We employ a new second-order extension of the Lax-Friedrichs scheme, with incompressibility imposed by means of a projection algorithm, to follow the evolution of the vorticity and stress fields for a Maxwell fluid in a two-dimensional periodic system initialized with two thin and concentrated shear layers. The scheme is simple, efficient, and robust, and is capable, in particular, of resolving large stress gradients.
Bibliographical noteFunding Information:
We are grateful to Professor Alexandre Chorin for his comments on the manuscript. R.K. was supported in part by the LBNL Directed Research and Development Program, and in part by the Applied Mathematical Sciences Subprogram of the Office of Energy Research, US Department of Energy, and M.M.D. by the Director, Office of Energy Research, Office of Basic Energy Sciences, Materials Science Division, U.S. Department of Energy, both under Contract Number DE-AC03-76SF-00098.
- Shear layers