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Absorbing Boundary Conditions for Compressible Flow at Low Mach Number and Free Surface Flows with Level-Set

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Automatic high order absorption layers by M.Storti et.al. Automatic high order absorption layers for advective-diffusive systems of equations by Mario Storti, Laura Battaglia, and Rodrigo Paz Centro Internacional de Me´todos Computacionales en Ingenierı´a - CIMEC INTEC, (CONICET-UNL), Santa Fe, Argentina <mario.storti at gmail.com> http://www.cimec.org.ar/mstorti Centro Internacional de Me´todos Computacionales en Ingenierı´a 1 ((version texstuff-1.0.36-102-gdb116be Thu Nov 3 09:14:55 2011 -0300) (date Thu Nov 3 09:15:35 2011 -0300)) Automatic high order absorption layers by M.Storti et.al. Motivation for Absorbing Boundary Conditions In wave-like propagation problems, not including ABC may lead to non-convergent solutions . utt = c2∆u, in Ω u = u¯(x, t), at Γb, u = 0, at Γ∞v u doesn’t converge to the correct solution irradiating energy from the source, even if Γ∞ →∞. A standing wave is always found. u is unbounded if u¯ emits in an eigenfrequency which is a resonance mode of the closed cavity. Absorbing boundary conditions must be added to the outer boundary in order to let energy be extracted from the domain. Centro Internacional de Me´todos Computacionales en Ingenierı´a 2 ((version texstuff-1.0.36-102-gdb116be Thu Nov 3 09:14:55 2011 -0300) (date Thu Nov 3 09:15:35 2011 -0300)) Automatic high order absorption layers by M.Storti et.al. Motivation for Absorbing Boundary Conditions (cont.) If a dissipative region is large enough so that many wavelengths are included in the region may act as an absorbing layer, i.e. as an absorbing boundary condition. However, it is a common misconception to assume that a coarse mesh adds dissipation and consequently may improve absorption. For instance for the wave equation a coarse mesh may lead to evanescent solutions and then to act as a fully reflecting boundary. dissipative dissipative?? coarse meshfine mesh Centro Internacional de Me´todos Computacionales en Ingenierı´a 3 ((version texstuff-1.0.3

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