A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh
A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain...
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| Published in: | International journal for numerical methods in fluids Vol. 93; no. 7; pp. 2065 - 2088 |
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| Main Authors: | , , , , , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Hoboken, USA
John Wiley & Sons, Inc
01.07.2021
Wiley Subscription Services, Inc |
| Subjects: | |
| ISSN: | 0271-2091, 1097-0363 |
| Online Access: | Get full text |
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| Abstract | A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at “solid centers” ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh. Several numerical tests are carried out to validate the proposed method. A second‐order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in‐line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in‐line oscillation of a circular cylinder, “flux correction” can eliminate the large spikes in the drag coefficient, and “including the body force in the momentum equation” helps suppress the small oscillations. For other tests, “storing the body force at the solid centers” has enormous impacts on the final results of moving boundary problems, “flux correction” has little effects and the necessity of “including the body force in the momentum equation” is case dependent.
Arbitrarily polyhedral mesh can be used for the proposed fictitious domain method. The sharpness of the solid–fluid boundary is acquired directly on the Eulerian background mesh without any additional mesh manipulation. Subgrid information is used for the discretization of the body force term to maintain the consistence, and for face flux correction to suppress the spurious force oscillations. |
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| AbstractList | A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at “solid centers” ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh. Several numerical tests are carried out to validate the proposed method. A second‐order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in‐line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in‐line oscillation of a circular cylinder, “flux correction” can eliminate the large spikes in the drag coefficient, and “including the body force in the momentum equation” helps suppress the small oscillations. For other tests, “storing the body force at the solid centers” has enormous impacts on the final results of moving boundary problems, “flux correction” has little effects and the necessity of “including the body force in the momentum equation” is case dependent. A consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at “solid centers” ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh. Several numerical tests are carried out to validate the proposed method. A second‐order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in‐line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in‐line oscillation of a circular cylinder, “flux correction” can eliminate the large spikes in the drag coefficient, and “including the body force in the momentum equation” helps suppress the small oscillations. For other tests, “storing the body force at the solid centers” has enormous impacts on the final results of moving boundary problems, “flux correction” has little effects and the necessity of “including the body force in the momentum equation” is case dependent. Arbitrarily polyhedral mesh can be used for the proposed fictitious domain method. The sharpness of the solid–fluid boundary is acquired directly on the Eulerian background mesh without any additional mesh manipulation. Subgrid information is used for the discretization of the body force term to maintain the consistence, and for face flux correction to suppress the spurious force oscillations. |
| Author | Shu, Qinglin Su, Junwei Zhang, Yigen Chai, Guoliang Wang, Le Gu, Zhaolin Yu, Chunlei |
| Author_xml | – sequence: 1 givenname: Guoliang orcidid: 0000-0002-1010-7018 surname: Chai fullname: Chai, Guoliang organization: Xi'an Jiaotong University – sequence: 2 givenname: Le surname: Wang fullname: Wang, Le organization: Xi'an Shiyou University – sequence: 3 givenname: Zhaolin orcidid: 0000-0002-1033-232X surname: Gu fullname: Gu, Zhaolin organization: Xi'an Jiaotong University – sequence: 4 givenname: Chunlei surname: Yu fullname: Yu, Chunlei organization: Shengli Oilfield Company, Sinopec group – sequence: 5 givenname: Yigen surname: Zhang fullname: Zhang, Yigen organization: Shengli Oilfield Company, Sinopec group – sequence: 6 givenname: Qinglin surname: Shu fullname: Shu, Qinglin organization: Shengli Oilfield Company, Sinopec group – sequence: 7 givenname: Junwei surname: Su fullname: Su, Junwei email: sujunwei@mail.xjtu.edu.cn organization: Xi'an Jiaotong University |
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| SubjectTerms | Algorithms Circular cylinders Collocation methods Continuity equation Cylinders Domains Drag coefficient Drag coefficients fictitious domain method Finite volume method Fluctuations Flux Magnetism Mathematical analysis Momentum Momentum equation moving boundary problems Numerical prediction OpenFOAM Oscillations polyhedral mesh sharp interface spurious force oscillations Tests |
| Title | A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh |
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