A nodal coarse-mesh method for the efficient numerical solution of laminar flow problems

Abstract

A coarse-mesh nodal method for the efficient numerical solution of incompressible laminar flow problems is developed using a transverse integration procedure followed by the introduction of locally-defined Green's tensors of the transverse-integrated in-node Navier-Stokes and mass conservation equations. In applications to 2-dimensional flow problems, including fully developed flow, inlet flow, and modified driven cavity problems (driven cavities with inlet and outlet sections), this new nodal Green's tensor method is demonstrated to have very high accuracy even when applied on very large nodes. The high accuracy of this new method on very coarse meshes leads to a high computational efficiency (reduced computer time for fixed accuracy requirements).