3 research outputs found
On Third-Order Limiter Functions for Finite Volume Methods
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 -order accuracy,
the new limiter is -order accurate for smooth solutions. In an
earlier work, such a -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.Comment: 8 pages, conference proceeding
Relations between WENO3 and Third-order Limiting in Finite Volume Methods
Weighted essentially non-oscillatory (WENO) and finite volume (FV) methods
employ different philosophies in their way to perform limiting. We show that a
generalized view on limiter functions, which considers a two-dimensional,
rather than a one-dimensional dependence on the slopes in neighboring cells,
allows to write WENO3 and -order FV schemes in the same fashion.
Within this framework, it becomes apparent that the classical approach of FV
limiters to only consider ratios of the slopes in neighboring cells, is overly
restrictive. The hope of this new perspective is to establish new connections
between WENO3 and FV limiter functions, which may give rise to improvements for
the limiting behavior in both approaches.Comment: 22 page
Conservative logarithmic reconstructions and finite volume methods
A class of high-order reconstruction methods based on logarithmic functions is presented. Inspired by Marquina's hyperbolic method, we introduce a double logarithmic ansatz of fifth order of accuracy. Low variation is guaranteed by the ansatz and (slope-) limiting is avoided. The method can reconstruct smooth extrema without order reduction. Fifth order of convergence is verified in a numerical experiment governed by the nonlinear Euler system. Numerical experiments, including the Osher-Shu shock/acoustic interaction, are presented