A first application of the space-time LATIN-PGD strategy for solving Newtonian incompressible laminar flows

Simulating flow problems is at the core of many engineering applications but often requires high computational effort, especially when dealing with complex models. This work presents a novel approach for resolving flow problems using the LATIN-PGD solver. Since this constitutes the first application of LATIN-PGD to fluid problems, the present work is restricted to the framework of incompressible, laminar, Newtonian flows. We propose two approaches in this contribution to address fluid problems with the LATIN-PGD solver: one solves a monolithic saddle-point problem at each global stage, while the other uses a projection method to separate the computation of the velocity and pressure field. Proper Generalized Decomposition (PGD) is natively included in the solver and enables significant computation gains compared to a full-order model. As a first step, the solver is validated on a problem for which an analytical solution is available. It is then applied to slightly more complex problems. The results show good agreement with the literature, and we expect that the solver could be used to compute more complicated material laws in the future.