ITERATION ACCELERATION RDSA METHOD FOR SOLVING ONE-DIMENSIONAL NEUTRON TRANSPORT EQUATION
A. D. Gadzhiev, I. A. Kondakov, A. A. Shestakov
VANT. Ser.: Mat. Mod. Fiz. Proc 2007. Вып.2. С. 3-19.
Diffusive-synthetic method for iteration acceleration based on ROMB scheme (RDSA method) is suggested. It conforms to difference method of transport equation solution. Multi-stage Larsen procedure is used for conformance. It includes:1) P1-design of difference equations for transport equation;2) P1-design of link ratio for transport equation;3) P1-design of boundary conditions;4) transition to Pi-equations in regard to corrections;5) transformation of obtained equations to the form with central differences and solution of obtained equations. Multi-stage Larsen procedure can be formally used for transport equations with all geometries and schemes. But for multidimensional curvilinear geometries the obtained averaged set of P1 equations turns out to be very complicated and execution of stage 5 becomes problematical. In particular, P1-equations can’t be re-arranged to the form with central differences for their subsequent solving. Larsen procedure is simplified with use of ROMB scheme. Transition to three-point form is not required on the stage 5 because the obtained set of Larsen procedure is simplified with use of ROMB scheme. Transition to three-point form is not required on the stage 5 because the obtained set of P1-equations is directly solved. Method is generalized to many-dimensional curvilinear geometries that may be an important advantage of new approach.
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