By Professor Dr. Bernard D. Coleman, Professor Dr. Martin Feinberg, Professor Dr. James Serrin (auth.)
This booklet offers a suite of papers giving the flavour of present examine actions in continuum mechanics, fluid mechanics, thermodynamics and the mathematical research regarding those themes. Written through major specialists within the box, the entire papers during this assortment were rigorously refereed based on the criteria of the "Archive for Rational Mechanics and Analysis."
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Extra resources for Analysis and Thermomechanics: A Collection of Papers Dedicated to W. Noll on His Sixtieth Birthday
O o o o o o o o o o Central differencing Upwind differencing Fig. 2 MURMAN & COLE studied the small disturbance equations. They derived a switching scheme of numerical analysis which tells the computer to use central differencing if the flow is subsonic and upwind differencing if the flow is supersonic. Their upwind differencing equation can be interpreted as approximating a differential equation with an artificial viscosity proportional to the mesh size . MURMAN & COLE'S method was the first success.
11. Classification of the Steady Flow Equations for a Class of Oldroyd Models 12. Quasilinear Systems for Simple Fluids with Fading Memory of the ColemanNoll Type . . . . . . . . . . . . . . . 213 215 217 222 225 213 216 217 218 220 224 227 1. Introduction The equations of steady gas dynamics change type when the speed of the fluid at some point exceeds the speed of sound. If this happens, then discon- 26 D. D. JOSEPH, M. -C. SAUT timiities can appear in the supersonic region. We are interested in the possibility that many strange effects in the flow of viscoelastic liquids, as well as difficulties in numerical simulation, are also associated with the appearance of real characteristics and a change of type, analogous to the sonic transition.
12) with 1p replacing C, is harmonic to within terms of lower order. , y, a interpreted as the physical components of velocity and stress in polar coordinates. 10. 1). 13) are useful for this. 1) requires for special flows. (i) First, we again conider the uniform flows discussed in § 8; u = U, v a = O. (2 ± V = 1 M2 - l' (= G~O») is the wave speed. The characteristics are straight lines which start as lines perpendicular to the flow at M = 1 and tilt more toward the free stream as M > 1 is increased.