A modified moving least square algorithm for solution transfer on a spacer grid surface

Solution transfer operators constructed from a moving least square basis have recently been researched for multiphysics simulations of pressurized water reactors. Useful for solution transfer between surfaces and volumes, moving least square schemes are attractive because they do not require a computational mesh but instead use a point cloud representation of the discretized domain. In addition, they are often able to achieve a very accurate and conservative solution reconstruction and are readily parallelized to scale on leadership class computing facilities. When studying the moving least square technique, we discovered that when the algorithm was applied to solution transfers on a spacer grid surface, numerical instabilities in the singular value decomposition algorithm used to generate the moving least square basis resulted in large errors after a few solution transfer iterations, rendering the method unusable in many situations. In this work we assess these instabilities and show that using a truncated singular value decomposition and simply augmenting the threshold in the algorithm does not alleviate the instabilities without introducing additional error into the solution transfer and adding an additional free parameter to the algorithm. We then modify the moving least square algorithm to ensure that the terms of the spatial polynomials used to construct the least square problem are linearly independent, resulting in a full rank linear system which can be used to calculate an optimal truncation threshold. We show that the new algorithm significantly improves the stability of repeated solution transfers on the spacer grid surface.