A 4TH-ORDER FINITE-VOLUME METHOD WITH COLOCATED VARIABLE ARRANGEMENT

A finite volume solution method for the two-dimensional Navier-Stokes equations and temperature equation with 4th order discretization on ca rtesian grids is presented. The method uses colocated variable arrange ment and the SIMPLE-kind of velocity-pressure coupling. The surface in tegrals (convection and diffusion fluxes through control volume faces) are approximated by Simpson's rule and polynomial interpolation, and the volume integrals (source terms) are approximated by fitting a four th-order polynomial through nine points and integrating it analyticall y. Applications to the solution of a scalar transport on a known veloc ity field and to the lid-driven and buoyancy-driven cavity flows show superior accuracy as compared to the first and second order schemes. T he approach can be readily extended to control volumes of arbitrary sh ape and unstructured grids.