Abstract
In this study, a stable and convergent finite difference (FD) scheme based on staggered meshes for two-dimensional (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.
Highlights
Let Ω ⊂ R be a bounded and connected domain
We have offered the theoretical analysis about the stability, convergence, and errors of the finite difference (FD) solutions and used some numerical experiments to confirm the validity of the FD scheme
This FD scheme is first established because at present there has not been any FD scheme reported for the 2D incompressible nonlinear viscoelastic fluid dynamics problem
Summary
Let Ω ⊂ R be a bounded and connected domain. Consider the following two-dimensional (2D) incompressible nonlinear viscoelastic fluid dynamics problem (see [1]):. This implies that the work here is improvement and development of the existing those mentioned.
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