Addressing Over-Solving in Multiphysics Codes with Nested Solvers

Abstract

Examples of multiphysics problems in the field of nuclear engineering are numerous. For light water reactors the coupling of neutronics with thermal-hydraulics is the most predominant. Often this coupling is modeled by combining existing codes in a Picard Iteration scheme, that is, by solving one physics then using that answer to solve the other and iterating until both answers stabilize. However, simply solving to a high precision on every Picard (multiphysics) iteration is much less efficient than progressively solving to higher precisions. This unneeded work is known as over-solving. Over-solving in single-physics solvers has been studied previously for the Newton method and Chebyshev iteration. Both of these methods solve an inner linear problem that determines the next update step for the outer loop. If the inner problem is solved to a high precision in every outer iteration, the result will be substantially more computational expense (over-solving) and a higher probability of reaching the 'wrong' solution. Methods for reducing over-solving in partitioned multiphysics codes have only been developed recently. This work introduces further improvements, including an investigation of over-solving methods on both the multiphysics and single-physics levels.