A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method.
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| Title: | A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method. |
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| Authors: | Yu, Jidu1,2 (AUTHOR) jyubu@connect.ust.hk, Zhao, Jidong1 (AUTHOR) jzhao@ust.hk |
| Source: | International Journal for Numerical Methods in Engineering. 6/30/2026, Vol. 127 Issue 12, p1-38. 38p. |
| Subjects: | Material point method, Heat flux, Computer simulation, Neumann boundary conditions, Numerical analysis, Boundary value problems |
| Abstract: | In the material point method (MPM), accurate enforcement of thermal boundary conditions, particularly convective heat flux boundaries, is crucial for the reliable simulation of thermally coupled multiphysics processes, such as natural heat‐convection phenomena on Earth. However, the MPM typically employs a fixed, regular background mesh, whereas material boundaries are often complex and evolve over time. As a result, the boundaries do not generally align with the mesh, making boundary tracking and the consistent application of boundary conditions challenging. This study introduces a virtual heat flux method (VHFM) that enables the simple and accurate imposition of nonconforming heat flux boundary conditions in the MPM. The core idea is to construct a virtual flux field that satisfies the prescribed boundary conditions and converts boundary integrals into volume integrals. This approach eliminates the need for explicit boundary tracking while maintaining ease of implementation and computational efficiency. A unified formulation of the virtual flux field is further developed, allowing the method to be readily extended to general Neumann boundary conditions. Through a series of numerical experiments, the proposed method is shown to achieve high accuracy and convergence across a wide range of nonconforming boundary configurations, including curved, moving, and evolving boundaries. The VHFM provides a potential way for Neumann thermal boundary imposition in thermo‐mechanical and other multiphysics MPM frameworks. [ABSTRACT FROM AUTHOR] |
| Copyright of International Journal for Numerical Methods in Engineering 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.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194916335 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Yu%2C+Jidu%22">Yu, Jidu</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<i> jyubu@connect.ust.hk</i><br /><searchLink fieldCode="AR" term="%22Zhao%2C+Jidong%22">Zhao, Jidong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> jzhao@ust.hk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Engineering%22">International Journal for Numerical Methods in Engineering</searchLink>. 6/30/2026, Vol. 127 Issue 12, p1-38. 38p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Material+point+method%22">Material point method</searchLink><br /><searchLink fieldCode="DE" term="%22Heat+flux%22">Heat flux</searchLink><br /><searchLink fieldCode="DE" term="%22Computer+simulation%22">Computer simulation</searchLink><br /><searchLink fieldCode="DE" term="%22Neumann+boundary+conditions%22">Neumann boundary conditions</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: In the material point method (MPM), accurate enforcement of thermal boundary conditions, particularly convective heat flux boundaries, is crucial for the reliable simulation of thermally coupled multiphysics processes, such as natural heat‐convection phenomena on Earth. However, the MPM typically employs a fixed, regular background mesh, whereas material boundaries are often complex and evolve over time. As a result, the boundaries do not generally align with the mesh, making boundary tracking and the consistent application of boundary conditions challenging. This study introduces a virtual heat flux method (VHFM) that enables the simple and accurate imposition of nonconforming heat flux boundary conditions in the MPM. The core idea is to construct a virtual flux field that satisfies the prescribed boundary conditions and converts boundary integrals into volume integrals. This approach eliminates the need for explicit boundary tracking while maintaining ease of implementation and computational efficiency. A unified formulation of the virtual flux field is further developed, allowing the method to be readily extended to general Neumann boundary conditions. Through a series of numerical experiments, the proposed method is shown to achieve high accuracy and convergence across a wide range of nonconforming boundary configurations, including curved, moving, and evolving boundaries. The VHFM provides a potential way for Neumann thermal boundary imposition in thermo‐mechanical and other multiphysics MPM frameworks. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of International Journal for Numerical Methods in Engineering 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/nme.70371 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 38 StartPage: 1 Subjects: – SubjectFull: Material point method Type: general – SubjectFull: Heat flux Type: general – SubjectFull: Computer simulation Type: general – SubjectFull: Neumann boundary conditions Type: general – SubjectFull: Numerical analysis Type: general – SubjectFull: Boundary value problems Type: general Titles: – TitleFull: A Virtual Heat Flux Method for Simple and Accurate Neumann Thermal Boundary Imposition in the Material Point Method. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Yu, Jidu – PersonEntity: Name: NameFull: Zhao, Jidong IsPartOfRelationships: – BibEntity: Dates: – D: 30 M: 06 Text: 6/30/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 00295981 Numbering: – Type: volume Value: 127 – Type: issue Value: 12 Titles: – TitleFull: International Journal for Numerical Methods in Engineering Type: main |
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