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Numerical manifold method was applied to directly solve Navier-Stokes (N-S) equations for incompressible viscous flow in this paper, and numerical manifold schemes for N-S equations coupled velocity and pressure were derived based on Galerkin weighted residuals method as well. Mixed cover with linear polynomial function for velocity and constant function for pressure was employed in finite element cover system. As an application, mixed cover 4-node rectangular manifold element has been used to simulate the incompressible viscous flow around a square cylinder in a channel. Numerical tests illustrate that NMM is an effective and high-order accurate numerical method for incompressible viscous flow N-S equations.

Direct Simulation of Low-Re Flow around a Square Cylinder by Numerical Manifold Method for Navier-Stokes Equations