Method of straight lines for a Bingham problem in cylindrical pipes Original Research Article

In this work a method of straight lines for a Bingham problem in cylindrical geometry is developed. A Bingham fluid has viscosity properties that produce a separation into two regions, a rigid zone and a viscous zone. We propose a method of lines with the time as a discrete variable. We prove that the method is well defined for all times, a monotone property, qualitative behaviours of the solution, and a convergence theorem. A numerical calculation is included to illustrate the theoretical results.