On Third-Order Limiter Functions for Finite Volume Methods

TL;DR

This paper introduces a third-order accurate finite volume limiter function for smooth solutions, improving upon classical second-order limiters, and clarifies the parameters needed for its implementation.

Contribution

It presents a new third-order limiter function for finite volume methods with explicit parameter specifications, enhancing accuracy over classical second-order limiters.

Findings

Achieves third-order accuracy for smooth solutions

Provides parameter details for the limiter function

Builds on previous third-order limiter proposals

Abstract

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield $2^{\text{nd}}$-order accuracy, the new limiter is $3^\text{rd}$-order accurate for smooth solutions. In an earlier work, such a $3^\text{rd}$-order limiter function was proposed and showed successful results [2]. However, it came with unspecified parameters. We close this gap by giving information on these parameters.