A PRECONDITIONING ALGORITHM FOR JFNK METHOD APPLIED TO MULTI-PHYSICS CALCULATIONS

摘要

Jacobian-free Newton Krylov (JFNK) method is frequently applied to the simulation of coupled multi-physical systems due to its efficiency and capability for large-scale nonlinear problems. For instance, the nuclear reactor involves neutronics, heat conduction and fluid dynamics. As an essential part of JFNK, good preconditioners could make the solution more stable and efficient. Incomplete lower-upper (ILU) factorization is one of the popular choices for preconditioners. However, its accuracy is negatively related to computation cost. In other words, the price to obtain an accurate ILU preconditioner will sharply rise, especially in large-scale multi-physical systems. To address this issue, a preconditioner called SIPLU is proposed. The matrix factorization process is extracted from strongly implicit procedure (SIP) and the preconditioner is a combination of SIPLU algorithm and block Jacobi approach in the implemented JFNK method. The proposed SIPLU preconditioner has been successfully applied to a two-dimensional multi-physics problem. Results indicate that the preconditioning cost of SIPLU preconditioner is lower than ILU preconditioners, since it has simple structure and effective operation. Meanwhile, SIPLU preconditioner is a high-quality approximation to the Jacobian matrix. Its preconditioning quality is close to ILU(6), which is in upper level of ILU preconditioners in the numerical tests. This feature makes a major contribution in reducing the computation time.