@Article{CiCP-10-1257,
author = {Ravi Kannan},
title = {A High Order Spectral Volume Formulation for Solving Equations Containing Higher Spatial Derivative Terms: Formulation and Analysis for Third Derivative Spatial Terms Using the LDG Discretization Procedure},
journal = {Communications in Computational Physics},
year = {2011},
volume = {10},
number = {5},
pages = {1257--1279},
abstract = {<p style="text-align: justify;">In this paper, we develop a formulation for solving equations containing
higher spatial derivative terms in a spectral volume (SV) context; more specifically the
emphasis is on handling equations containing third derivative terms. This formulation
is based on the LDG (Local Discontinuous Galerkin) flux discretization method, originally
employed for viscous equations containing second derivatives. A linear Fourier
analysis was performed to study the dispersion and the dissipation properties of the
new formulation. The Fourier analysis was utilized for two purposes: firstly to eliminate
all the unstable SV partitions, secondly to obtain the optimal SV partition. Numerical
experiments are performed to illustrate the capability of this formulation. Since
this formulation is extremely local, it can be easily parallelized and a <em>h-p</em> adaptation
is relatively straightforward to implement. In general, the numerical results are very
promising and indicate that the approach has a great potential for higher dimension
Korteweg-de Vries (KdV) type problems.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.070710.100111a},
url = {http://global-sci.org/intro/article_detail/cicp/7483.html}
}