Reduced Basis Methods for fluid dynamics problems arising from Smart water network modelling
This work aims at investigating the use of reduced basis (RB) methods to diminish the cost of resolution of parameter-dependent PDEs arising from water network modelling. Due to their low computational cost, 1D models are widely used. However for laminar flows, the uniform velocity assumption in the pipe cross-section may no longer be correct. In this case 2D or 3D models are necessary. Classical discretization techniques, such as finite volume (FV) or finite element (FE) methods can prove to be too costly and time consuming, hence our focus on model reduction.
In this study, we focused on small networks (tens of meters long) and laminar flows governed by the incompressible Navier-Stokes equations with Dirichlet boundary conditions. The varying parameters were the velocity of the inlet and outlet flows prescribed at the boundaries.
Computation Fluid Dynamics (CFD) simulation has become a routine design tool for i) predicting accurately the thermal performances of electronics set ups and devices such as cooling system and ii) optimizing configurations. Although CFD simulations using discretization methods such as finite volume or finite element can be performed at different scales, from component/board levels to larger system, these classical discretization techniques can prove to be too costly and time consuming, especially in the case of optimization purposes where similar systems, with different design parameters have to be solved sequentially.The design parameters can be of geometric nature or related to the boundary conditions.
This motivates our interest on model reduction and particularly on reduced basis methods.