Download PDF by R.D. Richtmyer: 4th Int'l Conference on Numerical Methods in Fluid Dynamics

By R.D. Richtmyer

ISBN-10: 3540071393

ISBN-13: 9783540071396

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Thus, only continuum models can be used for macroscopic phenomena of fluid flow. 4 Incompressible Flow In an incompressible fluid the density ρ does not change if we follow the motion of the fluid particles of the flow. We can express this fact in the differential equation form Du ρ ≡ ρ˙ + u · ∇ρ = 0, where Du ρ is the convective derivative of ρ with respect to the velocity u. We obtain the convective derivative by computing the change in time following the trajectory x(t) of a fluid particle satisfying the differential equation x(t) ˙ = u(x, t).

20 1 Main Objective Fig. 16. From Chapter 35: Adaptive mesh refinement for the flow past a NACA 0012: magnitude of the velocity (upper), dual solution (middle) representing sensitivity information related to the computation of lift and drag, and a corresponding (coarse) mesh under refinement (lower). 1 Computational Turbulent Incompressible Flow 21 Fig. 17. From Chapter 35: Midsections showing snapshots of a G2 simulation of the blood flow in a realistic bifurcation model of a human carotid bifurcation (upper), the dual solution corresponding to the computational error in wall shear stress (middle), and the corresponding mesh (lower).

In Sommerfeld’s Mystery from 1908 [104], mathematics predicts that the simplest of all flows, Couette flow with a stationary linear velocity profile, is stable and thus should exist. But nobody has ever observed this flow in a fluid with small viscosity. The cover up of d’Alembert’s Mystery is to blame the assumption of zero viscosity for the erroneous prediction: In reality there is always some possibly very very small viscosity (of some nature), which changes everything. We will below argue that such explanations are not scientifically satisfactory and we shall instead present a new resolution based on computational turbulence in the inviscid Euler equations.

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4th Int'l Conference on Numerical Methods in Fluid Dynamics by R.D. Richtmyer

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