Flows of materials with yield are analyzed by using a continuous viscoplastic equation (CVE) that eliminates the necessity of tracking material yield surfaces. These flows are computed by means of the Galerkin/finite element method and global Newton iteration.

Numerical difficulties stemming from the sigmoidal form of the CVE are avoided by appropriate selection of the initial estimation to the Newton iteration, or by solution continuation in the space of the exponential material parameter of the CVE. Simultaneously with the determination of the unknown velocity and pressure fields, the finite element scheme locates the characteristic material lines, such as interfaces and yield surfaces. Results are presented for two-dimensional flows over generalized flow conduits at driving gradients below and above yielding. It is shown that a general viscoplastic field consists of truly unyielded plug regions (UPR) carried by yielded flowing films (YFF) in contact with solid boundaries or intervening apparent unyielded regions (AUR).

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