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A Semi‐Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence.

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Title: A Semi‐Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence.
Authors: He, Xiaowei1 (AUTHOR) xiaowei@iscas.ac.cn, Liu, Shusen1 (AUTHOR), Guo, Yuzhong1 (AUTHOR), Shi, Jian2 (AUTHOR), Qiao, Ying1 (AUTHOR)
Source: Computer Graphics Forum. May2025, Vol. 44 Issue 2, p1-11. 11p.
Subjects: Compressible flow, Incompressible flow, Fluid dynamics, Iterative methods (Mathematics), Velocity
Abstract: In simulating fluids using position‐based dynamics, the accuracy and robustness depend on numerous numerical parameters, including the time step size, iteration count, and particle size, among others. This complexity can lead to unpredictable control of simulation behaviors. In this paper, we first reformulate the problem of enforcing fluid compressibility/incompressibility into an nonlinear optimization problem, and then introduce a semi‐implicit successive substitution method (SISSM) to solve the nonlinear optimization problem by adjusting particle positions in parallel. In contrast to calculating an intermediate variable, such as pressure, to enforce fluid incompressibility within the position‐based dynamics (PBD) framework, the proposed semi‐implicit approach eliminates the necessity of such calculations. Instead, it directly employs successive substitution of particle positions to correct density errors. This method exhibits reduced dependency to numerical parameters, such as particle size and time step variations, and improves consistency and stability in simulating fluids that range from highly compressible to nearly incompressible. We validates the effectiveness of applying a variety of different techniques in accelerating the convergence rate. [ABSTRACT FROM AUTHOR]
Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A Semi‐Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence.
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  Data: <searchLink fieldCode="JN" term="%22Computer+Graphics+Forum%22">Computer Graphics Forum</searchLink>. May2025, Vol. 44 Issue 2, p1-11. 11p.
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  Data: In simulating fluids using position‐based dynamics, the accuracy and robustness depend on numerous numerical parameters, including the time step size, iteration count, and particle size, among others. This complexity can lead to unpredictable control of simulation behaviors. In this paper, we first reformulate the problem of enforcing fluid compressibility/incompressibility into an nonlinear optimization problem, and then introduce a semi‐implicit successive substitution method (SISSM) to solve the nonlinear optimization problem by adjusting particle positions in parallel. In contrast to calculating an intermediate variable, such as pressure, to enforce fluid incompressibility within the position‐based dynamics (PBD) framework, the proposed semi‐implicit approach eliminates the necessity of such calculations. Instead, it directly employs successive substitution of particle positions to correct density errors. This method exhibits reduced dependency to numerical parameters, such as particle size and time step variations, and improves consistency and stability in simulating fluids that range from highly compressible to nearly incompressible. We validates the effectiveness of applying a variety of different techniques in accelerating the convergence rate. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Computer Graphics Forum is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1111/cgf.70043
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      – Code: eng
        Text: English
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        PageCount: 11
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    Subjects:
      – SubjectFull: Compressible flow
        Type: general
      – SubjectFull: Incompressible flow
        Type: general
      – SubjectFull: Fluid dynamics
        Type: general
      – SubjectFull: Iterative methods (Mathematics)
        Type: general
      – SubjectFull: Velocity
        Type: general
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      – TitleFull: A Semi‐Implicit SPH Method for Compressible and Incompressible Flows with Improved Convergence.
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            NameFull: He, Xiaowei
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            NameFull: Liu, Shusen
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            NameFull: Guo, Yuzhong
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            NameFull: Shi, Jian
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            – D: 01
              M: 05
              Text: May2025
              Type: published
              Y: 2025
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