A modified nodal scheme for the time-dependent, incompressible Navier-Stokes equations

摘要: Based on Poisson equation for pressure, a nodal numerical scheme is developed the time-dependent, incompressible Navier-Stokes equations. Derivation based local transverse-integrations over finite size brick-like cells that transform each partial differential to set of ordinary equations (ODEs). Solutions these ODEs transverse-averaged dependent variables are then utilized develop difference scheme. The discrete scalar velocities and averaged faces in (x,y,t) space. Cell-interior variation pressure spatial direction quadratic. velocity sum constant, linear an exponential term. Due introduction delayed coefficients, functions be evaluated only once at time step. semi-implicit has inherent upwinding. Results applications several test problems show very robust leads second-order error. As expected such coarse-mesh schemes, even relatively large lead small errors. Extension three dimensions straightforward.