Nonlinear Elliptic Problem Related to Flowing Granular Materials

摘要

Similarity solutions for the flow of granular materials are constructed. Unlike previous work, the present approach can be applied to non- axisymmetric containers. The steady state equations are reduced to a nonlinear Helmholtz equation on a subdomain of the sphere. Existence and local uniqueness of the solutions are established. A spectral numerical method using Fourier/ Chebyshev-Gauss-Radau collocation for discretization and Newton-GMRES as solver is proposed and implemented. Corresponding numerical experiments are discussed.