Absorbent boundary condition for general nonlinear hyperbolic PDE's with unknown Riemann Invariants

RODRIGO R. PAZ; MARIO A. STORTI; LUCIANO GARELLI

Rosario, Santa Fe

Congreso; II Congreso de Matemática Aplicada, Computacional e Industrial - MACI 2009; 2009

Asociación Argentina de Matemática Aplicada, Computacional e Industrial

A general methodology for developing absorbing boundary conditions for general non-linear hyperbolic advective-diffusive equations with unknown Riemann invariants is presented. In problems where the Riemann invariants (RI) are known (e.g. the flow in a shallow rectangular channel, the gas flow equations), the imposition of non-reflective boundary conditions is straightforward. In problems where Riemann invariants are unknown (e.g. the flow in a non-rectangular channels, the stratified 2D shallow water flows) it is possible to impose that kind of conditions analyzing the projection of the Jacobians of advective flux functions onto normal directions to fictitious surfaces or boundaries. The theoretical basis of this new condition is presented in this communication and the application of the dynamic absorbing boundary conditions to typical wave propagation problems with unknown Riemann invariants, likenon-linear Saint-Venant system of conservation laws for non-rectangular and non-prismatic 1D channels and stratified 1D/2D shallow water equations will be shown in the presentation.