Metodo de Diferencias Finitas para un Problema de Bingham Unidimensional

GERMÁN ARIEL TORRES; CRISTINA TURNER

MAT-Serie A

Departamento de Matemática de la Facultad de Ciencias Empresariales de la Universidad Austral

Lugar: Rosario - Santa Fe; Año: 2001 vol. 5 p. 11 - 26

1515-4904

In this work, a numerical method of finite differences is proposed to solve an unidimensional Bingham problem, and some theoretical properties of the solution are proved, and corroborated with numerical results. A Bingham fluid is a non-newtonian fluid, whose viscous behaviour makes his layers move only if shear stress is greater than a threshold value. There are some previous theoretical results that allows us to affirm existence and uniqueness of the solution under certain initial conditions. The proposed method is a finite difference scheme with spatial variable step, that is, while we move a fixed time step, we adjust the grid in such a way that the spatial step represents the free boundary advance. Using an internal calculus of fixed point is possible to reduce the number of flops, making feasible the implementation of the method in a computer. Besides that, a theorem of existence and uniqueness is proved for more general cases, and also a result about asymptotic behaviour is demonstrated.