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The early identification of self-similar solutions of the second kind can be found in problems of imploding shock waves (Guderley–Landau–Stanyukovich problem), analyzed by G. Guderley (1942) and Lev Landau and K. P. Stanyukovich (1944), [3] and propagation of shock waves by a short impulse, analysed by Carl Friedrich von Weizsäcker [4] and ...
In fluid dynamics, Stokes problem also known as Stokes second problem or sometimes referred to as Stokes boundary layer or Oscillating boundary layer is a problem of determining the flow created by an oscillating solid surface, named after Sir George Stokes.
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid ( liquids and gases ) with surfaces ...
The Navier–Stokes existence and smoothness problem concerns the mathematical properties of solutions to the Navier–Stokes equations, a system of partial differential equations that describe the motion of a fluid in space. Solutions to the Navier–Stokes equations are used in many practical applications.
A schematic diagram of the Blasius flow profile. The streamwise velocity component () / is shown, as a function of the similarity variable .. Using scaling arguments, Ludwig Prandtl [1] argued that about half of the terms in the Navier-Stokes equations are negligible in boundary layer flows (except in a small region near the leading edge of the plate).
This is an example of an implicit method since the unknown u(n + 1) has been used in evaluating the slope of the solution on the right hand side; this is not a problem to solve for u(n + 1) in this scalar and linear case. For more complicated situations like a nonlinear right hand side or a system of equations, a nonlinear system of equations ...
In fluid dynamics, Rayleigh problem also known as Stokes first problem is a problem of determining the flow created by a sudden movement of an infinitely long plate from rest, named after Lord Rayleigh and Sir George Stokes. This is considered as one of the simplest unsteady problems that have an exact solution for the Navier-Stokes equations.
Arnold–Beltrami–Childress flow – an exact solution of the incompressible Euler equations. Two solutions of the three-dimensional Euler equations with cylindrical symmetry have been presented by Gibbon, Moore and Stuart in 2003. [29] These two solutions have infinite energy; they blow up everywhere in space in finite time.