A pseudo-arclength continuation method for nonlinear eigenvalue problems
SIAM Journal on Numerical Analysis
A multigrid continuation method for elliptic problems with folds
SIAM Journal on Scientific and Statistical Computing
Existence results for the flow of viscoelastic fluids with a differential constitutive law
Nonlinear Analysis: Theory, Methods & Applications
A locally parameterized continuation process
ACM Transactions on Mathematical Software (TOMS)
SIAM Journal on Scientific Computing
Algorithm 832: UMFPACK V4.3---an unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Condition Estimates for Pseudo-Arclength Continuation
SIAM Journal on Numerical Analysis
Analysis of a defect correction method for viscoelastic fluid flow
Computers & Mathematics with Applications
A stable and convergent scheme for viscoelastic flow in contraction channels
Journal of Computational Physics
| Hi-index | 7.29 |
The numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter, the Weissenberg number, increases. Specifically, at a Weissenberg number larger than a critical value, the iterative nonlinear solver fails to converge, a phenomenon known as the high Weissenberg number problem. In this work we describe the application and implementation of continuation methods to the nonlinear Johnson-Segalman model for steady-state viscoelastic flows. Simple, natural, and pseudo-arclength continuation approaches in Weissenberg number are investigated for a discontinuous Galerkin finite element discretization of the equations. Computations are performed for a benchmark contraction flow and, several aspects of the performance of the continuation methods including high Weissenberg number limits, are discussed.