Differential optical absorption spectroscopy (DOAS) is a powerful tool for detecting and quantifying trace gases in atmospheric chemistry\cite {Platt_Stutz08}. DOAS spectra consist of a linear combination of complex multi-peak multi-scale structures. Most DOAS analysis routines in use today are based on least squares techniques, for example, the approach developed in the 1970s uses polynomial fits to remove a slowly varying background, and known reference spectra to retrieve the identity and concentrations of reference gases. An open problem is to identify unknown gases in the fitting residuals for complex atmospheric mixtures.

Wind power is an increasingly popular renewable energy. In the design process of the wind turbine blade, the accurate aerodynamic simulation is important. In the past, most of the wind turbine simulations were carried out with some low fidelity methods, such as the blade element momentum method [9]. Recently, with the rapid development of the supercomputers, high fidelity simulations based on 3D unsteady Navier-Stokes (N-S) equations become more popular. For example, Sorensen et al. studied the 3D wind turbine rotor using the Reynolds-Averaged Navier-Stokes (RANS) framework where a finite volume method and a semi-implicit method are used for the spatial and temporal discretization, respectively [17]. Bazilevs et al. investigated the aerodynamic of the NREL 5MW offshore baseline wind turbine rotor using large eddy simulation built with a deforming-spatial-domain/stabilized space-time

In this paper, we construct an adaptive multiscale method for solving H(curl)-elliptic problems in highly heterogeneous media. Our method is based on the generalized multiscale finite element method. We will first construct a suitable snapshot space, and a dimensional reduction procedure to identify important modes of the solution. We next develop and analyze an a posteriori error indicator, and the corresponding adaptive algorithm. In addition, we will construct a coupled offlineonline adaptive algorithm, which provides an adaptive strategy to the selection of offline and online basis functions. Our theory shows that the convergence is robust with respect to the heterogeneities and contrast of the media. We present several numerical results to illustrate the performance of our method.

In this paper, we develop bound-preserving discontinuous Galerkin (DG) methods for the coupled system of compressible miscible displacement problems. We consider the problem with two components and the (volumetric) concentration of the $i$th component of the fluid mixture, $c_i$, should be between $0$ and $1$. However, $c_i$ does not satisfy the maximum principle. Therefore, the numerical techniques introduced in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied directly. The main idea is to apply the positivity-preserving techniques to both $c_1$ and $c_2$, respectively and enforce $c_1+c_2=1$ simultaneously to obtain physically relevant approximations. By doing so, we have to treat the time derivative of the pressure $dp/dt$ as a source in the concentration equation. Moreover, $c_i's$ are not the conservative variables, as a result, the classical bound-preserving limiter in (X. Zhang and C.-W. Shu, Journal of Computational Physics, 229 (2010), 3091-3120) cannot be applied. Therefore, another limiter will be introduced. Numerical experiments will be given to demonstrate the accuracy in $L^\infty$-norm and good performance of the numerical technique.

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