Mass- and momentum-conserving spectral methods for Stokes flow

AbstractThe governing equations for Stokes flow are formulated in terms of a stream function and Airy stress function. This formulation ensures that mass and momentum are conserved identically. In terms of these new variables, the equations of motion are written as a second-order elliptic system. These equations are embedded in biharmonic equations and the boundary conditions appropriate for this higher-order system are determined using a least-squares process. This technique is applied to the planar stick-slip problem. A numerical solution to the problem is obtained using a spectral domain decomposition method. An algebraic mapping is used to treat the flow domain without truncation. The coefficients in a singular expansion of the stream function about the stick-slip singularity are computed using a post-processing technique