Tensor Train Representation of High-Dimensional Unsteady Flamelet Manifolds

TL;DR

This paper introduces a tensor train (TT) approach to efficiently represent high-dimensional unsteady flamelet manifolds in CFD, significantly reducing memory usage and increasing computational speed while maintaining accuracy.

Contribution

The study pioneers the use of tensor trains for high-dimensional flamelet manifolds, enabling scalable, memory-efficient, and accurate representations in combustion simulations.

Findings

TT representation achieves significant memory reduction.

TT-based sampling offers up to 2.4X speedup.

Method is broadly applicable beyond combustion models.

Abstract

This study, for the first time, investigates the use of tensor trains (TTs) to represent high-dimensional unsteady flamelet progress variable (UFPV) manifolds in chemically reacting computational fluid dynamics (CFD). The UFPV framework captures the thermochemical state of reacting flows using a reduced set of parameters and pre-computed manifolds, avoiding the need to transport all species or solve large stiff reaction systems. High-dimensional manifolds enhance accuracy by resolving coupled thermochemical effects critical in high-speed reacting flows but impose substantial memory demands. Here, a five-dimensional UFPV manifold is constructed and stored in the TT format to address this limitation. Several chemical mechanisms and table sizes are examined to evaluate TT compression performance and accuracy. The TT representation achieves significant memory reduction while preserving manifold fidelity and combustion behavior. A one-dimensional reacting-flow case using the discontinuous Galerkin (DG)-based JENRE Multiphysics Framework confirms that TT-compressed manifolds are interchangeable with standard UFPV tables. In addition to memory reduction, benchmark tests show that TT-based manifold sampling can achieve up to 2.4X speedup relative to dense tensor evaluation. Although demonstrated for UFPV combustion models, the proposed TT framework is broadly applicable to other tabulation-based combustion methodologies and provides a scalable alternative to machine learning (ML)-based approaches for representing high-dimensional combustion manifolds.