A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

Photochemical uncertainties in modeling planetary atmospheres: Review and consequences for Titan's case

Low-temperature photochemistry of planetary atmospheres is still poorly constrained by laboratory evidence Such uncertainties carried by the different parameters included in photochemical models of planetary atmospheres have yet rarely been considered even if they are supposed to be contributing mostly to the inconsistencies between observations and computed predictions We review exhaustively and originally these uncertainties included in an up-to-date 1D model of Titan s atmosphere focusing on the integration of recent laboratory measurements and theoretical breakthroughs in a relevant description of the photochemical scheme at representative conditions Since photochemical models of planetary atmospheres are strongly non-linear systems traditional sensitivity studies - varying each parameter in turn - are not representative of the overall uncertainty in the computed results Monte-Carlo calculations were thus performed on photochemical rates coefficients to introduce randomly their uncertainties in order to investigate their true significance on the modeling of Titan s atmosphere Despite the crude approximations adopted in the implemented physical processes and without adjusting artificially neither the eddy diffusion coefficient nor any surface fluxes this model may seem at first to better fit existing stratospheric observations over more elaborate models We conclude however that overall modeling uncertainties related to photochemical rates coefficients are important enough to question indeed any such comparisons with observations and any potential conclusion

Photochemical kinetics uncertainties in modeling Titan's atmosphere: A review

This paper is a review dealing with the photochemistry of Titan's atmosphere and its sources of uncertainties. It presents current knowledge on the active photochemistry occurring in Titan's atmosphere. A brief discussion of major dissociation paths and essential chemical reactions is given, which allows us to emphasize on the photochemical processes that are still not well represented in the models and might thus be contributing mostly to the overall imprecision of theoretical results. We present a method to evaluate uncertainty factors of the chemical rate constants at temperatures representative of Titan's atmosphere. This compilation can be used as a reference for future uncertainty propagation analysis in Titan's photochemical models developed in the frame of the Cassini–Huygens mission

Sensitivity effects of chemical kinetic uncertainties on photochemical modeling results : Application to Titan's atmosphere

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Photochemical kinetics uncertainties in modeling Titan's atmosphere: First consequences

Uncertainties carried by the different kinetic parameters included in photochemical models of planetary atmospheres have rarely been considered even if they are supposed to be contributing mostly to the inconsistencies between observations and computed predictions. In this paper, we report the first detailed analysis of the propagation of uncertainties carried by the reaction rate coefficients included in an up-to-date photochemical model of Titan's atmosphere. Monte Carlo calculations performed on these reaction rate coefficients have been used to introduce their uncertainties and to investigate their significance on the photochemical modeling of Titan's atmosphere. Crude approximations in the implemented physical processes have been adopted to limit the number of free parameters. This allows us to pinpoint specifically the importance of chemical processes uncertainties in Titan's photochemical models and to evaluate their chemical robustness. First implications of this preliminary study related to purely chemical rate coefficient uncertainties are discussed. They are important enough to question indeed any comparisons between theoretical models with observations as well as any potential conclusions subsequently inferred. Since the latest missions, such as Cassini–Huygens, are likely to induce an ever-increasing interest for such kind of comparing studies, our conclusions show that it is crucial to reform the way we think of, and use, current photochemical models to understand the processes occurring in the atmospheres of the outer Solar System

IR band intensities of DC3N and HC315N: Implication for observations of Titan's atmosphere

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