The use of sparse matrix techniques for solving the incompressible Navier-Stokes equations
The system of non linear equations arising in the calculation of fluid flows governed by the incompressible Navier-Stokes equations is considered. When using Newton or Picard iteration a system of linear equations of the form Ax = b has to be solved several times. Some sparse matrix techniques are introduced to solve these matrix equations.
Various computations of the laminar flow over a backward facing step are made. We do not take advantage of the special geometry of this problem and no restrictions are made with respect to the sparsity pattern of the coefficient matrices. The methods are tested for two different discretizations of the convective terms (upwind discretization and central differences) and for Reynoldsnumbers equal to 150 and 500.
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