The fluxintegral method for multidimensional convection and diffusion
Abstract
The fluxintegral method is a procedure for constructing an explicit, singlestep, forwardintime, conservative, control volume update of the unsteady, multidimensional convectiondiffusion equation. The convective plus diffusive flux at each face of a controlvolume cell is estimated by integrating the transported variable and its facenormal derivative over the volume swept out by the convecting velocity field. This yields a unique description of the fluxes, whereas other conservative methods rely on nonunique, arbitrary pseudofluxdifference splitting procedures. The accuracy of the resulting scheme depends on the form of the subcell interpolation assumed, given cellaverage data. Cellwise constant behavior results in a (very artificially diffusive) firstorder convection scheme. Secondorder convectiondiffusion schemes correspond to cellwise linear (or bilinear) subcell interpolation. Cellwise quadratic subcell interpolants generate a highly accurate convectiondiffusion scheme with excellent phase accuracy. Under constantcoefficient conditions, this is a uniformly thirdorder polynomial interpolation algorithm (UTOPIA).
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 August 1994
 Bibcode:
 1994STIN...9511245L
 Keywords:

 Convection;
 ConvectionDiffusion Equation;
 Diffusion;
 Finite Volume Method;
 Interpolation;
 Unsteady Flow;
 Algorithms;
 Diffusivity;
 Integral Equations;
 Velocity Distribution;
 Fluid Mechanics and Heat Transfer