On third-order limiter functions for finite volume methods

Schmidtmann, Birte; Abgrall, Rémi; Torrilhon, Manuel (2016). On third-order limiter functions for finite volume methods. Bulletin of the Brazilian Mathematical Society, N.S., 47(2):753-764.

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$^{rd}$-order accuracy, the new limiter is 3$^{rd}$-order accurate for smooth solution. In an earlier work, such a 3$^{rd}$-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.

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$^{rd}$-order accuracy, the new limiter is 3$^{rd}$-order accurate for smooth solution. In an earlier work, such a 3$^{rd}$-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.