Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations

This paper introduces tensorial calculus techniques in the framework of Proper Orthogonal Decomposition (POD) to reduce the computational complexity of the reduced nonlinear terms. The resulting method, named tensorial POD, can be applied to polynomial nonlinearities of any degree $p$. Such nonlinear terms have an on-line complexity of $\mathcal{O}(k^{p+1})$, where $k$ is the dimension of POD basis, and therefore is independent of full space dimension. However it is efficient only for quadratic nonlinear terms since for higher nonlinearities standard POD proves to be less time consuming once the POD basis dimension $k$ is increased. Numerical experiments are carried out with a two dimensional shallow water equation (SWE) test problem to compare the performance of tensorial POD, standard POD, and POD/Discrete Empirical Interpolation Method (DEIM). Numerical results show that tensorial POD decreases by $76\times$ times the computational cost of the on-line stage of standard POD for configurations using more than $300,000$ model variables. The tensorial POD SWE model was only $2-8\times$ slower than the POD/DEIM SWE model but the implementation effort is considerably increased. Tensorial calculus was again employed to construct a new algorithm allowing POD/DEIM shallow water equation model to compute its off-line stage faster than the standard and tensorial POD approaches.Comment: 23 pages, 8 figures, 5 table

Analysis, testing, and evaluation of faulted and unfaulted Wye, Delta, and open Delta connected electromechanical actuators

Mathematical models capable of simulating the transient, steady state, and faulted performance characteristics of various brushless dc machine-PSA (power switching assembly) configurations were developed. These systems are intended for possible future use as primemovers in EMAs (electromechanical actuators) for flight control applications. These machine-PSA configurations include wye, delta, and open-delta connected systems. The research performed under this contract was initially broken down into the following six tasks: development of mathematical models for various machine-PSA configurations; experimental validation of the model for failure modes; experimental validation of the mathematical model for shorted turn-failure modes; tradeoff study; and documentation of results and methodology

Development of the adjoint of GEOS-Chem

We present the adjoint of the global chemical transport model GEOS-Chem, focusing on the chemical and thermodynamic relationships between sulfate – ammonium – nitrate aerosols and their gas-phase precursors. The adjoint model is constructed from a combination of manually and automatically derived discrete adjoint algorithms and numerical solutions to continuous adjoint equations. Explicit inclusion of the processes that govern secondary formation of inorganic aerosol is shown to afford efficient calculation of model sensitivities such as the dependence of sulfate and nitrate aerosol concentrations on emissions of SOx, NOx, and NH3. The adjoint model is extensively validated by comparing adjoint to finite difference sensitivities, which are shown to agree within acceptable tolerances; most sets of comparisons have a nearly 1:1 correlation and R2>0.9. We explore the robustness of these results, noting how insufficient observations or nonlinearities in the advection routine can degrade the adjoint model performance. The potential for inverse modeling using the adjoint of GEOS-Chem is assessed in a data assimilation framework through a series of tests using simulated observations, demonstrating the feasibility of exploiting gas- and aerosol-phase measurements for optimizing emission inventories of aerosol precursors

A review of the analytical simulation of aircraft crash dynamics

A large number of full scale tests of general aviation aircraft, helicopters, and one unique air-to-ground controlled impact of a transport aircraft were performed. Additionally, research was also conducted on seat dynamic performance, load-limiting seats, load limiting subfloor designs, and emergency-locator-transmitters (ELTs). Computer programs were developed to provide designers with methods for predicting accelerations, velocities, and displacements of collapsing structure and for estimating the human response to crash loads. The results of full scale aircraft and component tests were used to verify and guide the development of analytical simulation tools and to demonstrate impact load attenuating concepts. Analytical simulation of metal and composite aircraft crash dynamics are addressed. Finite element models are examined to determine their degree of corroboration by experimental data and to reveal deficiencies requiring further development

Monolithic simulation of convection-coupled phase-change - verification and reproducibility

Phase interfaces in melting and solidification processes are strongly affected by the presence of convection in the liquid. One way of modeling their transient evolution is to couple an incompressible flow model to an energy balance in enthalpy formulation. Two strong nonlinearities arise, which account for the viscosity variation between phases and the latent heat of fusion at the phase interface. The resulting coupled system of PDE's can be solved by a single-domain semi-phase-field, variable viscosity, finite element method with monolithic system coupling and global Newton linearization. A robust computational model for realistic phase-change regimes furthermore requires a flexible implementation based on sophisticated mesh adaptivity. In this article, we present first steps towards implementing such a computational model into a simulation tool which we call Phaseflow. Phaseflow utilizes the finite element software FEniCS, which includes a dual-weighted residual method for goal-oriented adaptive mesh refinement. Phaseflow is an open-source, dimension-independent implementation that, upon an appropriate parameter choice, reduces to classical benchmark situations including the lid-driven cavity and the Stefan problem. We present and discuss numerical results for these, an octadecane PCM convection-coupled melting benchmark, and a preliminary 3D convection-coupled melting example, demonstrating the flexible implementation. Though being preliminary, the latter is, to our knowledge, the first published 3D result for this method. In our work, we especially emphasize reproducibility and provide an easy-to-use portable software container using Docker.Comment: 20 pages, 8 figure