Data-driven discrete closure models for large-eddy simulation of incompressible turbulence

Turbulent flows are ubiquitous in nature and engineering, yet their direct numerical simulation (DNS) remains prohibitively expensive at the high Reynolds numbers encountered in practice. Large-eddy simulation (LES) reduces this cost by resolving only the large-scale motions and modeling the effect of the unresolved scales through a closure model. This thesis develops new data-driven closure models for LES of incompressible turbulence, guided by the principle that the numerical discretization should be treated as a fundamental part of the LES formulation. The thesis is organized around three research directions. The first concerns discretization-consistent closure formulations. Starting from the linear convection equation with a non-uniform filter, intrusive and non-intrusive methods for learning the discretely filtered operator are compared, and derivative fitting is found to provide the best trade-off between accuracy and practicality. The ``discretize first, filter next'' approach is then extended to the incompressible Navier-Stokes equations, where a divergence-consistent face-averaging filter is proposed that ensures full model-data consistency and avoids pressure-related stability issues. It is shown that when the discretization is properly accounted for, a-priori training suffices for accurate and stable neural-network-based LES. Exact expressions for the unresolved stress tensor in discrete filtered conservation laws are further derived, revealing that this tensor is non-symmetric and non-local---properties absent from the classical continuous formulation. The second direction investigates the incorporation of physical structure into closure models. Unconstrained neural networks, tensor basis neural networks, and group-equivariant convolutional neural networks are compared for predicting the sub-filter stress. While unconstrained networks achieve the highest pointwise accuracy, symmetry-preserving architectures better respect the physical constraints of the equations, producing more physically consistent velocity-gradient statistics. Moreover, built-in symmetry constraints reduce the space of learnable functions, which may improve generalization to unseen Reynolds numbers and flow configurations. Symmetry-preserving models also cannot introduce spurious frame-dependent forces, improving numerical stability. The third direction addresses the software infrastructure needed for data-driven closure modeling. The open-source Julia package IncompressibleNavierStokes.jl is presented for DNS and LES on staggered Cartesian grids. The solver uses energy-conserving finite volume discretizations with hardware-agnostic kernels that run on both CPUs and GPUs, and is made fully differentiable through hand-written adjoint kernels, enabling a-posteriori training of neural network closure models embedded in the solver. The overarching conclusion is that before any LES modeling can take place, the filter, grid, numerical fluxes, and discretization scheme should be clearly defined. Closure models should be designed to act on top of the implicit dissipation already incorporated into the numerical scheme, so that sub-filter effects are not accounted for twice.

• View at Worldcat

Full Text ( Final Version , 19mb )