P1SA SCHEME FOR ACCELERATION OF INNER ITERATIONS CONVERGENCE CONSISTENT WITH THE WEIGHTED NODAL SCHEME FOR TRANSPORT EQUATION IN 1D GEOMETRIES

The P1SA scheme consistent with the nodal weighted LB/QC–weighted LD (WLB/QC-WLD) scheme is constructed and tested for 1D geometries case. The WLB/QC-WLD scheme is used as a tool in construction of an adaptive fix-up for the fourth order of accuracy linear best/quadratic continuous (LB/QC) scheme and the third order of accuracy linear discontinuous (LD) scheme. The algorithm described does not impose any restriction on the choice of the weighting coefficients of the differencing scheme used and reduces the solving of a quite complicated original P1 system to solving of the two-point equations system, similar to solved for the weighted diamond differencing (WDD) scheme case, that can be easily performed by the throughcomputations method. The interest to this algorithm is originated by the high accuracy in solving transport equation both in rectangular and curvilinear geometries, demonstrated by the adaptive WLB/QC-WLD and adaptive WLD schemes, and a need to construct an efficient algorithm for acceleration of inner iterations convergence for these schemes for 2D and 3D geometries. The proposed algorithm shows a possible way to resolve this problem with the use of early developed approach for solving the similar problem for the WDD scheme.