Dune-UDG: A Cut-Cell Framework for Unfitted Discontinuous Galerkin Methods
Simulations on complex shaped domains are of big interest as the mesh generation for such domains is still an involved process. Recently, cut-cell based methods are becoming very popular. These methods avoid the problems of mesh-generation by using unfitted discretizations on cut-cell meshes. We present the Dune-UDG module which allows an easy implementation of Unfitted Discontinuous Galerkin methods on cut-cell grids. Different geometry representations are available. Using the presented interfaces it is possible to implement completely new cut-cell representations with a minimum of work.
KeywordsQuadrature Rule Discontinuous Galerkin Method Domain Index Discontinuous Galerkin Scheme Complicated Domain
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- 3.Bastian, P., Engwer, C.: An unfitted finite element method using discontinuous Galerkin. International Journal for Numerical Methods in Engineering 79(12) (2009)Google Scholar
- 4.Bear, J.: Dynamics of fluids in porous media. Dover Publications (1988)Google Scholar
- 5.Belytschko, T., Moes, N., Usui, S., Parimi, C.: Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 50(4) (2001)Google Scholar
- 8.Dolbow, J.E.: An extended finite element method with discontinuous enrichment for applied mechanics. PhD thesis, Northwestern University (1999)Google Scholar
- 9.Engwer, C.: An Unfitted Discontinuous Galerkin Scheme for Micro-scale Simulations and Numerical Upscaling. PhD thesis, Universität Heidelberg (2009)Google Scholar
- 10.Engwer, C., Bastian, P., Kuttanikkad, S.P.: An unfitted discontinuous galerkin finite element method for pore scale simulations. In: 9th International Workshop on State-of-the-Art in Scientific and Parallel Computing. LNCS, Springer, Heidelberg (2008); (in press)Google Scholar
- 11.Bastian, P., Engwer, C., Fahlke, J., Ippisch, O.: An Unfitted Discontinuous Galerkin method for pore-scale simulations of solute transport. Mathematics and Computers in Simulation 81(10), 2051–2061 (2011), http://www.sciencedirect.com/science/article/pii/S0378475410004258 MathSciNetMATHCrossRefGoogle Scholar
- 12.Fidkowski, K.J.: A simplex cut-cell adaptive method for high-order discretizations of the compressible Navier-Stokes equations. PhD thesis, Massachusetts Institute of Technology (2007)Google Scholar
- 13.Heimann, F., Engwer, C., Ippisch, O., Bastian, P.: An unfitted interior penalty discontinuous Galerkin method for incompressible Navier-Stokes two-phase flow. International Journal for Numerical Methods in Fluids (2012), http://dx.doi.org/10.1002/fld.3653