Numerical Solution of Navier-Stokes Equations with
Non-Linear Source Terms
Nikolova, Ivanka Petkova, University of Pittsburgh, USA
Among the varieties of methods applied in numerical modeling of
fluid flows the Semi-Implicit Finite Differences Alternative
Directions(Splitting Operators) techniques ocupies special place.
It was created in 1978 in Moscow for numerical solving of
the Navier-Stockes equations along the energy and species conservation
equations.
Non-linearity here arrises because of the presence of convective
terms. But real strong non-linearity is due to the source terms
representing heat or mass source respectivelly.
The method allows to reduce a system of 5 or more PDE (usually coupled)
for the velocity, density (pressure), temperature and species
concentrations to a large system of algebraic equations, which is solved
by forward-backward matrix procedure. It realization is quite difficult
and computer time consuming. As compensation to this obstacles one gets
detailed picture of flow
behavior, namely the velocity, the temperature, the heat fluxes, other
special profiles and time-dependent characteristics.
Examples will be given for solving low Mach number flows with high
temperature gradients as they frequently ocure in compustion processes.