Propagation of geometric uncertainties in heat transfer problems solved by RBF-FD meshless method

Abstract

The design of engineering components must take into account the manufacturing tolerances of production processes since they lead to uncertainties in the behaviour of the products. It is therefore of valuable practical interest to quantify such uncertainties, with particular reference to problems involving geometrical uncertainties of the boundaries. This task is carried out in the present work by coupling the Non-Intrusive Polynomial Chaos (PC) method, employed for the quantification of uncertainties, with a Radial Basis Function Finite Differences (RBF-FD) meshless method, employed for the numerical simulations. The PC method with the Non-Intrusive formulation allows the use of existing deterministic solvers for the accurate prediction of the sought random response, i.e., the statistic moments of the involved variables. The RBF-FD method is therefore employed as a black box solver for the required set of problems defined over deterministic domains. The main advantage of the RBF-FD meshless method over traditional mesh-based methods is its capability of easily deal with practical problems defined over complex-shaped domains since no traditional mesh is required. The geometrical flexibility of the RBF-FD is even more advantageous in the context of geometric uncertainty quantification with the Non-Intrusive PC method since different solutions over different geometries are required. The applicability of the proposed approach to practical problems is then presented through the prediction of geometric uncertainty effects for a tube heat exchanger under natural convection where a 2D steady incompressible flow is considered.