The numerical analysis of the flow on the smooth and nonsmooth boundaries by IBEM/DBIEM

Gang Xu, Guangwei Zhao, Jing Chen, Shuqi Wang, Weichao Shi

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Abstract

The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.
Original languageEnglish
Article number4131683
Number of pages14
JournalMathematical Problems in Engineering
Volume2019
DOIs
Publication statusPublished - 7 Jul 2019

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Boundary Integral Equation Method
Boundary integral equations
Boundary element method
Boundary Elements
Numerical analysis
Numerical Analysis
Boundary value problems
Analytical Solution
Intersection
Boundary Value Problem
Boundary Value Methods
Fluid
Fluids
Normal vector
Velocity Distribution
Inaccurate
Velocity distribution
Flow Field
Flow fields
Singularity

Keywords

  • boundary value problem
  • boundary element method
  • hydrodynamic force

Cite this

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title = "The numerical analysis of the flow on the smooth and nonsmooth boundaries by IBEM/DBIEM",
abstract = "The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.",
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language = "English",
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The numerical analysis of the flow on the smooth and nonsmooth boundaries by IBEM/DBIEM. / Xu, Gang; Zhao, Guangwei; Chen, Jing; Wang, Shuqi; Shi, Weichao.

In: Mathematical Problems in Engineering, Vol. 2019, 4131683, 07.07.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The numerical analysis of the flow on the smooth and nonsmooth boundaries by IBEM/DBIEM

AU - Xu, Gang

AU - Zhao, Guangwei

AU - Chen, Jing

AU - Wang, Shuqi

AU - Shi, Weichao

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N2 - The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

AB - The value of the tangential velocity on the Boundary Value Problem (BVP) is inaccurate when comparing the results with analytical solutions by Indirect Boundary Element Method (IBEM), especially at the intersection region where the normal vector is changing rapidly (named nonsmooth boundary). In this study, the singularity of the BVP, which is directly arranged in the center of the surface of the fluid computing domain, is moved outside the computational domain by using the Desingularized Boundary Integral Equation Method (DBIEM). In order to analyze the accuracy of the IBEM/DBIEM and validate the above-mentioned problem, three-dimensional uniform flow over a sphere has been presented. The convergent study of the presented model has been investigated, including desingularized distance in the DBIEM. Then, the numerical results were compared with the analytical solution. It was found that the accuracy of velocity distribution in the flow field has been greatly improved at the intersection region, which has suddenly changed the boundary surface shape of the fluid domain. The conclusions can guide the study on the flow over nonsmooth boundaries by using boundary value method.

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