# A compact subcell WENO limiting strategy using immediate neighbors for Runge-Kutta Discontinuous Galerkin Methods

## TL;DR

This paper introduces a compact subcell WENO limiter for Discontinuous Galerkin Methods that uses only immediate neighbors, improving accuracy and efficiency in solving hyperbolic conservation laws.

## Contribution

It presents a novel CSWENO limiter utilizing only neighboring cells, enhancing performance over traditional WENO limiters in high-order DG methods.

## Key findings

- Slightly better performance than parent WENO limiter at higher orders
- Effective in 1D and 2D Burgers and Euler equations
- Maintains accuracy with a compact stencil

## Abstract

A compact subcell WENO (CSWENO) limiter is proposed for the solution of hyperbolic conservation laws with Discontinuous Galerkin Method which uses only the immediate neighbors of a given cell. These neighbors are divided into the required stencil for WENO reconstruction and an existing WENO limiting strategy is used. Accuracy tests and results for one-dimensional and two-dimensional Burgers equation and one-dimensional and two-dimensional Euler equations for Cartesian meshes are presented using this limiter. Comparisons with the parent WENO limiter are provided wherever appropriate and the performance of the current limiter is found to be slightly better than the parent WENO limiter for higher orders.