A discontinuous Galerkin overset scheme using WENO reconstruction and subcells for two-dimensional problems

TL;DR

This paper introduces a novel overset grid communication scheme for 2D problems using WENO reconstruction and subcells within the discontinuous Galerkin method, enhancing accuracy and shock handling.

Contribution

It presents a new overset grid communication scheme employing WENO reconstruction with subcells, improving accuracy and shock capturing in 2D discontinuous Galerkin methods.

Findings

Maintains higher order accuracy in tests.

Effectively captures shocks with limiter behavior.

Demonstrates improved communication between overset grids.

Abstract

A new scheme for communication between overset grids using subcells and Weighted Essentially Non Oscillatory (WENO) reconstruction for two-dimensional problems has been proposed. The effectiveness of this procedure is demonstrated using the discontinuous Galerkin method (DGM). This scheme uses WENO reconstruction using cell averages by dividing the immediate neighbors into subcells to find the degrees of freedom in cells near the overset interface. This also has the added advantage that it also works as a limiter if a discontinuity passes through the overset interface. Accuracy tests to demonstrate the maintenance of higher order are provided. Results containing shocks are also provided to demonstrate the limiter aspect of the data communication procedure.