Manifold reducibility for a Lagrangian finite element solver with remeshing

Lagrangian solvers are well suited for large deformation fluid problems containing non-trivial mesh distortions. This includes problems with evolving free surfaces, breaking waves, fluid-structure interaction problems, or free-flowing fluids with complex rheology. We focus on the Particle Finite Element Method (PFEM). This Lagrangian solver combines the advantages of a particle description of the fluid with a finite element solver and efficient remeshing algorithms. It creates vast data structures of varying sizes as model ouputs. As the mesh varies, regrouping the different fields of interest into a single solution manifold becomes non-trivial. This paper will discuss multiple strategies to reduce a posteriori the solution manifolds formed from PFEM simulations. Data reduction consists in a trade-off between preserving the original data precision and having smaller reduced data sets and is often an important first step towards surrogate models. Two novel mapping-based nonlinear reduction methods will be presented to reduce different high-fidelity PFEM simulations. The data reduction will be made on complete sets of time-dependent simulation snapshots and consists in the separation of space and time with the calculation of space and time modes. We will compare the precision - i.e. the L2 error of the reconstructed snapshot - the reducibility - i.e. the number of required modes for a given precision in the reduction - and the implementation complexity of the proposed methods.