Approximate inversion method for five point difference matrix equations

SIMMER, a best estimate computer program for LMFBR disrupted core analysis, is being developed at the Los Alamos Scientific Laboratory. Recent fluid dynamics methods development for SIMMER was concerned with enhancing numerical stability and reducing calculational effort. One such development considered the evaluation of the pressure change and material density change distributions during a time step. The spatially uncoupled approximate solution to be iterated was replaced with a correct spatially coupled simultaneous solution. This resulted in decreased calculational effort per time step as well as enhanced stability to allow much larger time steps to be taken. This improvement was realized by formulating the correct five diagonal matrix equations in two-dimensional rectilinear geometry and then solving them with an efficient matrix inversion routine. Initially, the Successive Line OverRelaxation (SLOR) method was used to solve these matrix equations. Instances of weakly diagonally dominant matrices requiring hundreds of SLOR iterations to invert them prompted consideration of a more efficient method. A new Approximate Inversion Method (AIM) was felt to have this efficiency. The method is a variation of the direct Crout--Cholesky forward elimination and backward substitute method. Crout--Cholwesky method element operations on a tridiagonal element matrix are applied in AIM as submatrix block operations on a tridiagonal block matrix. To make the method efficient, a submatrix collapsing approximation is applied. Making this approximation requires that the method be iterative. A description of this iterative algorithm and its approximate matrix inversion is included