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标题：Absorbing Boundary Condition for Nonlinear Hyperbolic Partial Diferential Equations with Unknown Riemann Invariants
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作者：Rodrigo R. Paz ; Mario A. Storti ; Luciano Garelli 等
期刊名称：Mecánica Computacional
印刷版ISSN：2591-3522
出版年度：2009
卷号：XXVIII
期号：19
页码：1593-1620
出版社：CIMEC-INTEC-CONICET-UNL
摘要：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 advantage of the method is that it is very easy to implement in a ﬁnite element code and is only based on computing the advective ﬂux functions (and the their Jacobian projections), then, imposing non-linear constraints via Lagrange Multipliers or Penalty Methods. The application of the dynamic absorbing boundary conditions to typical wave propagation problems with unknown Riemann invariants, like nonlinear Saint-Venant system of conservation laws for non-rectangular and non-prismatic 1D channels and stratiﬁed 1D/2D shallow water equations, is presented. Also, the new absorbent/dynamic condition can handle automatically the change of Jacobians structure when the ﬂow regime changes from subcritical to supercritical and viceversa, or when recirculating zones are present in regions near ﬁctitious walls.