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High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework

Diffusion in liquids; Flow of fluids; Lagrange multipliers; Laplace transforms; Mesh generation; Numerical methods; Poisson equation; Reynolds number; Continuity equations; Convection stability; Eulerian; Incompressible fluid flow; Moving particle semi-implicit; Moving particles; Particle distributi...

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Main Authors: Liu K.-S., Sheu T.W.-H., Hwang Y.-H., Ng K.-C.
Other Authors: 57195234742
Format: Article
Published: Elsevier B.V. 2023
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spelling my.uniten.dspace-231082023-05-29T14:37:48Z High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework Liu K.-S. Sheu T.W.-H. Hwang Y.-H. Ng K.-C. 57195234742 13302578200 7402311620 55310814500 Diffusion in liquids; Flow of fluids; Lagrange multipliers; Laplace transforms; Mesh generation; Numerical methods; Poisson equation; Reynolds number; Continuity equations; Convection stability; Eulerian; Incompressible fluid flow; Moving particle semi-implicit; Moving particles; Particle distributions; Second-order accuracy; Navier Stokes equations Owing to the fact that the Poisson equation of pressure for incompressible fluid flow is purely elliptic, it is therefore computationally improper to compute pressure on irregularly distributed moving particles as addressed in the recent Moving Particle with embedded Pressure Mesh (MPPM) method. In the current work, a modified MPPM method known as the Mixed Lagrangian�Eulerian (MLE) method is proposed for solving the incompressible Navier�Stokes equations. In the current velocity�pressure formulation, the momentum and continuity equations are approximated on the moving particles (Lagrangian) and the uniform Cartesian grid points, respectively. Meanwhile, the total derivative of velocity terms appeared in the momentum equations are estimated by simply advecting the moving particles, thereby eliminating the convection stability problem and increasing the flow accuracy without introducing false diffusion error. In the conventional Moving Particle Semi-implicit (MPS) and MPPM methods, numerical accuracies of the Laplacian and gradient operators are strongly dependent on the regularity of the particle distribution. In some implicit schemes, the gradient and Laplacian terms are of second-order and first-order accuracy, respectively. In the current work, the second-order accuracies of these differential terms exhibited on moving particles are realized by interpolating the derivative values from the uniform Cartesian grids calculated by using the high-order Combined Compact Difference (CCD) scheme. From the numerical results of Laplacian term approximation by using various numerical schemes, it is shown that the new MLE scheme is at least second-order accurate. The proposed Mixed Lagrangian�Eulerian (MLE) method can be easily applied to simulate fluid flow problems ranging from low to high Reynolds number. It is found that the numerical results compare well with the benchmark solutions. Moreover, it is more accurate than the recently proposed MPPM method. � 2017 Elsevier B.V. Final 2023-05-29T06:37:48Z 2023-05-29T06:37:48Z 2017 Article 10.1016/j.cma.2017.07.001 2-s2.0-85026363837 https://www.scopus.com/inward/record.uri?eid=2-s2.0-85026363837&doi=10.1016%2fj.cma.2017.07.001&partnerID=40&md5=16faf8851ccb58440c5d11f1631d3ad2 https://irepository.uniten.edu.my/handle/123456789/23108 325 77 101 Elsevier B.V. Scopus
institution Universiti Tenaga Nasional
building UNITEN Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tenaga Nasional
content_source UNITEN Institutional Repository
url_provider http://dspace.uniten.edu.my/
description Diffusion in liquids; Flow of fluids; Lagrange multipliers; Laplace transforms; Mesh generation; Numerical methods; Poisson equation; Reynolds number; Continuity equations; Convection stability; Eulerian; Incompressible fluid flow; Moving particle semi-implicit; Moving particles; Particle distributions; Second-order accuracy; Navier Stokes equations
author2 57195234742
author_facet 57195234742
Liu K.-S.
Sheu T.W.-H.
Hwang Y.-H.
Ng K.-C.
format Article
author Liu K.-S.
Sheu T.W.-H.
Hwang Y.-H.
Ng K.-C.
spellingShingle Liu K.-S.
Sheu T.W.-H.
Hwang Y.-H.
Ng K.-C.
High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
author_sort Liu K.-S.
title High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
title_short High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
title_full High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
title_fullStr High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
title_full_unstemmed High-order particle method for solving incompressible Navier�Stokes equations within a mixed Lagrangian�Eulerian framework
title_sort high-order particle method for solving incompressible navier�stokes equations within a mixed lagrangian�eulerian framework
publisher Elsevier B.V.
publishDate 2023
_version_ 1806423423238275072
score 13.211869

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