Local-in-Time Adjoint-Based Method for Optimal Control/Design Optimization of Unsteady Compressible Flows

.We study local-in-time adjoint-based methods for minimization of ow matching functionals subject to the 2-D unsteady compressible Euler equations. The key idea of the local-in-time method is to construct a very accurate approximation of the global-in-time adjoint equations and the corresponding sensitivity derivative by using only local information available on each time subinterval. In contrast to conventional time-dependent adjoint-based optimization methods which require backward-in-time integration of the adjoint equations over the entire time interval, the local-in-time method solves local adjoint equations sequentially over each time subinterval. Since each subinterval contains relatively few time steps, the storage cost of the local-in-time method is much lower than that of the global adjoint formulation, thus making the time-dependent optimization feasible for practical applications. The paper presents a detailed comparison of the local- and global-in-time adjoint-based methods for minimization of a tracking functional governed by the Euler equations describing the ow around a circular bump. Our numerical results show that the local-in-time method converges to the same optimal solution obtained with the global counterpart, while drastically reducing the memory cost as compared to the global-in-time adjoint formulation

Adjoint-Based Methodology for Time-Dependent Optimization

This paper presents a discrete adjoint method for a broad class of time-dependent optimization problems. The time-dependent adjoint equations are derived in terms of the discrete residual of an arbitrary finite volume scheme which approximates unsteady conservation law equations. Although only the 2-D unsteady Euler equations are considered in the present analysis, this time-dependent adjoint method is applicable to the 3-D unsteady Reynolds-averaged Navier-Stokes equations with minor modifications. The discrete adjoint operators involving the derivatives of the discrete residual and the cost functional with respect to the flow variables are computed using a complex-variable approach, which provides discrete consistency and drastically reduces the implementation and debugging cycle. The implementation of the time-dependent adjoint method is validated by comparing the sensitivity derivative with that obtained by forward mode differentiation. Our numerical results show that O(10) optimization iterations of the steepest descent method are needed to reduce the objective functional by 3-6 orders of magnitude for test problems considered

In situ measurements of tropospheric volcanic plumes in Ecuador and Colombia during TC

A NASA DC‐8 research aircraft penetrated tropospheric gas and aerosol plumes sourced from active volcanoes in Ecuador and Colombia during the Tropical Composition, Cloud and Climate Coupling (TC4 ) mission in July–August 2007. The likely source volcanoes were Tungurahua (Ecuador) and Nevado del Huila (Colombia). The TC4 data provide rare insight into the chemistry of volcanic plumes in the tropical troposphere and permit a comparison of SO2 column amounts measured by the Ozone Monitoring Instrument (OMI) on the Aura satellite with in situ SO2 measurements. Elevated concentrations of SO2, sulfate aerosol, and particles were measured by DC‐8 instrumentation in volcanic outflow at altitudes of 3–6 km. Estimated plume ages range from ∼2 h at Huila to ∼22–48 h downwind of Ecuador. The plumes contained sulfate‐rich accumulation mode particles that were variably neutralized and often highly acidic. A significant fraction of supermicron volcanic ash was evident in one plume. In‐plume O3 concentrations were ∼70%–80% of ambient levels downwind of Ecuador, but data are insufficient to ascribe this to O3 depletion via reactive halogen chemistry. The TC4 data record rapid cloud processing of the Huila volcanic plume involving aqueous‐phase oxidation of SO2 by H2O2, but overall the data suggest average in‐plume SO2 to sulfate conversion rates of ∼1%–2% h−1 . SO2 column amounts measured in the Tungurahua plume (∼0.1–0.2 Dobson units) are commensurate with average SO2 columns retrieved from OMI measurements in the volcanic outflow region in July 2007. The TC4 data set provides further evidence of the impact of volcanic emissions on tropospheric acidity and oxidizing capacit

In situ measurements of tropospheric volcanic plumes in Ecuador and Colombia during TC^4

A NASA DC-8 research aircraft penetrated tropospheric gas and aerosol plumes sourced from active volcanoes in Ecuador and Colombia during the Tropical Composition, Cloud and Climate Coupling (TC^4) mission in July–August 2007. The likely source volcanoes were Tungurahua (Ecuador) and Nevado del Huila (Colombia). The TC^4 data provide rare insight into the chemistry of volcanic plumes in the tropical troposphere and permit a comparison of SO_2 column amounts measured by the Ozone Monitoring Instrument (OMI) on the Aura satellite with in situ SO_2 measurements. Elevated concentrations of SO_2, sulfate aerosol, and particles were measured by DC-8 instrumentation in volcanic outflow at altitudes of 3–6 km. Estimated plume ages range from ~2 h at Huila to ~22–48 h downwind of Ecuador. The plumes contained sulfate-rich accumulation mode particles that were variably neutralized and often highly acidic. A significant fraction of supermicron volcanic ash was evident in one plume. In-plume O_3 concentrations were ~70%–80% of ambient levels downwind of Ecuador, but data are insufficient to ascribe this to O_3 depletion via reactive halogen chemistry. The TC^4 data record rapid cloud processing of the Huila volcanic plume involving aqueous-phase oxidation of SO_2 by H_2O_2, but overall the data suggest average in-plume SO_2 to sulfate conversion rates of ~1%–2% h^(−1). SO_2 column amounts measured in the Tungurahua plume (~0.1–0.2 Dobson units) are commensurate with average SO_2 columns retrieved from OMI measurements in the volcanic outflow region in July 2007. The TC^4 data set provides further evidence of the impact of volcanic emissions on tropospheric acidity and oxidizing capacity

