Ray method for flow of a compressible viscous fluid
Abstract
The author describes an asymptotic method to solve the linearized NavierStokes equations governing the flow of a compressible viscous fluid subject to free surface and rigid bottom boundary conditions. The solution of these equations is assumed to consist of a phase function and an amplitude function. It is found that the phase function satisfies the HamiltonJacobi equation, and the first order approximation to the amplitude function satisfies a transport equation. The HamiltonJacobi equation may be solved by means of the method of characteristics, which reduces the equation to a set of ordinary differential equations. Their solutions determine a family of timespace curves called rays. The transport equation can be easily integrated along each ray to yield the socalled conservation relation. At certain anomalies the amplitude function becomes infinite and a uniform expansion is then constructed to remove these difficulties.
 Publication:

Technical Summary Report Wisconsin Univ
 Pub Date:
 March 1983
 Bibcode:
 1983wisc.reptS....S
 Keywords:

 Compressible Fluids;
 Fluid Flow;
 Viscous Fluids;
 Asymptotic Series;
 Differential Equations;
 NavierStokes Equation;
 Viscous Flow;
 Wave Propagation;
 Fluid Mechanics and Heat Transfer