A space-time LATIN-PGD strategy for solving Newtonian compressible flows

TL;DR

This paper introduces a novel space-time LATIN-PGD solver for Newtonian compressible laminar flows, enabling efficient decoupling of pressure and velocity fields with promising validation results and potential for more complex material laws.

Contribution

The paper presents a new space-time LATIN-PGD solver that decouples pressure and velocity in compressible flows, integrating PGD for independent space-time decompositions.

Findings

Validated on analytical solutions with good accuracy

Successfully applied to more complex flow problems

Demonstrates potential for future complex material law simulations

Abstract

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.