A dynamical approach to large eddy simulation of turbulent flows: Existence of weak solutions

Mathematical Methods in the Applied Sciences

Volumn 29, Issue 1, 2006, Pages 99-121

  Świerczewska, Agnieszka ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

Dynamic Germano model; Large eddy simulation; Non local operators; Smagorinsky model; Young measures

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NAVIER STOKES EQUATIONS; TURBULENCE; VELOCITY MEASUREMENT;

DYNAMIC GERMANO MODEL; LARGE EDDY SIMULATION; NON-LOCAL OPERATORS; SMAGORINSKY MODEL; YOUNG MEASURES;

TURBULENT FLOW;

EID: 29344464359     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.667     Document Type: Article

References (23)

1. Świerczewska A. Large eddy simulation. Existence of stationary solutions to the dynamical model. Zeitschrift für Angewandte Mathematik und Mechanik 2005; 85(8):593-604.
2. Sagaut P. Large eddy simulation for incompressible flows. Scientific Computation. Springer: Berlin, 2001.
3. Aldama AA. Filtering Techniques for Turbulent Flow Simulation. Lecture Notes in Engineering, vol. 56. Springer: Berlin, 1990.
4. Lions JL. Quelques méthodes de résolution des problèmes aux limites non linéaires. Gauthier-Villars: Dunod, Paris, 1969.
5. Ladyženskaja OA. New equations for the description of the motions of viscous incompressible fluids, and global solvability for their boundary value problems. Trudy Matematicheskogo Instituta Steklova 1967; 102:85-104.
6. Parés C. Existence, uniqueness and regularity of solution of the equations of a turbulence model for incompressible fluids. Applicable Analysis 1992; 43(3-4):245-296.
7. John V. Large Eddy Simulation of Turbulent Incompressible Flows. Analytical and Numerical Results for a Class of LES Models. Lecture Notes in Computational Science and Engineering, vol. 34. Springer: Berlin, 2004.
8. Germano M, Piomelli U, Moin P, Cabot WH. A dynamic subgrid-scale eddy viscosity model. Physics of Fluids A 1991; 3(7):1760-1765.
9. Lilly D. A proposed modification of the Germano subgrid-scale closure method. Physics of Fluids A 1992; 4(3):633-635.
10. Van der Ven H. A family of large eddy simulation (LES) filters with nonuniform filter widths. Physics of Fluids A 1995; 7(5): 1171-1172.
11. Berselli L, Grisanti C, John V. On commutation errors in the derivation of the space averaged Navier-Stokes equations. 2004, Preprint.
12. Berselli L, John V. On the comparison of a commutation error and the Reynolds stress tensor for flows obeying a wall law. 2004, Preprint.
13. Dunca A, John V, Layton WJ. The commutation error of the space averaged Navier-Stokes equations on a bounded domain. Contributions to Current Challenges in Mathematical Fluid Mechanics. Advances in Mathematics and Fluid Mechanics. Birkhäuser: Basel, 2004; 53-78.
14. Málek J, Nečas J, Růžička M. On the non-Newtonian incompressible fluids. Mathematical Models and Methods in Applied Sciences 1993; 3(1):35-63.
15. Málek J, Nečas J, Rokyta M, Růžička M. Weak and measure-valued solutions to evolutionary PDEs. Applied Mathematics and Mathematical Computation, vol. 13. Chapman & Hall: London, 1996.
16. Fuchs M. On stationary incompressible Norton fluids and some extensions of Korn's inequality. Zeitschrift fur Analysis und Ihre Anwendungen 1994; 13(2):191-197.
17. Evans LC. Partial Differential Equations. Graduate Studies in Mathematics, vol. 19. American Mathematical Society: Providence, RI, 1998.
18. Temam R. Navier-Stokes equations. Theory and Numerical Analysis. North-Holland: Amsterdam, 1977.
19. Gwiazda P, Świerczewska A. Large eddy simulation turbulence model with Young measures. Applied Mathematics Letters 2005; 18(8):923-929.
20. Ball JM. A version of the fundamental theorem for Young measures. PDEs and Continuum Models of Phase Transitions (Nice, 1988). Lecture Notes in Physics, vol. 344. Springer: Berlin, 1989; 207-215.
21. Müller S. Variational models for microstructure and phase transitions. Calculus of Variations and Geometric Evolution Problems (Cetraro, 1996). Lecture Notes in Mathematics, vol. 1713. Springer: Berlin, 1999; 85-210.
22. Elstrodt J. Maß- und Integrationstheorie. (Measure and Integration Theory). Springer: Berlin, 2002.
23. Zeidler E. Nonlinear Functional Analysis and its Applications, II/A. Springer: New York, 1990.