符号付き距離関数を形状表現に用いた流体ソルバーの精度(距離と法線情報を利用した界面近傍における差分と補間の提案)

Translated title of the contribution: Numerical Accuracy of Fluid Solver Using Signed Distance Function for Shape Representation (Difference and Interpolation Methods near Interfaces Based on Distance and Normal)

沖田 浩平, 小野 謙二

Research output: Contribution to journalArticle

Abstract

A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2nd-order central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating three-dimensional Poiseuille flows. As the grid spacing decreases, L<sup>2</sup> and L<sup>∞</sup> norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2nd-order of accuracy in space.
Original languageUndefined/Unknown
Pages (from-to)1813-1825
Number of pages13
JournalNihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B
Volume77
Issue number781
DOIs
Publication statusPublished - 2011

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Interfaces (computer)
interpolation
Interpolation
laminar flow
Fluids
fluids
Boundary conditions
oscillating flow
boundary conditions
Oscillating flow
incompressible flow
Incompressible flow
viscous flow
Viscous flow
norms
mesh
velocity distribution
grids
spacing

Cite this

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title = "符号付き距離関数を形状表現に用いた流体ソルバーの精度(距離と法線情報を利用した界面近傍における差分と補間の提案)",
abstract = "A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2nd-order central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating three-dimensional Poiseuille flows. As the grid spacing decreases, L2 and L∞ norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2nd-order of accuracy in space.",
author = "浩平 沖田 and 謙二 小野",
year = "2011",
doi = "10.1299/kikaib.77.1813",
language = "未定義",
volume = "77",
pages = "1813--1825",
journal = "Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B",
issn = "0387-5016",
publisher = "The Japan Society of Mechanical Engineers",
number = "781",

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TY - JOUR

T1 - 符号付き距離関数を形状表現に用いた流体ソルバーの精度(距離と法線情報を利用した界面近傍における差分と補間の提案)

AU - 沖田, 浩平

AU - 小野, 謙二

PY - 2011

Y1 - 2011

N2 - A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2nd-order central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating three-dimensional Poiseuille flows. As the grid spacing decreases, L2 and L∞ norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2nd-order of accuracy in space.

AB - A fluid solver using signed distance function (SDF) for shape representation was developed based on the immersed boundary method to simulate incompressible viscous flows. The forcing velocities near boundary are extrapolated by trilinear interpolation with taking into account a boundary condition using SDF. SMAC method is employed for solving basic equations for unsteady incompressible flows. The equations are discretized in space by 2nd-order central difference method, where the discretization near boundary is improved by SDF to satisfy a Dirichlet boundary condition for velocity. The fluid solver was verified in both steady and oscillating three-dimensional Poiseuille flows. As the grid spacing decreases, L2 and L∞ norm of the error of the axial velocity profile respectively decrease by the order of 1.96 and 1.89 for the oscillating flow. Therefore, the fluid solver enables to analyze the Poiseuille flow using Cartesian mesh by 2nd-order of accuracy in space.

U2 - 10.1299/kikaib.77.1813

DO - 10.1299/kikaib.77.1813

M3 - 記事

VL - 77

SP - 1813

EP - 1825

JO - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B

JF - Nihon Kikai Gakkai Ronbunshu, B Hen/Transactions of the Japan Society of Mechanical Engineers, Part B

SN - 0387-5016

IS - 781

ER -