Filtering techniques for turbulent flow simulation. (English) Zbl 0724.76002
Lecture Notes in Engineering, 56. Berlin etc.: Springer-Verlag. viii, 397 p. DM 102.00 (1990).
This perspicuous monograph is an excellent account of theoretical analysis of filtering techniques for turbulent flow simulation.
Researchers and graduate students will find this reference very useful and stimulating. After the introductory remarks in Chapter 1, the author reviews the present state of the art in turbulence modeling.
Specifically, the main characteristics of the conventional turbulence modeling and large eddy simulation approaches have been described. It is concluded that the latter is superior in principle to the former, but the need for improvements has been pointed out. Chapter 3 examines one such modification, viz., the introduction of time filtering in addition to space filtering and the development of the corresponding theory. This includes the rigorous derivation for an approximation for the so called ‘cross terms’, which represent a random forcing of the unresolved scales on the resolved ones. Proofs of the asymptotic nature of the Leonard approximation for the ‘large scale’ advective terms and of the approximations of the cross terms have been provided. A Fourier space theory has been developed and it has been concluded that the approximations in question are equivalent to approximating the Gaussian filter in Fourier space by an osculating paraboloid.
The theory corresponding to the three-scale filtering approach is developed in Chapter 4. Here all flow variables have been subdivided into ‘macroscale’, ‘mesoscale’ and ‘microscale’ components. Governing equations for the first two have been derived and the effects of the last one have been parametrised through the use of the Smagorinsky-Lilly model. It has been established that two-scale results can be reconstructed by using three-scale information. Both the space-time and the three-scale filtering approaches are numerously tested in the context of random Burgers’ flow. This interesting discussion appears in three chapters. Finally the last Chapter 8 contains the conclusions of the study, and summarises the main contributions. Recommendations for future research in the concluding Chapter present several related open problems.
Researchers and graduate students will find this reference very useful and stimulating. After the introductory remarks in Chapter 1, the author reviews the present state of the art in turbulence modeling.
Specifically, the main characteristics of the conventional turbulence modeling and large eddy simulation approaches have been described. It is concluded that the latter is superior in principle to the former, but the need for improvements has been pointed out. Chapter 3 examines one such modification, viz., the introduction of time filtering in addition to space filtering and the development of the corresponding theory. This includes the rigorous derivation for an approximation for the so called ‘cross terms’, which represent a random forcing of the unresolved scales on the resolved ones. Proofs of the asymptotic nature of the Leonard approximation for the ‘large scale’ advective terms and of the approximations of the cross terms have been provided. A Fourier space theory has been developed and it has been concluded that the approximations in question are equivalent to approximating the Gaussian filter in Fourier space by an osculating paraboloid.
The theory corresponding to the three-scale filtering approach is developed in Chapter 4. Here all flow variables have been subdivided into ‘macroscale’, ‘mesoscale’ and ‘microscale’ components. Governing equations for the first two have been derived and the effects of the last one have been parametrised through the use of the Smagorinsky-Lilly model. It has been established that two-scale results can be reconstructed by using three-scale information. Both the space-time and the three-scale filtering approaches are numerously tested in the context of random Burgers’ flow. This interesting discussion appears in three chapters. Finally the last Chapter 8 contains the conclusions of the study, and summarises the main contributions. Recommendations for future research in the concluding Chapter present several related open problems.
Reviewer: R.C.Gupta (Singapore)
MSC:
| 76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |
| 76F05 | Isotropic turbulence; homogeneous turbulence |
| 76F10 | Shear flows and turbulence |
