Accession Number : ADA266374


Title :   Incompressible Spectral-Element Method-Derivation of Equations


Descriptive Note : Technical memorandum


Corporate Author : NATIONAL AERONAUTICS AND SPACE ADMINISTRATION CLEVELAND OH LEWIS RESEARCH CENTER


Personal Author(s) : DeAnna, Russell G


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a266374.pdf


Report Date : Apr 1993


Pagination or Media Count : 88


Abstract : A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (non- linear, pressure, viscous) schemes. The non-linear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the non-linear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient, By combining this predicted pressure gradient with the non-linear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity. Numerical, Spectral-element method, Computational fluid dynamics


Descriptors :   *SPLITTING , *NAVIER STOKES EQUATIONS , *CALCULUS OF VARIATIONS , VELOCITY , PRESSURE GRADIENTS , COMPUTATIONAL FLUID DYNAMICS , TIME , VARIABLES , GRADIENTS , FLUID DYNAMICS , VARIATIONS , COEFFICIENTS , FLUIDS , EXPANSION , SUBSTITUTES


Subject Categories : Theoretical Mathematics
      Fluid Mechanics


Distribution Statement : APPROVED FOR PUBLIC RELEASE