Stochastic Eulerian Lagrangian methods for fluid–structure interactions with thermal fluctuations
We present approaches for the study of fluid–structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for...
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| Published in | Journal of computational physics Vol. 230; no. 8; pp. 2821 - 2837 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Kidlington
Elsevier Inc
20.04.2011
Elsevier |
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| Abstract | We present approaches for the study of fluid–structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid–structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid–structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid–structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations. |
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| AbstractList | We present approaches for the study of fluid–structure interactions subject to thermal fluctuations. A mixed mechanical description is utilized combining Eulerian and Lagrangian reference frames. We establish general conditions for operators coupling these descriptions. Stochastic driving fields for the formalism are derived using principles from statistical mechanics. The stochastic differential equations of the formalism are found to exhibit significant stiffness in some physical regimes. To cope with this issue, we derive reduced stochastic differential equations for several physical regimes. We also present stochastic numerical methods for each regime to approximate the fluid–structure dynamics and to generate efficiently the required stochastic driving fields. To validate the methodology in each regime, we perform analysis of the invariant probability distribution of the stochastic dynamics of the fluid–structure formalism. We compare this analysis with results from statistical mechanics. To further demonstrate the applicability of the methodology, we perform computational studies for spherical particles having translational and rotational degrees of freedom. We compare these studies with results from fluid mechanics. The presented approach provides for fluid–structure systems a set of rather general computational methods for treating consistently structure mechanics, hydrodynamic coupling, and thermal fluctuations. |
| Author | Atzberger, Paul J. |
| Author_xml | – sequence: 1 givenname: Paul J. surname: Atzberger fullname: Atzberger, Paul J. email: atzberg@math.ucsb.edu organization: University of California, Department of Mathematics, Santa Barbara, CA 93106, United States |
| BackLink | http://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=23944939$$DView record in Pascal Francis https://www.osti.gov/biblio/21499791$$D View this record in Osti.gov |
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| Keywords | Thermal fluctuations Fluid–structure interaction Fluid dynamics SELM Fluctuating hydrodynamics Stochastic Eulerian Lagrangian method Statistical mechanics Operator Fluid mechanics Degrees of freedom Lagrangian Probability distribution Numerical method Stochastic method Fluid-structure interaction Calculation methods Random field Referential Differential equations Calculation Spherical particle Lagrangian method Temperature fluctuation Invariant distribution Stochastic equation |
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| SubjectTerms | APPROXIMATIONS CALCULATION METHODS CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS COMPARATIVE EVALUATIONS Computation Computational techniques DEGREES OF FREEDOM DIFFERENTIAL EQUATIONS Driving EQUATIONS EVALUATION Exact sciences and technology Fluctuating hydrodynamics Fluctuation FLUCTUATIONS Fluid dynamics FLUID MECHANICS Fluid-structure interaction FLUID-STRUCTURE INTERACTIONS Formalism FUNCTIONS HYDRODYNAMICS LAGRANGIAN FUNCTION MATHEMATICAL METHODS AND COMPUTING Mathematical methods in physics MATHEMATICAL MODELS MECHANICAL STRUCTURES MECHANICS Physics PROBABILITY SELM STATISTICAL MECHANICS Stochastic Eulerian Lagrangian method STOCHASTIC PROCESSES Stochasticity Thermal fluctuations VARIATIONS |
| Title | Stochastic Eulerian Lagrangian methods for fluid–structure interactions with thermal fluctuations |
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