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The k-ε model is one of the most widely used closure models in which two additional equations are solved for variables k (turbulent kinetic energy) and ε (turbulent dissipation). This model is complete, in that these two variables can be manipulated to describe a a turbulent length and time scale. The assumptions made in using this model are that the two k and ε transport equations are valid, and the turbulent viscosity hypothesis, that the Reynolds stresses are proportional to the mean rate of strain (similar to the Newtonian hypothesis relating stress and strain that is used in the Navier Stokes equations).
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