Lagrangian finite element method for free surface Navier‐Stokes flow using fractional step methods

Hayashi, Masahiro; Hatanaka, Katsumori; Kawahara, Mutsuto

doi:10.1002/fld.1650130702

Cited by 46 publications

(19 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The fractional step method [5] is applied to the incompressible Navier-Stokes equation. Velocity and pressure fields can be solved separately by the fractional method.…”

Section: Temporal Discretizationmentioning

confidence: 99%

An Analysis of the Flow around a Wind Propeller Using the Finite Element Method

Hoshiko

Kawahara

2012

Journal of Algorithms & Computational Technology

Self Cite

View full text Add to dashboard Cite

To analyze the wind flow around a wind propeller is important in wind engineering. The wind tunnel experiment has issue of cost and time. Additionally, because the shape of a wind propeller influences energy efficiency, wind tunnel experiments must be performed many times. The finite element method is one of the effective numerical approach to simulate wind propeller. But, it is necessary to generate the finite element mesh. To generate the 3-dimensional finite element mesh is almost impossible by hand. Generating any complicated 3-dimensional mesh automatically is very important. In this study, automatic 3-dimensional mesh generation is performed. Additionally, it is fluid-structure interaction analysis. In the finite element method, it is necessary to consider the moving boundaries. The purpose of this study, to generate the complicated 3-dimensional models and to analyze moving boundary problems. In this study, a re-meshing technique for moving boundaries is introduced, and to generate finite element mesh, the Delaunay method is applied. The character of this method is generating mesh from arbitrary nodal distribution of nodal points.

show abstract

“…The fractional step method [5] is applied to the incompressible Navier-Stokes equation. Velocity and pressure fields can be solved separately by the fractional method.…”

Section: Temporal Discretizationmentioning

confidence: 99%

An Analysis of the Flow around a Wind Propeller Using the Finite Element Method

Hoshiko

Kawahara

2012

Journal of Algorithms & Computational Technology

Self Cite

View full text Add to dashboard Cite

show abstract

“…To resolve the turbulence, the k-ω model of Wilcox [4] is used. The k-ω model consists of a transport equation for the turbulent kinetic energy k and the dissipation of the turbulent kinetic energy ω. Hayashi et al [5] applied a finite element analysis on the Lagrangian description, combined with a fractional step method to solve unsteady incompressible viscous fluid flow governed by Navier-Stokes equations. Lemos [6] solved the unsteady flow equations and updated the free surface in time using the volume of fluid method and modelled turbulence using the k-e closure equations.…”

Section: Introductionmentioning

confidence: 99%

“…φ is a scalar which is referred to as the correction potential base on the Fractional step method presented by Hayashi and Hatanaka [5]. By dividing the total time t into a number of short time increments ∆t, the equations of motion, continuity and kinematic boundary condition can be discretized into:…”

Section: Variational Equations In the Transformed Domainmentioning

confidence: 99%

Model of Flow Over Rippled Bed Using Arbitrary Lagrangian Eulerian Approach With Mapping Technique

Lohrasbi¹,

Lavaei²,

Lohrasbi³

et al. 2016

Topical Problems of Fluid Mechanics 2016

View full text Add to dashboard Cite

This article is about flow over rippled bed considering unsteady, incompressible viscous flow with free surface. The method solves the two dimensional Navier-Stokes equations for conservation of momentum, continuity equation, and full nonlinear kinematic free-surface equation for Newtonian fluids, as the governing equations in a vertical plane. A mapping was developed to trace the deformed free surface by transforming the governing equations from the physical domain to a computational domain. Finally, a numerical scheme is developed using finite element modelling technique to predict the flow over ripples with using Arbitrary Lagrangian Eulerian algorithm. The results are compared with other researches and gave good result.

show abstract

“…However, the imposition of these boundary conditions on the surfaces is difficult for numerical solutions because the free water surface moves and deforms with time. Conventional numerical methods using sophisticated boundary fitting mesh systems have been adopted and provided useful results (1) - (8) , but generally it is not easy to deform the mesh chasing the moving surface and many schemes based on the mesh deformation require highly complex numerical procedures.…”

Section: Introductionmentioning

confidence: 99%

Development of CIP-Reversed Weighted Residual Method for Water Flow with Free Water Surface and Arbitrary Topography (Algorithmic Improvements and Applications)

Nakamura

Kudo

Ishikawa

2004

JSME international journal. Ser. B, Fluids and thermal engineer

View full text Add to dashboard Cite

A new numerical method for solving a flow with a free water surface and an arbitrary topography is described. The method is based on the constrained interpolation profile (CIP) scheme and the finite-element method (FEM). Although advection terms are accurately solved using the conventional CIP scheme, nonadvection terms are solved by FEM. To solve nonadvection terms, the reversed weighted residual method (RWRM) based on FEM is proposed. Using the RWRM, surface boundary conditions can be imposed on an arbitrarily curved water surface appropriately even if a simple Cartesian mesh system is employed and the surface is not fitted to the boundaries of a computational mesh. Furthermore, in this paper, an algorithmic improvement in the pressure acceleration phase is proposed. By using the improved numerical procedure, the computational cost due to a matrix-solution can be reduced efficiently. The improved CIP-RWRM solver is applied to 2-D solutions to examine its efficiency and accuracy. The computational results show good agreements with the results calculated by other numerical methods for a multiphase flow.

show abstract

Lagrangian finite element method for free surface Navier‐Stokes flow using fractional step methods

Cited by 46 publications

References 9 publications

An Analysis of the Flow around a Wind Propeller Using the Finite Element Method

An Analysis of the Flow around a Wind Propeller Using the Finite Element Method

Model of Flow Over Rippled Bed Using Arbitrary Lagrangian Eulerian Approach With Mapping Technique

Development of CIP-Reversed Weighted Residual Method for Water Flow with Free Water Surface and Arbitrary Topography (Algorithmic Improvements and Applications)

Contact Info

Product

Resources

About