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Asymptotic and Non-Asymptotic Model Reduction for Kinetic Descriptions of Plasma
Asymptotic and Non-Asymptotic Model Reduction for Kinetic Descriptions of Plasma
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211152638
- ISBN
- 9798384096573
- DDC
- 530
- 서명/저자
- Asymptotic and Non-Asymptotic Model Reduction for Kinetic Descriptions of Plasma
- 발행사항
- [Sl] : University of Washington, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 191 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Shumlak, Uri;Hu, Jingwei.
- 학위논문주기
- Thesis (Ph.D.)--University of Washington, 2024.
- 초록/해제
- 요약Plasma dynamics are coupled across microscopic and macroscopic scales by a variety of nonlinear mechanisms. These include repartition of energy due to kinetic microinstabilities, suppression of fluid instabilities by kinetic stabilization effects, and other mechanisms. At the macroscopic scale plasmas are well-described by fluid equations, whose formal validity depends on the long-time regularization of the phase space distribution function by collisions and magnetic gyrotropization. However, accurately capturing multiscale coupling requires multiscale reduced models which are both efficient and accurate in transition regimes. These regimes, where either collisional or magnetic gyrotropic regularization are marginal, are characterized by the ratio of the (collisional or magnetic) mean free path to a characteristic gradient scale length. This work studies two families of reduced plasma models for transition regimes in depth. The first is an asymptotic expansion for Braginskii-type transport coefficients in the so-called drift ordering for low-beta plasmas. The expansion captures leading-order finite Larmor radius effects for arbitrary collisionality. We present a new derivation of this expansion, evaluate its performance numerically, and provide a numerically feasible approximation. The second family of methods is dynamical low-rank (DLR) methods, which are not based on an asymptotic expansion and have the potential to overcome the curse of dimensionality for kinetic equations. We present two novel DLR schemes for plasma kinetic equations with a focus on fluid-kinetic coupling. One is a DLR method that retains low rank in the highly collisional asymptotic limit. The other is a fully locally conservative DLR method for the Vlasov-Dougherty-Fokker-Planck equation which achieves second-order accuracy in time. All discretizations are described in detail and accompanied by numerical results demonstrating the merit of the proposed approach.
- 일반주제명
- Computational physics
- 일반주제명
- Plasma physics
- 일반주제명
- Applied mathematics
- 일반주제명
- Fluid mechanics
- 키워드
- Fluid equations
- 키워드
- Plasma dynamics
- 기타저자
- University of Washington Applied Mathematics
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■00520250211152638
■006m o d
■007cr#unu||||||||
■020 ▼a9798384096573
■035 ▼a(MiAaPQ)AAI31484836
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a530
■1001 ▼aCoughlin, John B.
■24510▼aAsymptotic and Non-Asymptotic Model Reduction for Kinetic Descriptions of Plasma
■260 ▼a[Sl]▼bUniversity of Washington▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a191 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Shumlak, Uri;Hu, Jingwei.
■5021 ▼aThesis (Ph.D.)--University of Washington, 2024.
■520 ▼aPlasma dynamics are coupled across microscopic and macroscopic scales by a variety of nonlinear mechanisms. These include repartition of energy due to kinetic microinstabilities, suppression of fluid instabilities by kinetic stabilization effects, and other mechanisms. At the macroscopic scale plasmas are well-described by fluid equations, whose formal validity depends on the long-time regularization of the phase space distribution function by collisions and magnetic gyrotropization. However, accurately capturing multiscale coupling requires multiscale reduced models which are both efficient and accurate in transition regimes. These regimes, where either collisional or magnetic gyrotropic regularization are marginal, are characterized by the ratio of the (collisional or magnetic) mean free path to a characteristic gradient scale length. This work studies two families of reduced plasma models for transition regimes in depth. The first is an asymptotic expansion for Braginskii-type transport coefficients in the so-called drift ordering for low-beta plasmas. The expansion captures leading-order finite Larmor radius effects for arbitrary collisionality. We present a new derivation of this expansion, evaluate its performance numerically, and provide a numerically feasible approximation. The second family of methods is dynamical low-rank (DLR) methods, which are not based on an asymptotic expansion and have the potential to overcome the curse of dimensionality for kinetic equations. We present two novel DLR schemes for plasma kinetic equations with a focus on fluid-kinetic coupling. One is a DLR method that retains low rank in the highly collisional asymptotic limit. The other is a fully locally conservative DLR method for the Vlasov-Dougherty-Fokker-Planck equation which achieves second-order accuracy in time. All discretizations are described in detail and accompanied by numerical results demonstrating the merit of the proposed approach.
■590 ▼aSchool code: 0250.
■650 4▼aComputational physics
■650 4▼aPlasma physics
■650 4▼aApplied mathematics
■650 4▼aFluid mechanics
■653 ▼aAsymptotic analysis
■653 ▼aFluid equations
■653 ▼aKinetic equations
■653 ▼aLow-rank approximation
■653 ▼aPlasma dynamics
■653 ▼aDynamical low-rank
■690 ▼a0216
■690 ▼a0759
■690 ▼a0364
■690 ▼a0204
■71020▼aUniversity of Washington▼bApplied Mathematics.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0250
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17163206▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
