A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier–Stokes–Korteweg equations

Martínez, Abel; Ramírez, Luis; Nogueira, Xesús; Khelladi, Sofiane; Navarrina, F.

doi:10.1016/j.camwa.2019.07.021

Cited by 7 publications

(2 citation statements)

References 35 publications

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“…In this way, the time taken from design to analysis is reduced, resulting in dramatic efficiency gains. Currently, IGA has been applied successfully in numerous fields, such as solid mechanics [46][47][48] , heat transfer analysis [49][50][51] fluid mechanics [52][53][54] , fluid-structure interaction (FSI) simulations [55][56][57] etc. Up until now, research efforts have focused on establishing a practical framework for achieving the concept of 'design through analysis', but there are still no comprehensive studies of potential applications of computer-aided tolerancing (CAT).…”

Section: Introductionmentioning

confidence: 99%

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

Liu,

Li,

Liu

et al. 2024

Int J Adv Manuf Technol

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Geometric deviations and clamping constraints are the two major variation factors in thin-walled structure assembly processes. Geometric deviations are caused by inevitable uncertainties in manufacturing processes and have a significant impact on dimensional control for compliant assembly processes. Due to the flexibility of thin-walled structures, the clamping constraints during assembly greatly affect the compliant deformation of assembled structures. In this paper, a new method based on isogeometric analysis (IGA) considering geometric deviations and clamping constraints is proposed. The geometric deviations of thin-walled structures can be obtained by offsetting along the control points in an ideal part based on Nonuniform Rational B-Splines (NURBS), and the clamping constraints, such as fixture positioning deviations and connection matching deviations, are converted into displacement boundary conditions by the Lagrange multiplier method. Furthermore, the elastic force induced by initial geometric deviations is calculated using Kirchhoff-Love shell elements. Considering the coordination constraint relationship between shape closure and force closure in the compliant assembly process, a variation propagation model is developed using NURBS-based IGA. It integrates geometric deviations and compliant deformations into a unified mathematical representation framework by embedding exact geometry into assembly analysis. In addition, a numerical example is presented to demonstrate the accuracy and effectiveness of the developed method.

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Section: Introductionmentioning

confidence: 99%

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

Liu,

Li,

Liu

et al. 2024

Int J Adv Manuf Technol

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“…Likewise, there is a large variety of contributions on the numerical discretization, e.g. [10,11,12,13,14,15,16,17,18,19,20]. Numerical work on the NSK model has to face two fundamental issues which are not present in the NSE.…”

Section: Introductionmentioning

confidence: 99%

A Parabolic Relaxation Model for the Navier-Stokes-Korteweg Equations

Hitz,

Keim,

Munz

et al. 2019

Preprint

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The isothermal Navier-Stokes-Korteweg system is a classical diffuse interface model for compressible two-phase flow. However, the numerical solution faces two major challenges: due to a third-order dispersion contribution in the momentum equations, extended numerical stencils are required for the flux calculation. Furthermore, the equation of state given by a Van-der-Waals law, exhibits non-monotone behaviour in the two-phase state space leading to imaginary eigenvalues of the Jacobian of the first-order fluxes.In this work a lower-order parabolic relaxation model is used to approximate solutions of the classical NSK equations. Whereas an additional parabolic evolution equation for the relaxation variable has to be solved, the system involves no differential operator of higher as second order. The use of a modified pressure function guarantees that the first-order fluxes remain hyperbolic. Altogether, the relaxation system is directly accessible for standard compressible flow solvers.

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A Diffuse Interface Model for Cavitation, Taking Into Account Capillary Forces

Ait‐Ali,

Khelladi,

Bakir

et al. 2024

Numerical Methods in Fluids

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We consider the moving least squares method to solve compressible two‐phase water‐water vapor flow with surface tension. A diffuse interface model based on the Navier–Stokes and Korteweg equations is coupled with a suitable system of state equations that allows for a more realistic estimation of the pressure jump across the liquid–vapor interface as a function of temperature. We propose a simple formulation for computing the capillarity coefficient based on the surface tension and the thickness of the diffuse interface. A convergence analysis using pressure jump in the test case of static bubble is conducted to verify our solver. We present several numerical test cases that illustrate the ability of our model to reproduce qualitatively and quantitatively the effects of surface tension on cavitation bubbles in general situations.

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A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier–Stokes–Korteweg equations

Cited by 7 publications

References 35 publications

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

Compliant assembly variation modeling for thin-walled structures considering clamping constraints and geometric deviations based on isogeometric analysis

A Parabolic Relaxation Model for the Navier-Stokes-Korteweg Equations

A Diffuse Interface Model for Cavitation, Taking Into Account Capillary Forces

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