1,498 research outputs found
eXtended hybridizable discontinuous Galerkin for incompressible flow problems with unfitted meshes and interfaces
The eXtended hybridizable discontinuous Galerkin (X-HDG) method is developed for the solution of Stokes problems with void or material interfaces. X-HDG is a novel method that combines the hybridizable discontinuous Galerkin (HDG) method with an eXtended finite element strategy, resulting in a high-order, unfitted, superconvergent method, with an explicit definition of the interface geometry by means of a level-set function. For elements not cut by the interface, the standard HDG formulation is applied, whereas a modified weak form for the local problem is proposed for cut elements. Heaviside enrichment is considered on cut faces and in cut elements in the case of bimaterial problems. Two-dimensional numerical examples demonstrate that the applicability, accuracy, and superconvergence properties of HDG are inherited in X-HDG, with the freedom of computational meshes that do not fit the interfacesPeer ReviewedPostprint (author's final draft
Parallel adaptive mesh refinement for incompressible flow problems
We present an algorithm for the solution of the incompressible Navier-
Stokes equations combined with local refinement of the mesh based on an error estimation. Our solution strategy is based on well-established CFD techniques and has been designed to be efficient and scalable in a parallel environment. This has proved to be specially challenging for the mesh refinement, for which we propose an algorithm designed to use as little non-local information as possible. We complement the discussion with a numerical example.Postprint (published version
Finite element pressure stabilizations for incompressible flow problems
Discretizations of incompressible flow problems with pairs of finite element spaces that do not satisfy a discrete inf-sup condition require a so-called pressure stabilization. This paper gives an overview and systematic assessment of stabilized methods, including the respective error analysis
h-multigrid agglomeration based solution strategies for discontinuous Galerkin discretizations of incompressible flow problems
In this work we exploit agglomeration based -multigrid preconditioners to
speed-up the iterative solution of discontinuous Galerkin discretizations of
the Stokes and Navier-Stokes equations. As a distinctive feature -coarsened
mesh sequences are generated by recursive agglomeration of a fine grid,
admitting arbitrarily unstructured grids of complex domains, and agglomeration
based discontinuous Galerkin discretizations are employed to deal with
agglomerated elements of coarse levels. Both the expense of building coarse
grid operators and the performance of the resulting multigrid iteration are
investigated. For the sake of efficiency coarse grid operators are inherited
through element-by-element projections, avoiding the cost of numerical
integration over agglomerated elements. Specific care is devoted to the
projection of viscous terms discretized by means of the BR2 dG method. We
demonstrate that enforcing the correct amount of stabilization on coarse grids
levels is mandatory for achieving uniform convergence with respect to the
number of levels. The numerical solution of steady and unsteady, linear and
non-linear problems is considered tackling challenging 2D test cases and 3D
real life computations on parallel architectures. Significant execution time
gains are documented.Comment: 78 pages, 7 figure
IFISS : a computational laboratory for investigating incompressible flow problems
The IFISS Incompressible Flow & Iterative Solver Software package contains software which can be run with MATLAB or Octave to create a computational laboratory for the interactive numerical study of incompressible flow problems. It includes algorithms for discretization by mixed finite element methods and a posteriori error estimation of the computed solutions, together with state-of-the-art preconditioned iterative solvers for the resulting discrete linear equation systems. In this paper we give a flavour of the code's main features and illustrate its applicability using several case studies. We aim to show that IFISS can be a valuable tool in both teaching and research
Computational fluid mechanics utilizing the variational principle of modeling damping seals
A computational fluid dynamics code for application to traditional incompressible flow problems has been developed. The method is actually a slight compressibility approach which takes advantage of the bulk modulus and finite sound speed of all real fluids. The finite element numerical analog uses a dynamic differencing scheme based, in part, on a variational principle for computational fluid dynamics. The code was developed in order to study the feasibility of damping seals for high speed turbomachinery. Preliminary seal analyses have been performed
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