NUMERICAL PROPERTIES OF GAUGE METHOD FOR THE INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

ABSTRACT. The representative numerical algorithms to solve the time dependent Navier-Stokes equations are projection type methods. Lots of projection schemes have been developed to find more accurate solutions. But most of projection methods [4, 11] suffer from inconsistency and requesting unknown datum. E and Liu in [5] constructed the gauge method which splits the velocity u = a + ∇φ to make consistent and to replace requesting of the unknown values to known datum of non-physical variables a and φ. The errors are evaluated in [9]. But gauge method is not still obvious to find out suitable combination of discrete finite element spaces and to compute boundary derivative of the gauge variable φ. In this paper, we define 4 gauge algorithms via combining both 2 decomposition operators and 2 boundary conditions. And we derive variational derivative on boundary and analyze numerical results of 4 gauge algorithms in various discrete spaces combinations to search right discrete space relation. 1