### SWEEPS OF SOLVER

At each iteration step, Flint will solve the governing equations pertaining
to all the relevant field variables one at a time by calling the matrix solver.
The matrix solver uses a line-by-line method which is a combination of the
Gauss-Seidel method combined with the TDMA (TriDiagonal Matrix Algorithm) method.
This is known as the Line Gauss-Seidel (LGS) Method.

TDMA method can be used for the solution of one dimensional flow problems,
where the field equations yield a tri-diagonal coefficients matrix thus making
it extremely easy to solve the problem directly by a forward and backwards
substitution method.

Unfortunately no such technique can be applied to the direct solution of two and
three dimensional systems as the coefficients matrix no longer retains its
tri-diagonal shape. Never the less, it is possible to apply the TDMA techniques
to a line of cells at a time, thus reducing the problem to N*M systems of one
dimensional TDMA problems. Where; N and M are the number of planes of cells in the
second and third dimensions.

The gauss-seidell method comes into effect when the latest values of the
field variable along the two adjacent lines of cells are used while calculating
the TDMA coefficients of a line of cells, which is sandwiched between them.

The matrix solver carries out the TDMA technique on all the lines of cells
along a predefined direction, known as the * SWEEP DIRECTION *.
When the sweep direction is 1 all the cells along the I direction form a TDMA
line. I.e. along each line J is constant. Similarly when the sweep direction is
2 all the cells along the J direction form a TDMA line. It is recommended
that the sweep direction should be choosen to be orthogonal to the primary
flow direction.

Sweeps of solver for each of the field variables define, how many times,
during each iteration step, the matrix solver is called to recalculate the
values of that variable. This is normally once per variable, except pressure
which is five times. This is because the pressure equation is usually harder to
converge.