The production and persistence of ΣRONO2 in the Mexico City plume

Alkyl and multifunctional nitrates (RONO2, ΣANs) have been observed to be a significant fraction of NOy in a number of different chemical regimes. Their formation is an important free radical chain termination step ending production of ozone and possibly affecting formation of secondary organic aerosol. ΣANs also represent a potentially large, unmeasured contribution to OH reactivity and are a major pathway for the removal of nitrogen oxides from the atmosphere. Numerous studies have investigated the role of nitrate formation from biogenic compounds and in the remote atmosphere. Less attention has been paid to the role ΣANs may play in the complex mixtures of hydrocarbons typical of urban settings. Measurements of total alkyl and multifunctional nitrates, NO2, total peroxy nitrates (ΣPNs), HNO3 and a representative suite of hydrocarbons were obtained from the NASA DC-8 aircraft during spring of 2006 in and around Mexico City and the Gulf of Mexico. ΣANs were observed to be 10–20% of NOy in the Mexico City plume and to increase in importance with increased photochemical age. We describe three conclusions: (1) Correlations of ΣANs with odd-oxygen (Ox) indicate a stronger role for ΣANs in the photochemistry of Mexico City than is expected based on currently accepted photochemical mechanisms, (2) ΣAN formation suppresses peak ozone production rates by as much as 40% in the near-field of Mexico City and (3) ΣANs play a significant role in the export of NOy from Mexico City to the Gulf Region

An Instrument to Enable Identification of Anthropogenic CO2 Emissions Using Concurrent CO Measurements

We have developed an instrument concept that will enable the measurement of CO from the top of the atmosphere to the Earth's surface with very high sensitivity and at the high spatial and temporal resolutions required by the NRC Decadal Survey mission Active Sensing of Carbon Dioxide (CO2) over Nights, Days and Seasons (ASCENDS). We are developing an innovative CO sensor that will enable the ASCENDS mission to differentiate between anthropogenic and natural sources and sinks of global carbon. The NRC Decadal Survey places particular emphasis on retrieving CO information for the planetary boundary layer. Measurement made using both the 2.3 micron and 4.7 micron channels are needed to achieve the sensitivity required in the lower atmosphere where the degree of CO - CO2 correlation is indicative of anthropogenic sources of CO2. Measurements made using only the 4.7 micron channel cannot provide sufficient sensitivity to CO in the very lowest layers of the atmosphere. The fundamental method we use is Gas Filter Correlation Radiometry (GFCR), a highly successful technique used in other airborne and space-based missions for detecting trace species in the Earth's atmosphere. Our version of GFCR overcomes many of the limitations encountered by prior and existing instruments, allowing us to measure weak signals from small targets very quickly and with extremely high specificity by employing a new dual beam radiometer concept using a focal plane array. Our design will provide a means to make the desired CO measurements for the ASCENDS mission. A simple change in gas filter cell contents would allow the same hardware to measure CH4 with high precision under the nominal ASCENDS mission spatial and temporal constraints. All critical components in the sensor design are mature, many subsystems tested, and the system has been extensively modeled, bringing it to a present Technology Readiness Level (TRL) of 3 (though some individual components are at TRLs 6-9). We are presently developing critical components for the new spectrometer and advancing our understanding of the measurement requirements for both CO and CH4. This new GFCR technique/sensor will enable measurements of trace gases with high sensitivity while maintaining the inherent robustness and simplicity of the more traditional radiometer hardware. Initial estimates of cost/risk of a spacebased 2-channel GFCR indicate that our design is extremely cost effective and will fit within existing ASCENDS mission budget constraints as determined by the NRC Decadal Survey and a NASA-sponsored mission study

Bidirectionally Tolerating Inconsistency: Partial Transformations

Abstract. A foundational property of bidirectional transformations is that they should be correct: that is, the transformation should succeed in restoring consistency between any models it is given. In practice, how-ever, transformation engines sometimes fail to restore consistency, e.g. because there is no consistent model to return, or because the tool is unable to select a best model to return from among equally good candi-dates. In this paper, we formalise properties that may nevertheless hold in such circumstances and discuss relationships and implications.

Towards Verification of Unstructured-Grid Solvers

New methodology for verification of computational methods using unstructured grids is presented. The discretization order properties are studied in computational windows, easily constructed within a collection of grids or a single grid. The windows can be adjusted to isolate the interior discretization, the boundary discretization, or singularities. A major component of the methodology is the downscaling test, introduced previously for studying the convergence rates of truncation and discretization errors of finite-volume discretization schemes on general unstructured grids. Demonstrations of the method are shown, including a comparative accuracy assessment of commonly-used schemes on general mixed grids and the identification of local accuracy deterioration at intersections of tangency and inflow/outflow boundaries. Recommendations for the use of the methodology in large-scale computational simulations are given