Local Absorbent Boundary Condition for Nonlinear Hyperbolic Problems with Unknown Riemann Invariants

PAZ, R.R.; STORTI MARIO

San Luis

Congreso; Enief 2008, XVII Congreso sobre Métodos Numéricos y sus Aplicaciones; 2008

Asociación Argentina de Mecánica Computacional - AMCA

A general methodology for developing absorbing boundary conditions for general non-linear advective-diffusive system of equations is presented. In problems where the Riemann invariants are known (e.g. the flow in a shallow rectangular channel, the gas flow equations), the superimposition of non-reflective boundary conditions is straightforward. In problems where Riemann Invariants are un- known (e.g. the flow in a non-rectangular channels, the stratified two-dimensional (2D) shallow water flows) it is possible to impose that kind of conditions analyzing the projection of the Jacobians of advec- tive flux functions onto normal directions to fictitious surfaces. Moreover, with the technique proposed here the state variables of the system can be force to achieve a given "reference state". The advantage of the method is that is very easy to implement it in a production finite element code and that is based on imposing non-linear constraints via Lagrange Multipliers and/or Penalty Methods. The application of the dynamic absorbing boundary conditions to typical wave propagation problems with unknown Riemann Invariants, like non-linear Saint-Venant system of conservation laws for non-rectangular and non-prismatic one-dimensional channels and stratified 2D shallow water equations, is presented.