A KP1 Scheme for Acceleration of Inner Iterations for the Transport Equation in 3D Geometry Consistent with Nodal Schemes: 2. Splitting Method for Solving the P1 System for Acceleration Corrections

Abstract

An algorithm is proposed for solving the \({{P}_{1}}\) system for acceleration corrections that arises in constructing a \(K{{P}_{1}}\) scheme for accelerating the convergence of inner iterations consistent with the nodal LD (Linear Discontinues) and LB (Linear Best) schemes of third and fourth-order accuracy in space for the transport equation in three-dimensional \(r,\;\vartheta ,\;z\) geometry. The algorithm is based on a cyclic splitting method combined with the through-computation algorithm for solving auxiliary two-point equations system. A modification of the algorithm is considered for three-dimensional \(x,\;y,\;z\) geometry.