@Article{CiCP-18-4,
author = {},
title = {A Slope Constrained 4th Order Multi-Moment Finite Volume Method with WENO Limiter},
journal = {Communications in Computational Physics},
year = {2015},
volume = {18},
number = {4},
pages = {901--930},
abstract = {<p style="text-align: justify;">This paper presents a new and better suited formulation to implement the
limiting projection to high-order schemes that make use of high-order local reconstructions
for hyperbolic conservation laws. The scheme, so-called MCV-WENO4 (multi-moment
Constrained finite Volume with WENO limiter of 4th order) method, is an
extension of the MCV method of Ii &amp; Xiao (2009) by adding the 1st order derivative
(gradient or slope) at the cell center as an additional constraint for the cell-wise local
reconstruction. The gradient is computed from a limiting projection using the WENO
(weighted essentially non-oscillatory) reconstruction that is built from the nodal values
at 5 solution points within 3 neighboring cells. Different from other existing methods
where only the cell-average value is used in the WENO reconstruction, the present
method takes account of the solution structure within each mesh cell, and thus minimizes
the stencil for reconstruction. The resulting scheme has 4th-order accuracy and
is of significant advantage in algorithmic simplicity and computational efficiency. Numerical
results of one and two dimensional benchmark tests for scalar and Euler conservation
laws are shown to verify the accuracy and oscillation-less property of the
scheme.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.081214.250515s},
url = {https://global-sci.com/article/80348/a-slope-constrained-4th-order-multi-moment-finite-volume-method-with-weno-limiter}
}