A mixed method for unsteady flow problems

Abstract

A mixed method using both the finite element technique and the finite difference method is developed for the solution of unsteady flow problems. The method is based on choosing an interpolation function which is dependent only on the time domain. The resulting local Galerkin finite element equations are obtained and assembled into a global form. The spatial derivatives of a variable at the nodes are replaced by a spatial operator (finite difference operator). The discretized nonlinear algebraic system is solved by an iterative scheme. The method is used to obtain the solution for the one-dimensional Burger's equation (model problem). The agreement of the results with other numerical and analytical solutions is quite good for cases in which the viscous effects are small (v≥0,1). The effects induced by changes in the step sizes are discussed. A quantitative comparison of the computing time is made of the related numerical techniques.

Keywords:

• Unsteady flows
• Galerkin finite element in time
• Viscous-incompressible flows
• Non-linear partial differential equations

C.R. Categories:

• 5.17