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A Sommerfeld non-reflecting boundary condition for the wave equation in mixed form
Espinoza Román, Héctor Gabriel; Codina, Ramon; Badia, Santiago
Universitat Politècnica de Catalunya. Departament de Resistència dels Materials i Estructures en Enginyeria; Universitat Politècnica de Catalunya. (MC)2 - Grup de Mecànica Computacional en Medis Continus
In this paper we develop numerical approximations of the wave equation in mixed form supplemented with non-reflecting boundary conditions (NRBCs) of Sommerfeld-type on artificial boundaries for truncated domains. We consider three different variational forms for this problem, depending on the functional space for the solution, in particular, in what refers to the regularity required on artificial boundaries. Then, stabilized finite element methods that can mimic these three functional settings are described. Stability and convergence analyses of these stabilized formulations including the NRBC are presented. Additionally, numerical convergence test are evaluated for various polynomial interpolations, stabilization methods and variational forms. Finally, several benchmark problems are solved to determine the accuracy of these methods in 2D and 3D.
Peer Reviewed
Àrees temàtiques de la UPC::Informàtica::Aplicacions de la informàtica::Aplicacions informàtiques a la física i l‘enginyeria
Boundary layer--Mathematical models
Non-reflecting boundary condition
Open boundary condition
Artificial boundary condition
Wave equation
Stabilized finite element methods
Variational multi-scale method
Capa límit (Dinàmica de fluids)

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