TY - JOUR
T1 - A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes
AU - Guo , Yunrui
AU - Tang , Lingyan
AU - Zhang , Hong
AU - Song , Songhe
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 114
EP - 137
PY - 2018
DA - 2018/10
SN - 10
DO - http://doi.org/10.4208/aamm.OA-2016-0196
UR - https://global-sci.org/intro/article_detail/aamm/10504.html
KW - Triangular meshes, WENO, scaling limiter, maximum-principle-preserving.
AB - <p style="text-align: justify;">We modify the construction of the third order finite volume WENO scheme
on triangular meshes and present a simplified WENO (SWENO) scheme. The novelty
of the SWENO scheme is the less complexity and lower computational cost when
deciding the smoothest stencil through a simple mechanism. The LU decomposition
with iterative refinement is adopted to implement ill-conditioned interpolation matrices
and improves the stability of the SWENO scheme efficiently. Besides, a scaling technique
is used to circumvent the growth of condition numbers as mesh refined. However,
weak oscillations still appear when the SWENO scheme deals with complex low
density equations. In order to guarantee the maximum-principle-preserving (MPP)
property, we apply a scaling limiter to the reconstruction polynomial without the loss
of accuracy. A novel procedure is designed to prove this property theoretically. Finally,
numerical examples for one- and two-dimensional problems are presented to verify
the good performance, maximum principle preserving, essentially non-oscillation and
high resolution of the proposed scheme.</p>