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eXtended hybridizable discontinuous Galerkin (X-HDG) for void and bimaterial problems
Gurkan, Ceren; Sala Lardies, Esther; Kronbichler, Martin; Fernandez Mendez, Sonia
Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental; Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Difference equations
Fluid dynamics (Mathematics)
A strategy for the Hybridizable Discontinuous Galerkin (HDG) solution of problems with voids
inclusions
free surfaces
and material interfaces is proposed. It is based on an eXtended Finite Element (X-FEM) philosophy with a level-set description of interfaces where the computational mesh is not required to fit the interface (i.e. the boundary). This reduces the cost of mesh generation and
in particular
avoids continuous remeshing for evolving interfaces. Differently to previous proposals for the HDG solution with unfitting meshes
the computational mesh covers the domain in our approach
avoiding extrapolations and ensuring the robustness of the method. The local problem in elements not cut by the interface and the global problem are discretized as usual in HDG. A modified local problem is considered for elements cut by the interface. At every cut element
an auxiliary trace variable on the boundary is introduced
which is eliminated afterwards using interface conditions
keeping the original unknowns ...
Equacions en diferències
Mecànica de fluids
Classificació AMS::65 Numerical analysis::65Q05 Difference and functional equations, recurrence relations
Classificació AMS::76 Fluid mechanics::76M Basic methods in fluid mechanics
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/submittedVersion
info:eu-repo/semantics/bookPart
Springer
         

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