arXiv subjects

Pierre-Alain Boucard

Publications and source records attributed to Pierre-Alain Boucard.

2 recordsLinked to original sources

arXiv2026

A space-time LATIN-PGD strategy for solving Newtonian compressible 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. In this contribution, we place ourselves within the framework of Newtonian compressible and laminar flows. This specific and relatively simple case enables focusing on flows for which a state equation provides a direct relation between pressure and density. It is then possible to use the LATIN solver to set up a pressure-velocity decoupling algorithm. Moreover, Proper Generalised Decomposition (PGD) is natively included in the solver and yields two independent space-time decompositions for the velocity and the pressure fields. 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.

math.NA↗

arXiv2025

A strategy with reduced models dedicated to parametrized nonlinear strongly coupled thermo-poroelasticity problems

This paper offers an approach to deal with parametrized nonlinear strongly coupled thermo-poroelasticity problems. The approach uses the LATIN-PGD method and extends previous work in multiphysics problems. Proper Generalized Decomposition (PGD) allows the building of independent reduced-order bases for each physics. This point is particularly appropriate for thermo-poroelasticity problems whose physics present different dynamics. In parametrized problems dealing with material variability, a new computation is initialized with the result of a previous simulation to speed up the computation times. As a first step, the solver is validated on a standard benchmark in thermo-poroelasticity. The solver shows good performance even in the nonlinear frame. Then, the approach for parametrized problems is addressed on an academic problem and a more complex one, which is part of an industrial process. The results show that the method is effective and less time-consuming than naive approaches.

physics.class-ph↗