@Article{CiCP-21-271,
author = {Boscheri , Walter and Loubère , Raphaël},
title = {High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms},
journal = {Communications in Computational Physics},
year = {2018},
volume = {21},
number = {1},
pages = {271--312},
abstract = {<p style="text-align: justify;">In this paper we present a 2D/3D high order accurate finite volume scheme
in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic
systems of partial differential equations with non-conservative products and stiff
source terms. This scheme is constructed with a single stencil polynomial reconstruction
operator, a one-step space-time ADER integration which is suitably designed for
dealing even with stiff sources, a nodal solver with relaxation to determine the mesh
motion, a path-conservative integration technique for the treatment of non-conservative
products and an a posteriori stabilization procedure derived from the so-called Multidimensional
Optimal Order Detection (MOOD) paradigm. In this work we consider
the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative
model involving non-conservative products as well as relaxation source
terms which are allowed to become stiff. The new scheme is validated against a set
of test cases on 2D/3D unstructured moving meshes on parallel machines and the
high order of accuracy achieved by the method is demonstrated by performing a numerical
convergence study. Classical Riemann problems and explosion problems with
exact solutions are simulated in 2D and 3D. The overall numerical code is also profiled
to provide an estimate of the computational cost required by each component of the
whole algorithm.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2015-0024},
url = {http://global-sci.org/intro/article_detail/cicp/11240.html}
}