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A novel methodology is developed to extract accurate skeletal reaction models for nuclear combustion. Local sensitivities of isotope mass fractions with respect to reaction rates are modeled based on the forced optimally time-dependent (f-OTD) scheme. These sensitivities are then analyzed temporally to generate skeletal models. The methodology is demonstrated by conducting skeletal reduction of constant density and temperature burning of carbon and oxygen relevant to SNe Ia. The 495-isotopes Torch model is chosen as the detailed reaction network. A map of maximum production of $^{56}\text{Ni}$ in SNe Ia is produced for different temperatures, densities, and proton to neutron ratios. The f-OTD simulations and the sensitivity analyses are then performed with initial conditions from this map. A series of skeletal models are derived and their performances are assessed by comparison against currently existing skeletal models. Previous models have been constructed intuitively by assuming the dominance of $\alpha$-chain reactions. The comparison of the newly generated skeletal models against previous models is based on the predicted energy release and $^{44}\text{Ti}$ and $^{56}\text{Ni}$ abundances by each model. The consequences of $\mathtt{y}_e \neq 0.5$ in the initial composition are also explored where $\mathtt{y}_e$ is the electron fraction. The simulated results show that $^{56}\text{Ni}$ production decreases by decreasing $\mathtt{y}_e$ as expected, and that the $^{43}\text{Sc}$ is a key isotope in proton and neutron channels toward $^{56}\text{Ni}$ production. It is shown that an f-OTD skeletal model with 150 isotopes can accurately predict the $^{56}\text{Ni}$ abundance in SNe Ia for $\mathtt{y}_e \lesssim 0.5$ initial conditions.

Sensitivity analysis with forced optimally time dependent (f-OTD) modes is introduced and its application for skeletal model reduction is demonstrated. f-OTD expands the sensitivity coefficient matrix into a lowdimensional, time dependent, orthonormal basis which captures directions of the phase space associated with most dominant sensitivities. These directions highlight the instantaneous active species and reaction paths. Evolution equations for the orthonormal basis and the projections of sensitivity matrix onto the basis are derived, and the application of f-OTD for skeletal reduction is described. In this framework, the sensitivity matrix is modeled, stored in a factorized manner, and never reconstructed at any time during the calculations. For demonstration purposes, sensitivity analysis is conducted of constant pressure ethylene-air burning in a zero-dimensional reactor and new skeletal models are generated. The flame speed, the ignition delay, and the extinction curve of resulted models are compared against some of the existing skeletal models. The results demonstrate the ability of f-OTD approach to eliminate unimportant reactions and species in a systematic, efficient and accurate manner.

We investigate relationships between statistics obtained from filtering and from ensemble or Reynolds-averaging turbulence flow fields as a function of length scale. Generalized central moments in the filtering approach are expressed as inner products of generalized fluctuating quantities, $q'(\xi,x)=q(\xi)-\overline q(x)$, representing fluctuations of a field $q(\xi)$, at any point $\xi$, with respect to its filtered value at $x$. For positive-definite filter kernels, these expressions provide a scale-resolving framework, with statistics and realizability conditions at any length scale. In the small-scale limit, scale-resolving statistics become zero. In the large-scale limit, scale-resolving statistics and realizability conditions are the same as in the Reynolds-averaged description. Using direct numerical simulations (DNS) of homogeneous variable density turbulence, we diagnose Reynolds stresses, $\mathcal{T}_{ij}$, resolved kinetic energy, $k_r$, turbulent mass-flux velocity, $a_i$, and density-specific volume covariance, $b$, defined in the scale-resolving framework. These variables, and terms in their governing equations, vary smoothly between zero and their Reynolds-averaged definitions at the small and large scale limits, respectively. At intermediate scales, the governing equations exhibit interactions between terms that are not active in the Reynolds-averaged limit. For example, in the Reynolds-averaged limit, $b$ follows a decaying process driven by a destruction term; at intermediate length scales it is a balance between production, redistribution, destruction, and transport, where $b$ grows as the density spectrum develops, and then decays when mixing becomes strong enough. This work supports the notion of a generalized, length-scale adaptive model that converges to DNS at high resolutions, and to Reynolds-averaged statistics at coarse resolutions.

