*Bijan Mohammadi and Olivier Pironneau*

- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199546909
- eISBN:
- 9780191720482
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199546909.003.0003
- Subject:
- Mathematics, Mathematical Physics

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for ...
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This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for high Reynolds number flows when the topology of the answer is not known. The fundamental equations of fluid dynamics are recalled; this is because applied OSD for fluids requires a good understanding of the state equation: Euler and Navier–Stokes equations in this case, with and without turbulence models together with the inviscid and/or incompressible limits. The chapter recalls wall-laws also used for OSD as low complexity models. By wall-laws domain decomposition with a reduced dimension model near the wall is understood. In other words, there is no universal wall-laws and when using a wall-function, it needs to be compatible with the model used far from the wall. Large eddy simulation is giving a new life to the wall-functions especially to simulate high-Reynolds external flows.Less

This chapter describes the governing equations considered throughout the book. The equations of fluid dynamics are recalled, together with the k-epsilon turbulence model, which is used later on for high Reynolds number flows when the topology of the answer is not known. The fundamental equations of fluid dynamics are recalled; this is because applied OSD for fluids requires a good understanding of the state equation: Euler and Navier–Stokes equations in this case, with and without turbulence models together with the inviscid and/or incompressible limits. The chapter recalls wall-laws also used for OSD as low complexity models. By wall-laws domain decomposition with a reduced dimension model near the wall is understood. In other words, there is no universal wall-laws and when using a wall-function, it needs to be compatible with the model used far from the wall. Large eddy simulation is giving a new life to the wall-functions especially to simulate high-Reynolds external flows.

*Sauro Succi*

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0024
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter introduces the main ideas behind the application of LBE methods to the problem of turbulence modeling, namely the simulation of flows which contain scales of motion too small to be ...
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This chapter introduces the main ideas behind the application of LBE methods to the problem of turbulence modeling, namely the simulation of flows which contain scales of motion too small to be resolved on present-day and foreseeable future computers. Many real-life flows of practical interest exhibit Reynolds numbers far too high to be directly simulated in full resolution on present-day computers and arguably for many years to come. This raises the challenge of predicting the behavior of highly turbulent flows without directly simulating all scales of motion which take part to turbulence dynamics, but only those that fall within the computer resolution at hand.Less

This chapter introduces the main ideas behind the application of LBE methods to the problem of turbulence modeling, namely the simulation of flows which contain scales of motion too small to be resolved on present-day and foreseeable future computers. Many real-life flows of practical interest exhibit Reynolds numbers far too high to be directly simulated in full resolution on present-day computers and arguably for many years to come. This raises the challenge of predicting the behavior of highly turbulent flows without directly simulating all scales of motion which take part to turbulence dynamics, but only those that fall within the computer resolution at hand.

*Sauro Succi*

- Published in print:
- 2018
- Published Online:
- June 2018
- ISBN:
- 9780199592357
- eISBN:
- 9780191847967
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780199592357.003.0020
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics, Condensed Matter Physics / Materials

This chapter presents the main ideas behind the application of LB methods to the simulation of turbulent flows. The attention is restricted to the case of direct numerical simulation, in which all ...
More

This chapter presents the main ideas behind the application of LB methods to the simulation of turbulent flows. The attention is restricted to the case of direct numerical simulation, in which all scales of motion within the grid resolution are retained in the simulation. Turbulence modeling, in which the effect of unresolved scales on the resolved ones is taken into account by various forms of modeling, will be treated in a subsequent chapter.Less

This chapter presents the main ideas behind the application of LB methods to the simulation of turbulent flows. The attention is restricted to the case of direct numerical simulation, in which all scales of motion within the grid resolution are retained in the simulation. Turbulence modeling, in which the effect of unresolved scales on the resolved ones is taken into account by various forms of modeling, will be treated in a subsequent chapter.