A Stable and Convergent Finite Difference Scheme for 2D Incompressible Nonlinear Viscoelastic Fluid Dynamics Problem

Abstract

In this study, a stable and convergent finite difference (FD) scheme based on staggered meshes for twodimensional (2D) incompressible nonlinear viscoelastic fluid dynamics problem including the velocity vector field and the pressure field as well as the deformation tensor matrix is established in order to find numerical solutions for the problem. The stability, convergence, and errors of the FD solutions are analyzed. Some numerical experiments are presented to show that the FD scheme is feasible and efficient for simulating the phenomena of the velocity and the pressure as well as the deformation tensor in an estuary.