High-resolution limiters for projection-based low-rank methods

Develop Minmod- and WENO-type high-resolution limiters for projection-based low-rank methods, including the Reduced Augmentation Implicit Low-rank (RAIL) framework and other dynamical low-rank methods, while maintaining their factorized solution structure over neighboring spatial cells.

Background

The paper presents a rank-adaptive solver for a hybrid kinetic-ion, fluid-electron Vlasov-Fokker-Planck model. Its velocity-space solution is represented in factorized low-rank form and advanced using the RAIL projection-based implicit-explicit integrator. The authors note that nonlinear high-resolution methods are difficult to incorporate into rank-adaptive frameworks because numerical limiters must operate on factorized solutions defined over neighboring cells.

Minmod and WENO-type limiters have already been used in other rank-adaptive settings, including discontinuous Galerkin and sketching-based low-rank methods. However, their application to projection-based methods such as RAIL and related dynamical low-rank schemes remains unresolved, motivating the stated open research direction.