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Blind image deconvolution is one of the most challenging problems in image restoration. Inspired by the work on sparsity constraint and deblurring of blind motion, we propose a model with fractiona...

In this paper, we propose approximate solvers for two-phase fluids with general equations of state (EOS) in high dimension. The standard finite volume scheme is used for each fluid away from material interface. The two-phase interfaces are captured by the level set method coupled with a multi-resolution algorithm. For the Riemann solver of two-phase fluids with general equations of state, we construct an iterative approximation method by the solver for binomial equations of state. The velocity of the interface and the interface exchange fluxes are obtained precisely. With the help of the adaptive multi-resolution algorithms, we extend the method to three space dimensions conveniently. Numerical examples are carried out to demonstrate the strength and robustness of this method.

In this paper, we consider a layer of a viscous incompressible electrically conducting fluid interacting with the magnetic field in a horizontally periodic setting. The upper boundary is bounded by a free boundary and below bounded by a flat rigid interface. We prove the global well-posedness of the problem for both the case with and without surface tension. Moreover, we show that the global solution decays to the equilibrium exponentially in the case with surface tension, however the global solution decays to the equilibrium at an almost exponential rate in the case without surface tension.

In this paper, we propose a nonconvex regularization model for images damaged by Cauchy noise and blur. This model is based on the method of the total variational proposed by Federica, Dong and Zeng [SIAM J. Imaging Sci.(2015)], where a variational approach for restoring blurred images with Cauchy noise is used. Here we consider the nonconvex regularization, namely a weighted difference of \begin{document}$ l_1 $\end{document}-norm and \begin{document}$ l_2 $\end{document}-norm coupled with wavelet frame, the alternating direction method of multiplier is carried out for this minimization problem, we describe the details of the algorithm and prove its convergence. Numerical experiments are tested by adding different levels of noise and blur, results show that our method can denoise and deblur the image better.

In this paper, we consider the incompressible limit of strong solution for the compressible nematic liquid crystal flows in a 3D bounded domain Ω⊂R3 where the the velocity field satisfies the Diric...

This paper presents an efficient alternating method for image deblurring and denoising, it is based on our new model with TV norm to denoise the deblurred image which is penalized by l0 norm of the...

It is crucial to understand the degradation of implosion performance caused by three-dimensional physics and the implementation of 3-D spherical mesh is challenging. In this paper a mesh generation method based on the cube spherical projection is proposed for 3D implosion problem in Inertial Confinement Fusion (ICF). This kind of mesh has the advantage of good quality, convenient adding radiation source and adaptive moving in the radial direction. Together, a mathematical model of radiation hydrodynamics with ion-electron non-equilibrium is present. The equations of radiation hydrodynamics are solved with the operator splitting method, such that the hydrodynamics equations are solved explicitly making use of the capability of well understood explicit schemes while the radiation diffusion and electron/ion conduction parts are solved implicitly by an eleven-point scheme on the non-orthogonal mesh. We present results from several benchmark problems in order to validate our numerical scheme. And finally, we investigate the development of fourth-order modes and compute the disturbance growth process of hot spot boundary, which shown that it conforms to the physical law.

In this paper, we consider the low Mach number limit of the full compressible MHD equations in a 3-D bounded domain with Dirichlet boundary condition for velocity field, Neumann boundary condition for temperature and perfectly conducting boundary condition for magnetic field. First, the uniform estimates in the Mach number for the strong solutions are obtained in a short time interval, provided that the initial density and temperature are close to the constant states. Then, we prove the solutions of the full compressible MHD equations converge to the isentropic incompressible MHD equations as the Mach number tends to zero.

In this paper, we present a conservative sharp interface numerical method for compressible reactive flows. This method is developed by modified finite volume scheme in Eulerian framework. Applying the level set method, discretized scheme is obtained for each material separated by material interface, and small cut cells are merged into neighboring cells. To get accurate interface exchanges for reactive fluids, the Riemann problem with a combustion wave is analyzed. One- and two-dimensional numerical examples for deflagration and detonation problems demonstrate the scheme is robust and effective.

The dynamic programming interface reconstruction (DPIR) method introduced by Dumas et al.[1] is a volume-preserving and continuous interface reconstruction method. It is a two-step method, which comprises of an optimized step and a correction step. At first, in the optimized step, it minimizes a target function by the dynamic programming method to obtain a continuous interface. Then, it corrects the interface in each mixed cell to preserve the conservative of the volume fraction. However, only the difference of volume fraction is considered, and the interface normal is neglected in the target function. These make it easy to obtain different optimal results in the optimized step, and hence the resulting continuous interfaces always suffer from oscillations (i.e., the ‘wave effects’ [1] ). In this paper, to suppress the continuous interfaces’ oscillations in the optimized step and improve its accuracy, we constructed a non-dimensional target function based on the moment-of-fluid method’s objective function, and also proposed a new correction method. Finally, several numerical tests are performed to show the new method’s superiority over the original one of Dumas et al. [1] .

We first prove the uniqueness of weak solutions (ψ,A) to the 3-D Ginzburg–Landau model in superconductivity with zero magnetic diffusivity and the Coulomb gauge if (ψ,A)∈W:=(ψ,A)ψ∈L20,T;L∞∩L20,T;H1,A∈C[0,T];L3, which is a critical space for some positive constant T. We also prove the global existence of solutions when ψ0∈L∞∩W23,32 and A0∈L3. Copyright © 2016 John Wiley & Sons, Ltd.

Summary This paper presents an efficient method to simulate the reactive flow for general equation of states with the compressible fluid model coupled with reactive rate equation. The important aspect is to deal with mixture of different phases in one cell, which will inevitably happen in the Eulerian method for reactive flow. Physical variables such as the pressure,velocity, and speed of sound in each cell need to be reconstructed for the Harten-Lax-Leer-Contact (HLLC) Riemann solver, which will result in nonlinear algebra equations, and these reconstructed variables are used to obtain the flux. Numerical examples of stable and unstable detonations with different equation of states demonstrate the accuracy and efficiency of this method. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we propose a model for image restoration with blur and impulse noise, it is composed of l 1 data fitting term and a nonconvex regularization term, which is the weighted difference of l 1 -norm and l 2 -norm based on wavelet frame. The combined model is difficult to solve by the corresponding Euler Lagrangian equations, here we solve it by alternating direction method of multipliers (ADMM). We describe the detailed process of the algorithm, and establish the convergence of the algorithm. The experimental outcomes on different blurs and different impulse noises demonstrate that the proposed approach is better than those existing methods in terms of standard signal-to-noise ratio (PSNR), relative error (ReErr), and visual quality.

A modified gas kinetic scheme (MGKS) for collisional laser-plasma interaction model is proposed in this paper. Splitting method is applied for the kinetic and electromagnetic parts, to describe the behavior of relativistic electrons in phase space, modification is considered in the reconstruction of equilibrium and transport process, a higher order reconstruction method is designed on the flux reconstruction to reduce the energy error, and accurate Fourier interpolation is applied to Maxwell equation. Numerical experiments are tested by the stimulated Raman scattering (SRS) problems, including forward and backward Raman scattering, which show this scheme can give satisfied results.