Practical Ship Hydrodynamics

30 Practical Ship Hydrodynamics
Input data
Initial values for all unknowns
Determine coeff. + source terms
for momentum equations
Solve momentum equations
Determine mass flux and coeff. + source terms
for pressure correction equation
Solve pressure correction equation
Correct pressures, cell centre velocities, mass flux
No
Update cell face velocities
Invoke turbulence model
Convergence ?
Yes
STOP
Figure 1.4 Flow chart for SIMPLE algorithm
method is generally preferred to the SIMPLE method due to its better stability.
The discretization of the fundamental differential equations leads to very large
systems of linear equations which are usually sparse, i.e. most of the elements
of the matrix are zero. (This is fundamentally different from boundary element
methods where full matrices with an often not dominant main diagonal need
to solved.) Direct solvers like Gauss elimination or matrix inversion have
prohibitively excessive computational time and storage requirements. In addition,
the solution of the system of equations is embedded in an outer iteration
which requires only an approximate solution, because the coefficients due to the
non-linearity of the differential equations and the pressure–velocity coupling
require further corrections. Therefore field methods generally employ iterative
solvers:
ž Gauss–Seidel method (point iterative)