Domain decomposition methods for domain composition purpose: Chimera, overset, gluing and sliding mesh methods

Domain composition methods (DCM) consist in obtaining a solution to a problem, from the formulations of the same problem expressed on various subdomains. These methods have therefore the opposite objective of domain decomposition methods (DDM). Indeed, in contrast to DCM, these last techniques are usually applied to matching meshes as their purpose consists mainly in distributing the work in parallel environments. However, they are sometimes based on the same methodology as after decomposing, DDM have to recompose. As a consequence, in the literature, the term DDM has many times substituted DCM. DCM are powerful techniques that can be used for different purposes: to simplify the meshing of a complex geometry by decomposing it into different meshable pieces; to perform local refinement to adapt to local mesh requirements; to treat subdomains in relative motion (Chimera, sliding mesh); to solve multiphysics or multiscale problems, etc. The term DCM is generic and does not give any clue about how the fragmented solutions on the different subdomains are composed into a global one. In the literature, many methodologies have been proposed: they are mesh-based, equation-based, or algebraic-based. In mesh-based formulations, the coupling is achieved at the mesh level, before the governing equations are assembled into an algebraic system (mesh conforming, Shear-Slip Mesh Update, HERMESH). The equation-based counterpart recomposes the solution from the strong or weak formulation itself, and are implemented during the assembly of the algebraic system on the subdomain meshes. The different coupling techniques can be formulated for the strong formulation at the continuous level, for the weak formulation either at the continuous or at the discrete level (iteration-by-subdomains, mortar element, mesh free interpolation). Although the different methods usually lead to the same solutions at the continuous level, which usually coincide with the solution of the problem on the original domain, they have very different behaviors at the discrete level and can be implemented in many different ways. Eventually, algebraic- based formulations treat the composition of the solutions directly on the matrix and right-hand side of the individual subdomain algebraic systems. The present work introduces mesh-based, equation-based and algebraicbased DCM. It however focusses on algebraic-based domain composition methods, which have many advantages with respect to the others: they are relatively problem independent; their implicit implementation can be hidden in the iterative solver operations, which enables one to avoid intensive code rewriting; they can be implemented in a multi-code environment

Instrument intercomparison of glyoxal, methyl glyoxal and NO2 under simulated atmospheric conditions

The α-dicarbonyl compounds glyoxal (CHOCHO) and methyl glyoxal (CH[Subscript: 3]C(O)CHO) are produced in the atmosphere by the oxidation of hydrocarbons and emitted directly from pyrogenic sources. Measurements of ambient concentrations inform about the rate of hydrocarbon oxidation, oxidative capacity, and secondary organic aerosol (SOA) formation. We present results from a comprehensive instrument comparison effort at two simulation chamber facilities in the US and Europe that included nine instruments, and seven different measurement techniques: broadband cavity enhanced absorption spectroscopy (BBCEAS), cavity-enhanced differential optical absorption spectroscopy (CE-DOAS), white-cell DOAS, Fourier transform infrared spectroscopy (FTIR, two separate instruments), laser-induced phosphorescence (LIP), solid-phase micro extraction (SPME), and proton transfer reaction mass spectrometry (PTR-ToF-MS, two separate instruments; for methyl glyoxal only because no significant response was observed for glyoxal). Experiments at the National Center for Atmospheric Research (NCAR) compare three independent sources of calibration as a function of temperature (293–330 K). Calibrations from absorption cross-section spectra at UV-visible and IR wavelengths are found to agree within 2% for glyoxal, and 4% for methyl glyoxal at all temperatures; further calibrations based on ion–molecule rate constant calculations agreed within 5% for methyl glyoxal at all temperatures. At the European Photoreactor (EUPHORE) all measurements are calibrated from the same UV-visible spectra (either directly or indirectly), thus minimizing potential systematic bias. We find excellent linearity under idealized conditions (pure glyoxal or methyl glyoxal, R[Superscript: 2] > 0.96), and in complex gas mixtures characteristic of dry photochemical smog systems (o-xylene/NO[Subscript: x] and isoprene/NOx, R[Superscript: 2] > 0.95; R2 ∼ 0.65 for offline SPME measurements of methyl glyoxal). The correlations are more variable in humid ambient air mixtures (RH > 45%) for methyl glyoxal (0.58 < R[Superscript: 2] < 0.68) than for glyoxal (0.79 < R[Superscript: 2] < 0.99). The intercepts of correlations were insignificant for the most part (below the instruments' experimentally determined detection limits); slopes further varied by less than 5% for instruments that could also simultaneously measure NO[Subscript: 2]. For glyoxal and methyl glyoxal the slopes varied by less than 12 and 17% (both 3-σ) between direct absorption techniques (i.e., calibration from knowledge of the absorption cross section). We find a larger variability among in situ techniques that employ external calibration sources (75–90%, 3-σ), and/or techniques that employ offline analysis. Our intercomparison reveals existing differences in reports about precision and detection limits in the literature, and enables comparison on a common basis by observing a common air mass. Finally, we evaluate the influence of interfering species (e.g., NO[Subscript: 2], O[Subscript: 3] and H[Subscript: 2]O) of relevance in field and laboratory applications. Techniques now exist to conduct fast and accurate measurements of glyoxal at ambient concentrations, and methyl glyoxal under simulated conditions. However, techniques to measure methyl glyoxal at ambient concentrations remain a challenge, and would be desirable