# Comparison of semi-Lagrangian discontinuous Galerkin schemes for linear and nonlinear transport simulations

## TL;DR

This paper reviews and compares semi-Lagrangian discontinuous Galerkin methods for linear and nonlinear transport problems, providing practical guidance based on extensive numerical results.

## Contribution

It offers a comprehensive comparison of splitting and non-splitting SLDG methods, highlighting their performance differences for multi-dimensional transport simulations.

## Key findings

- Splitting SLDG methods perform better in certain scenarios.
- Non-splitting SLDG methods offer advantages in others.
- Guidelines for selecting optimal SLDG schemes are provided.

## Abstract

Transport problems arise across diverse fields of science and engineering. Semi-Lagrangian (SL) discontinuous Galerkin (DG) methods are a class of high order deterministic transport solvers that enjoy advantages of both SL approach and DG spatial discretization. In this paper, we review existing SLDG methods to date and compare numerical their performances. In particular, we make a comparison between the splitting and non-splitting SLDG methods for multi-dimensional transport simulations. Through extensive numerical results, we offer a practical guide for choosing optimal SLDG solvers for linear and nonlinear transport simulations.