Efficient coupling algorithms and reduced-order methods for high-fidelity multiphysics simulations of nuclear reactors

Abstract

The Residual Balance method and PGD each address parallel challenges of high-fidelity multiphysics simulations. The Residual Balance method is a coupling scheme that helps multiphysics simulations run efficiently. Proper Generalized Decomposition is a reduced-order method that efficiently solves highly-refined single-physics problems. Each provides improved computational efficiency, which is becoming increasingly important in nuclear reactor analysis. The improved efficiency provided by these methods can also be leveraged to facilitate new modeling applications.

As computational resources expand, researchers are able to develop and execute more detailed numerical models of physical systems. Greater fidelity can be obtained by coupling several physical models into a combined multiphysics simulation. An example in nuclear reactor analysis is combining a thermal-hydraulic code with a neutron transport code in order to obtain an accurate distribution of both neutron flux and temperature. The combination of numerical solvers that are individually computationally intensive can potentially result in a coupled system that is impractical to solve. Despite the exponential growth in computational capabilities over the past decades, experience has shown that the demand for more complex simulations grows just as fast. Therefore the need to use computational resources wisely still remains. The primary focus of this research is to improve multiphysics simulations by increasing their computational efficiency through new algorithms.

Several new improvements on a standard coupling method are developed in this work for the purpose of improving the performance of partitioned multiphysics problems. It is found that significant time savings result from eliminating over-solving from the iterative solution process. The Residual Balance method is developed to eliminate over-solving—that is, solving the constituent single-physics problems to an unnecessarily tight tolerance—from partitioned problems without sacrificing accuracy. It performs well across a variety of problems because it utilizes information about the coupled problem's convergence rate and the norms of the single-physics residuals in order to specify the best tolerance. For a reactor transient benchmark the performance is improved by a factor of 2.2.

After describing efficient implementations of multiphysics coupling methods, the focus turns to the single-physics solvers. Reduced-order methods can be leveraged to avoid runaway computing costs due to highly refined multidimensional meshes. Proper Generalized Decomposition (PGD) is a new method that creates a reduced-order basis on the fly instead of relying on time-consuming offline process. In this work, PGD is applied to the neutron diffusion equations and its performance is characterized for a wide variety of problem specifications. PGD solvers are developed for two neutron energy groups as well as three spatial dimensions. An eigenvalue solver is also demonstrated. The performance benefit of the PGD method is dependent upon the mesh refinement and the rank (degree of separability) of the solution. PGD is found to break even with a standard full-order solver on a mesh of approximately 250×250 elements in two dimensions, and about 35×35×20 elements in three dimensions. Further mesh refinement rapidly increases the advantage of PGD over the full-order solver.