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There are three kinds of forces important to fluid mechanics: gravity (body force), pressure forces, and viscous forces (due to friction). Gravity force, Body forces act on the entire element, rather than merely at its surfaces.
What are the dependent variable in the Navier-Stokes equation?
Explanation: There are six dependent variables in the Navier-Stokes equations. They are pressure (p), temperature (T), density (ρ) and three components of the velocity vector (u,v,w).
What do diffusive terms represent?
Convection is a physical process that occurs in a flow of gas in which some property is transported by the ordered motion of the flow. The terms on the right hand side of the momentum equations that are multiplied by the inverse Reynolds number are called the diffusion terms.
Incompressible flow The incompressible momentum Navier–Stokes equation results from the following assumptions on the Cauchy stress tensor: the stress is Galilean invariant: it does not depend directly on the flow velocity, but only on spatial derivatives of the flow velocity.
Why is Navier-Stokes non linear?
The nonlinear term in Navier–Stokes equations of Equation (1.17) is the convection term, and most of the numerical difficulties and stability issues for fluid flow are caused by this term. For the fluid flow with a high Reynolds number, the flow can be turbulence with multiscale responses.
Who Solved Navier-Stokes?
They’re not easy – a correct solution to any one results in a US$1,000,000 prize being awarded by the institute. Russian mathematician Grigori Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only problem that’s been solved.
Throughout the middle of the 19th century, British physicist and mathematician Sir George Gabriel Stokes improved on this work, though complete solutions were obtained only for the case of simple two-dimensional flows. Stokes and Navier each contributed a viscous diffusion term to account for the viscosity of a fluid.
What is advective transport?
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy.
Who Solved the Navier-Stokes problem?
Russian mathematician Grigori Perelman was awarded the Prize on March 18 last year for solving one of the problems, the Poincaré conjecture – as yet the only problem that’s been solved. Famously, he turned down the $1,000,000 Millennium Prize.
The Navier-Stokes Millennium problem has been completely solved in a my paper published in 2008. Partial results were obtained in some works published starting from 1985.
Is Navier Stokes equation linear?
This chapter describes the Navier-Stokes (N-S) equations. The N-S equations form a quasi-linear differential system, and such systems can be studied through linearized equations.