ParMooN is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MooNMD [28]: strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and a geometric multigrid preconditioner with the option to use different finite element spaces on different levels of the multigrid hierar- * Corresponding author.Email addresses: ulrich.wilbrandt@wias-berlin.de (Ulrich Wilbrandt), clemens.bartsch@wias-berlin.de (Clemens Bartsch), naveed.ahmed@wias-berlin.de (Naveed Ahmed), najib.alia@wias-berlin.de (Najib Alia), felix.anker@wias-berlin.de (Felix Anker), laura.blank@wias-berlin.de (Laura Blank), alfonso.caiazzo@wias-berlin.de (Alfonso Caiazzo), sashi@cds.iisc.ac.in (Sashikumaar Ganesan), swetlana.giere@wias-berlin.de (Swetlana Giere), gunar.matthies@tu-dresden.de (Gunar Matthies), raviteja@cmg.cds.iisc.ac.in (Raviteja Meesala), shamim@cmg.cds.iisc.ac.in (Abdus Shamim), jagan@cmg.cds.iisc.ac.in (Jagannath Venkatesan), volker.john@wias-berlin.de (Volker John)1 The work of Najib Alia has been supported by a funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 675715 (MIMESIS).2 The work of Felix Anker has been supported by grant Jo329/10-2 within the DFG priority programme 1679: Dynamic simulation of interconnected solids processes.3 The work of Sashikumaar Ganesan has partially been supported by the Naval Research Board, DRDO, India through the grant NRB/4003/PG/368. 4 The work of Volker John has partially been supported by grant Jo329/10-2 within the DFG priority programme 1679: Dynamic simulation of interconnected solids processes. chy. After having presented some thoughts about in-house research codes, this paper focuses on aspects of the parallelization for a distributed memory environment, which is the main novelty of ParMooN. Numerical studies, performed on compute servers, assess the efficiency of the parallelized geometric multigrid preconditioner in comparison with some parallel solvers that are available in the library PETSc. The results of these studies give a first indication whether the cumbersome implementation of the parallelized geometric multigrid method was worthwhile or not.
Abstract-A mesh-dependent relation for the slip number in the Navier-slip with friction boundary condition for computations of impinging droplets with sharp interface methods is proposed. The relation is obtained as a function of Reynolds number, Weber number and the mesh size. The proposed relation is validated for several test cases by comparing the numerically obtained wetting diameter with the experimental results. Further, the computationally obtained maximum wetting diameter using the proposed slip relation is verified with the theoretical predictions. The relative error between the computationally obtained maximum wetting diameter and the theoretical predictions is less than 10% for impinging droplet on a hydrophilic surface, and the error increases in the case of hydrophobic surface.
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