The two-fluid plasma equations for a single ion species, with full transport terms, including temperature and magnetic field dependent ion and electron viscous stresses and heat fluxes, frictional drag force, and ohmic heating term have been implemented in the CFDNS code and solved by using sixth-order non-dissipative compact finite differences for plasma flows in several different regimes. In order to be able to fully resolve all the dynamically relevant time and length scales, while maintaining computational feasibility, the assumptions of infinite speed of light and negligible electron inertia have been made. Non-dimensional analysis of the two-fluid plasma equations shows that, by varying the characteristic/background number density, length scale, temperature, and magnetic strength, the corresponding Hall, resistive, and ideal magnetohydrodynamics (MHD) equations can be recovered as limiting cases. The accuracy and robustness of this two-fluid plasma solver in handling plasma flows in different regimes have been validated against four canonical problems: Alfven and whistler dispersion relations, electromagnetic plasma shock, and magnetic reconnection. For all test cases, by using physical dissipation and diffusion, with negligible numerical dissipation/diffusion, fully converged Direct Numerical Simulations (DNS)-like solutions are obtained when the ion Reynolds number based on grid size is smaller than a threshold value which is about 2.3 in this study. For the magnetic reconnection problem, the results show that the magnetic flux saturation time and value converge when the ion and magnetic Reynolds numbers are large enough. Thus, the DNS-like results become relevant to practical problems with much larger Reynolds numbers., Comment: Accepted for publication in Physics of Plasmas

The growth rate of the compressible Rayleigh-Taylor instability is studied in the presence of a background temperature gradient, $\Theta$, using a normal mode analysis. The effect of $\Theta$ variation is examined for three interface types corresponding to combinations of the viscous properties of the fluids (inviscid-inviscid, viscous-viscous and viscous-inviscid) at different Atwood numbers, $At$, and, when at least one of the fluids' viscosity is non-zero, as a function of the Grashof number. For the general case, the resulting ordinary differential equations are solved numerically; however, dispersion relations for the growth rate are presented for several limiting cases. An analytical solution is found for the inviscid-inviscid interface and the corresponding dispersion equation for the growth rate is obtained in the limit of a large $\Theta$. For the viscous-inviscid case, a dispersion relation is derived in the incompressible limit and $\Theta=0$. Compared to $\Theta=0$ case, the role of $\Theta<0$ (hotter light fluid) is destabilizing and becomes stabilizing when $\Theta>0$ (colder light fluid). The most pronounced effect when $\Theta\neq 0$ is found at low $At$ and/or at large perturbation wavelengths relative to the domain size for all interface types. On the other hand, at small perturbation wavelengths relative to the domain size, the growth rate for $\Theta<0$ case exceeds the infinite domain incompressible constant density result. The results are applied to two practical examples, using sets of parameters relevant to Inertial Confinement Fusion coasting stage and solar corona plumes. The role of viscosity on the growth rate reduction is discussed together with highlighting the range of wavenumbers most affected by viscosity. The viscous effects further increase in the presence of background temperature gradient, when the viscosity is temperature dependent.

Kuzmin-Oseledets formulations of compressible Euler equations case are considered. Exact results and physical interpretations are given. One such exact result for the compressible barotropic case is the potential helicity Lagrange invariant. In recognition of the fundamental physical implications of this Lagrange invariant clarified here, this invariant is shown to hold for compressible non-barotropic cases as well upon using a stronger gauge condition. Symmetry restoration taking place at the Lagrangian level in the Kuzmin-Oseledets formulation is pointed out. The Kuzmin-Oseledets formulation in the compressible barotropic case is shown to admit an exact solution that physically describes a density wave on a steady irrotational flow with the Kuzmin-Oseledets velocity q growing monotonically with it and hence specifying some information about the fluid impulse that is needed to set up the flow in question.