@Article{DeiterdingDomiSchn:2020:CaStEu,
author = "Deiterding, Ralf and Domingues, Margarete Oliveira and Schneider,
Kai",
affiliation = "{University of Southampton} and {Instituto Nacional de Pesquisas
Espaciais (INPE)} and {Aix-Marseille Universit{\'e}}",
title = "Multiresolution analysis as a criterion for effective dynamic mesh
adaptation: a case study for Euler equations in the SAMR framework
AMROC",
journal = "Computers and Fluids",
year = "2020",
volume = "205",
pages = "e104583",
month = "June",
keywords = "Block-structured parallel adaptive mesh refinement, Adaptation
criteria, Multiresolution analysis, Wavelets, Compressible EULER
equations, AMROC.",
abstract = "Dynamic mesh adaptation methods require suitable refinement
indicators. In the absence of a comprehensive error estimation
theory, adaptive mesh refinement (AMR) for nonlinear hyperbolic
conservation laws, e.g. compressible Euler equations, in practice
utilizes mainly heuristic smoothness indicators like combinations
of scaled gradient criteria. As an alternative, we describe in
detail an easy to implement and computationally inexpensive
criterion built on a two-level wavelet transform that applies
projection and prediction operators from multiresolution analysis.
The core idea is the use of the amplitude of the wavelet
coefficients as smoothness indicator, as it can be related to the
local regularity of the solution. Implemented within the fully
parallelized and structured adaptive mesh refinement (SAMR)
software system AMROC (Adaptive Mesh Refinement in Object-oriented
C++), the proposed criterion is tested and comprehensively
compared to results obtained by applying the scaled gradient
approach. A rigorous quantification technique in terms of
numerical adaptation error versus used finite volume cells is
developed and applied to study typical two- and three-dimensional
problems from compressible gas dynamics. It is found that the
proposed multiresolution approach is considerably more efficient
and also identifies besides discontinuous shock and contact waves
in particular smooth rarefaction waves and their interaction as
well as small-scale disturbances much more reliably. Aside from
pathological cases consisting solely of planar shock waves, the
majority of realistic cases show reductions in the number of used
finite volume cells between 20 to 40%, while the numerical error
remains basically unaltered.",
doi = "10.1016/j.compfluid.2020.104583",
url = "http://dx.doi.org/10.1016/j.compfluid.2020.104583",
issn = "0045-7930",
language = "en",
urlaccessdate = "03 jun. 2024"
}