 formula_1
Due to the non-linearity of the convective term in the momentum equation that is written above, this problem is solved with a nested-loop approach.While so called "global"
or "inner iterations" represent the real time-steps and are used to update the variables formula_2 and formula_3, based on a linearized system, and boundary conditions; there is also an "outer loop" for updating the coefficients of the linearized system.The outer iterations comprise two steps