Multigrid preconditioning of steam generator two-phase mixture balance equations in the Genepi software

Within the framework of averaged two-phase mixture flow simulations of PWR Steam Generators (SG), this paper provides a geometric version of a pseudo-FMG FAS preconditioning of the balance equations used in the CEA Genepi code. The 3D steady-state flow is reached by a transient computation using a fractional step algorithm and a projection method. Our application is based on the PVM package. The difficulties of applying geometric FAS multigrid methods to the balance equations solver are addressed. The effects on the convergence behaviour of the numerical parameters are investigated. An original parallel red-black pseudo-FMG FAS multigrid algorithm is also presented. The use of dynamic multigrid cycles leads to perceptible improvements in the computation convergences. Numerical tests (academic and industrial simulations) underline a noticeable computation speed-up, essentially for a large number of freedom degrees: the speed-up reached for 2 or 3 grids ranges between 2 and 3.