with a force balance on each droplet governing the motion, and derivatives approximated using a smoothed particle hydrodynamics (SPH) like approach. The proposed model is thoroughly validated by comparing results against analytical solutions, against the results of the shallow-water equations for thin film flow, and also against results from a full 3-D resolved Navier-Stokes model. We also present the use of the DDM on an industrial test case. The results highlight the effectiveness of the model for simulations of flows with thin films.

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Lagrangian differencing dynamics for incompressible flows

Cited by 11 publications

References 66 publications

Consistent splitting schemes for incompressible viscoelastic flow problems

Consistent splitting schemes for incompressible viscoelastic flow problems

Volume and Mass Conservation in Lagrangian Meshfree Methods

A Discrete Droplet Method for Modelling Thin Film Flows

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