Asymptotic behavior of traveling wave solutions of the equations for the flow of a fluid with small viscosity and capillarity
Abstract
The qualitative behavior of the travelingwave (TW) solutions of the onedimensional flow equations for fluids with low viscosity (epsilon) and capillarity (delta) is investigated analytically, with a focus on the structure of the shock layers for a strictly hyperbolic system. The results are presented graphically, and the TW solutions are shown to have oscillations which increase in amplitude as epsilon and delta approach zero. Exceptions are the cases delta = o(epsilon squared), where the amplitude goes to zero, and delta = epsilon squared, where delta and epsilon have no effect on the shape of the TW.
 Publication:

Quarterly of Applied Mathematics
 Pub Date:
 January 1987
 Bibcode:
 1987QApMa..44..697B
 Keywords:

 Asymptotic Methods;
 Capillary Flow;
 Flow Equations;
 Oscillating Flow;
 Shock Layers;
 Traveling Waves;
 Computational Fluid Dynamics;
 Existence Theorems;
 Inviscid Flow;
 Fluid Mechanics and Heat Transfer