| An effective method based on a Lagrangian finite difference approximation is presented for calculation of two-dimensional and axisymmetric time transient incompressible viscoelastic flows with integral multi-mode Maxwell model. The method uses an approximate projection method coupled with second-order spatial derivative and a Crank-Nicholson method for diffusive terms. The primitive variables, differences of displacements and pressure, are used and are defined on the collocated node points which track the material particles. All equations are discretized in convected coordinates with the help of boundary fitted curvilinear coordinate theory. This algorithm does well at computing a broad range of viscoelasticity of material including purely incompressible viscous and purely elastic materials. It can also solve problems with rigid boundaries and contact problems etc.To verify this method, some typical problems of viscous, viscoelastic and elastic materials are calculated. Finally, as an application, squeezing of a moving elastic and viscoelastic layer by a rolling cylinder is simulated. |
