# A L2-norm regularized incremental-stencil WENO scheme for compressible flows

## TL;DR

This paper introduces a novel L2-norm regularized incremental-stencil WENO scheme that enhances robustness and accuracy in simulating compressible flows with complex structures by adaptively modulating stencil weights.

## Contribution

It proposes a new L2-norm regularization approach integrated into WENO weighting, improving accuracy and efficiency in flow simulations over existing methods.

## Key findings

- Achieves high robustness in complex flow simulations.
- Resolves fine flow structures effectively.
- Demonstrates improved computational efficiency.

## Abstract

For the simulation of compressible flow with a broadband of length scales and discontinuities, the WENO schemes using incremental stencil sizes other than uniform ones are promising for more robustness and less numerical dissipation. However, in smooth region, large weights may be assigned to smaller stencils due to the lack of high-order derivatives in the smoothness indicator compared with that of larger stencils, and may degrade the order accuracy and lead too much numerical dissipation to resolve fine flow structures. In order to cope with this drawback, based on the stencil selection of WENO-IS [Wang et al., IJMF 104 (2018): 20-31], we propose a L2-norm regularized incremental-stencil WENO scheme. In this method, a new L2-norm regularization is introduced into the WENO weighting strategy to modulate the weights of incremental-width stencils by taking account the L2-norm error term. A high-order non-dimensional discontinuity detector is then utilized as the regularization parameter for adaptive control. In addition, a hybrid method is adopted to further improve the performance and the computational efficiency. A number of benchmark cases suggest that the present scheme achieves very good robustness and fine-structure resolving capabilities.