@inproceedings{ee080635408a4df1a222fa4671c34654,

title = "A highly parallel code for strongly coupled fluid-transport equations",

abstract = "We developed a finite volume package FVM and a solver HYMLS, both based on elements of the Trilinos EPETRA-package (see http://trilinos.sandia.gov/). HYMLS is a linear system solver for steady state incompressible Navier-Stokes equations coupled to transport equations in 2 and 3D [1, 2, 3]. We constructed recently a multilevel variant of it, which makes it possible to solve 3D problems of over 10 million unknowns quickly on a parallel computer. The behavior of the method is very much like that of multigrid methods. In fact one could see it as the father of the multigrid method. The solver is very robust. For the problem described in [4], it allowed a quick increase in the Reynolds number to get into the interesting region around Re=2000. Here we will show the performance of the method on the Rayleigh-B{\'e}nard convection in a cube, with six no-slip walls [5]. Also here we employ HYMLS to solve the linear systems resulting from a Cayley transform of the generalized eigenvalue problem.",

keywords = "High performance computing, Multilevel ILU, Multiphysics problems, Numerical methods",

author = "Weiyan Song and Wubs, {Fred W.} and Jonas Thies",

year = "2014",

month = jul,

day = "1",

language = "English",

series = "11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014",

publisher = "International Center for Numerical Methods in Engineering",

pages = "199--210",

editor = "Antonio Huerta and Eugenio Onate and Xavier Oliver",

booktitle = "11th World Congress on Computational Mechanics, WCCM 2014, 5th European Conference on Computational Mechanics, ECCM 2014 and 6th European Conference on Computational Fluid Dynamics, ECFD 2014",

note = "Joint 11th World Congress on Computational Mechanics, WCCM 2014, the 5th European Conference on Computational Mechanics, ECCM 2014 and the 6th European Conference on Computational Fluid Dynamics, ECFD 2014 ; Conference date: 20-07-2014 Through 25-07-2014",

}