Krylov Methods
Published:
Krylov Methods for Large Systems of Linear Equations
Krylov methods are explored on large systems of linear equations arising from the implicit solution of incompressible, laminar, 2D energy equation with a given velocity field. The assembled implicit system is solved only once to study the effect of the linear system solver in use. The computational domain is a rectangular channel with a size of 40 in $x$ direction and 1 in $y$ direction. The velocity field in all cases is assumed to be fully developed. This velocity profile is a parabolic distribution. We assume that the temperature distribution on the bottom and top walls are constant and equal to 0 and 1, respectively. Further, the temperature at outlet is assumed to be fully developed and $T(y)=y$ at the inlet. Also, we have Re$=25$, Pr$=0.7$, and Ec=$0.1$. Time step is also set equal to 0.25.
