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All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

Sharp Observability Estimates for a System of Two Coupled Nonconservative Hyperbolic Equations

We consider a system of two coupled nonconservative wave equations. For this system, we prove several observability estimates. Those observability estimates are sharp in the sense that they lead by duality to the controllability (exact or approximate) of the coupled system with a single control acting through one of the equations only while keeping the same controllability time as for a single equation. Existing results in the literature either require two controls, or in the case of a single control, they have a controllability time that blows up as the coupling parameter goes to zero. Our proofs rely on: (i) Carleman estimates, (ii) energy estimates and (iii) localizing arguments. The results obtained complement and improve, in some sense, earlier results while at the same time providing new uniqueness results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Diffuse-Interface Capturing Methods for Compressible Two-Phase Flows

Simulation of compressible flows became a routine activity with the appearance of shock-/contact-capturing methods. These methods can determine all waves, particularly discontinuous ones. However, additional difficulties may appear in two-phase and multimaterial flows due to the abrupt variation of thermodynamic properties across the interfacial region, with discontinuous thermodynamical representations at the interfaces. To overcome this difficulty, researchers have developed augmented systems of governing equations to extend the capturing strategy. These extended systems, reviewed here, are termed diffuse-interface models, because they are designed to compute flow variables correctly in numerically diffused zones surrounding interfaces. In particular, they facilitate coupling the dynamics on both sides of the (diffuse) interfaces and tend to the proper pure fluid–governing equations far from the interfaces. This strategy has become efficient for contact interfaces separating fluids that are governed by different equations of state, in the presence or absence of capillary effects, and with phase change. As a result, more sophisticated materials than fluids (e.g., elastic–plastic materials) have been considered as well.

42 ENGINEERING↗