author = "Deiterding, Ralf and Domingues, Margarete Oliveira and Schneider, 
          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 
              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 = "17 jan. 2021"