On Third-Order Limiter Functions for Finite Volume Methods
This provides a concrete improvement for computational fluid dynamics practitioners using MUSCL-type schemes, though it is an incremental refinement of an existing method.
The authors propose a third-order accurate limiter function for finite volume methods on three-point stencils, closing a gap in prior work by specifying previously undefined parameters.
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.