Modified Nodal Integral Method for the Three-Dimensional, Time-Dependent, Incompressible Navier-Stokes Equations

摘要: A modified nodal integral method (MNIM) for two-dimensional, time-dependent Navier-Stokes equations is extended to three dimensions. The based on local transverse integrations over finite size cells that reduce each partial differential equation a set of ordinary (ODEs). Solutions these ODEs in cell the transverse-averaged dependent variables are then utilized develop difference schemes. discrete scalar velocities and pressure, averaged faces bricklike cells. development MNIM different from conventional two ways: (a) it Poisson-type pressure (b) convection terms retained left side transverse-integrated thus contribute homogeneous part solution. first feature leads symmetric all velocities, second yields distributions constant + linear exponential form velocities. scheme tested three-dimensional lid-driven cavity problems cube- prism-shaped cavities. Results obtained using fairly coarse meshes comparable with reference solutions much finer meshes.