The combustion instability is investigated computationally for a multi-injector rocket engine using the flamelet progress variable (FPV) model. A C++ code is developed based on OpenFOAM 4.0 to apply the combustion model. Flamelet tables are generated
for methane/oxygen combustion at the background pressure of $200$ bar using a 12-species chemical mechanism. A power law is determined for rescaling the reaction rate for the progress variable to address the pressure effect. The combustion is also simulated by the one-step-kinetics (OSK) method for comparison with the FPV approach. A study of combustion instability shows that a longitudinal mode of $1500$ Hz and a tangential standing wave of $2500$ Hz are dominant for both approaches. While the amplitude of the longitudinal mode remains almost the same for both approaches, the tangential standing wave achieves a larger amplitude in the FPV simulation. A preliminary study of the resonance in the injectors, which is driven by the longitudinal-mode oscillation in the combustion chamber, is also presented.
In this paper, high order semi-implicit well-balanced and asymptotic preserving finite difference WENO schemes are proposed for the shallow water equations with a non-flat bottom topography. We consider the Froude number ranging from O(1) to 0, which
in the zero Froude limit becomes the lake equations for balanced flow without gravity waves. We apply a well-balanced finite difference WENO reconstruction, coupled with a stiffly accurate implicit-explicit (IMEX) Runge-Kutta time discretization. The resulting semi-implicit scheme can be shown to be well-balanced, asymptotic preserving (AP) and asymptotically accurate (AA) at the same time. Both one- and two-dimensional numerical results are provided to demonstrate the high order accuracy, AP property and good performance of the proposed methods in capturing small perturbations of steady state solutions.
During the last few decades, online controlled experiments (also known as A/B tests) have been adopted as a golden standard for measuring business improvements in industry. In our company, there are more than a billion users participating in thousand
s of experiments simultaneously, and with statistical inference and estimations conducted to thousands of online metrics in those experiments routinely, computational costs would become a large concern. In this paper we propose a novel algorithm for estimating the covariance of online metrics, which introduces more flexibility to the trade-off between computational costs and precision in covariance estimation. This covariance estimation method reduces computational cost of metric calculation in large-scale setting, which facilitates further application in both online controlled experiments and adaptive experiments scenarios like variance reduction, continuous monitoring, Bayesian optimization, etc., and it can be easily implemented in engineering practice.
In this paper, we will develop a class of high order asymptotic preserving (AP) discontinuous Galerkin (DG) methods for nonlinear time-dependent gray radiative transfer equations (GRTEs). Inspired by the work cite{Peng2020stability}, in which stabili
ty enhanced high order AP DG methods are proposed for linear transport equations, we propose to pernalize the nonlinear GRTEs under the micro-macro decomposition framework by adding a weighted linear diffusive term. In the diffusive limit, a hyperbolic, namely $Delta t=mathcal{O}(h)$ where $Delta t$ and $h$ are the time step and mesh size respectively, instead of parabolic $Delta t=mathcal{O}(h^2)$ time step restriction is obtained, which is also free from the photon mean free path. The main new ingredient is that we further employ a Picard iteration with a predictor-corrector procedure, to decouple the resulting global nonlinear system to a linear system with local nonlinear algebraic equations from an outer iterative loop. Our scheme is shown to be asymptotic preserving and asymptotically accurate. Numerical tests for one and two spatial dimensional problems are performed to demonstrate that our scheme is of high order, effective and efficient.
We study spin-resolved noise in Coulomb blockaded double quantum dots coupled to ferromagnetic electrodes. The modulation of the interdot coupling and spin polarization in the electrodes gives rise to an intriguing dynamical spin $uparrow$-$uparrow$
($downarrow$-$downarrow$) blockade mechanism: Bunching of up (down) spins due to dynamical blockade of an up (down) spin. In contrast to the conventional dynamical spin $uparrow$-$downarrow$ bunching (bunching of up spins entailed by dynamical blockade of a down spin), this new bunching behavior is found to be intimately associated with the spin mutual-correlation, i.e., the noise fluctuation between opposite spin currents. We further demonstrate that the dynamical spin $uparrow$-$uparrow$ and $uparrow$-$downarrow$ bunching of tunneling events may be coexistent in the regime of weak interdot coupling and low spin polarization.
