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Stabilized Discretizations for Fluid Flows and Coupled Poromechanics
Stabilized Discretizations for Fluid Flows and Coupled Poromechanics
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211151406
- ISBN
- 9798382234052
- DDC
- 531
- 서명/저자
- Stabilized Discretizations for Fluid Flows and Coupled Poromechanics
- 발행사항
- [Sl] : Stanford University, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 169 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 85-11, Section: B.
- 주기사항
- Advisor: Tchelepi, Hamdi.
- 학위논문주기
- Thesis (Ph.D.)--Stanford University, 2024.
- 초록/해제
- 요약In this thesis we develop various stabilized spatial discretizations for fluid flow problems and coupled poromechanics. We start by considering isogeometric collocation methods, which have arisen as an efficient alternative to Galerkin discretizations for high-order simulations of mechanics. We wish to apply theses schemes to incompressible flow problems, which requires the development of appropriate stabilization strategies. The classical SUPG method is extended to a collocation setting, which stabilizes spline collocation schemes in highly advective regimes. Simultaneously, we show that PSPG stabilization allows one to collocation mixed problems with an equal-order scheme. We show that these stabilizations are effective are removing instabilities while also retaining the inherent high-order accuracy of spline collocation methods when applied to the scalar advection, incompressible Stokes, and incompressible Navier-Stokes equations.Continuing the focus on isogeometric collocation methods, we move on to consider applications in compressible flows. Stabilization strategies are again needed, in this case so that the scheme can handle shocks. We extend a residual-based, artificial viscosity method for this purpose, and we develop a projection-inspired alternative to SUPG stabilization. Results on a variety of conservation laws show the robustness of the stabilized scheme, again without sacrificing accuracy on smooth problems.We then turn away from isogeometric collocation methods and pure fluid flow problems. The latter half of the thesis considers coupled poromechanics, or the coupled problem of flow through a deformable porous media. We consider spatial discretization using a coupled finite element - finite volume approach using piecewise linear and piecewise constant representations for mechanics and flow, respectively. While commonly used in practice, this discretization choice will exhibit pressure instabilities as undrained conditions are approached due to a lack of inf-sup stability. We show that pressure jump stabilization is effective at removing spurious pressure oscillations that appear in the nearly undrained burden regions when simulating CO2 sequestration, and study numerical properties such as the proper selection of stabilization constants for different meshes.Finally, we consider the performance of iteratively, or sequentially, coupled schemes for poromechanics when undrained regions are present. We clarify the relationship between fractional step schemes and the inf-sup condition, and in particular note that the fact that sequential schemes do not form or invert the full saddle-point matrix at any point is not enough to conclude that spurious pressure oscillations will not appear. However, pressure jump stabilization can be trivially extended to the fixed-stress method considered, and this both removes spurious pressure oscillations and improves the efficiency of the scheme.
- 일반주제명
- Mechanics
- 일반주제명
- Fluid mechanics
- 키워드
- Poromechanics
- 기타저자
- Stanford University.
- 기본자료저록
- Dissertations Abstracts International. 85-11B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211151406
■006m o d
■007cr#unu||||||||
■020 ▼a9798382234052
■035 ▼a(MiAaPQ)AAI31255827
■035 ▼a(MiAaPQ)wn737ys8898
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a531
■1001 ▼aAronson, Ryan Michael.
■24510▼aStabilized Discretizations for Fluid Flows and Coupled Poromechanics
■260 ▼a[Sl]▼bStanford University▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a169 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 85-11, Section: B.
■500 ▼aAdvisor: Tchelepi, Hamdi.
■5021 ▼aThesis (Ph.D.)--Stanford University, 2024.
■520 ▼aIn this thesis we develop various stabilized spatial discretizations for fluid flow problems and coupled poromechanics. We start by considering isogeometric collocation methods, which have arisen as an efficient alternative to Galerkin discretizations for high-order simulations of mechanics. We wish to apply theses schemes to incompressible flow problems, which requires the development of appropriate stabilization strategies. The classical SUPG method is extended to a collocation setting, which stabilizes spline collocation schemes in highly advective regimes. Simultaneously, we show that PSPG stabilization allows one to collocation mixed problems with an equal-order scheme. We show that these stabilizations are effective are removing instabilities while also retaining the inherent high-order accuracy of spline collocation methods when applied to the scalar advection, incompressible Stokes, and incompressible Navier-Stokes equations.Continuing the focus on isogeometric collocation methods, we move on to consider applications in compressible flows. Stabilization strategies are again needed, in this case so that the scheme can handle shocks. We extend a residual-based, artificial viscosity method for this purpose, and we develop a projection-inspired alternative to SUPG stabilization. Results on a variety of conservation laws show the robustness of the stabilized scheme, again without sacrificing accuracy on smooth problems.We then turn away from isogeometric collocation methods and pure fluid flow problems. The latter half of the thesis considers coupled poromechanics, or the coupled problem of flow through a deformable porous media. We consider spatial discretization using a coupled finite element - finite volume approach using piecewise linear and piecewise constant representations for mechanics and flow, respectively. While commonly used in practice, this discretization choice will exhibit pressure instabilities as undrained conditions are approached due to a lack of inf-sup stability. We show that pressure jump stabilization is effective at removing spurious pressure oscillations that appear in the nearly undrained burden regions when simulating CO2 sequestration, and study numerical properties such as the proper selection of stabilization constants for different meshes.Finally, we consider the performance of iteratively, or sequentially, coupled schemes for poromechanics when undrained regions are present. We clarify the relationship between fractional step schemes and the inf-sup condition, and in particular note that the fact that sequential schemes do not form or invert the full saddle-point matrix at any point is not enough to conclude that spurious pressure oscillations will not appear. However, pressure jump stabilization can be trivially extended to the fixed-stress method considered, and this both removes spurious pressure oscillations and improves the efficiency of the scheme.
■590 ▼aSchool code: 0212.
■650 4▼aMechanics
■650 4▼aFluid mechanics
■653 ▼aPoromechanics
■653 ▼aNavier-Stokes equations
■653 ▼aStabilization strategies
■653 ▼aFluid flow problems
■690 ▼a0346
■690 ▼a0204
■71020▼aStanford University.
■7730 ▼tDissertations Abstracts International▼g85-11B.
■790 ▼a0212
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17161510▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
