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The asymptotics of a singularly perturbed problem is constructed. describing the transport of a polydisperse impurity in the atmosphere, taking into account the processes of precipitation and wind pick-up, as well as the processes of…
This paper considers the iterative solution of linear systems arising from discretization of the anisotropic radiative transfer equation with discontinuous elements on the sphere. In order to achieve robust convergence behavior in the…
Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation…
Kinetic transport models are mesoscopic mathematical descriptions of the transport of particles as well as their interactions with the background media or among themselves, and they have wide applications in many areas of mathematical…
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…
A method is developed within an adaptive framework to solve quasilinear diffusion problems with internal and possibly boundary layers starting from a coarse mesh. The solution process is assumed to start on a mesh where the problem is badly…
Radiative transfer is essential in astronomy, both for interpreting observations and simulating various astrophysical phenomena. However, self-consistent line radiative transfer is computationally expensive, especially in 3D. To reduce the…
As an extension of our previous work in Sun et.al (2018) [41], we develop a discontinuous Galerkin method for solving cross-diffusion systems with a formal gradient flow structure. These systems are associated with non-increasing entropy…
In this paper, we propose a high order semi-implicit well-balanced finite difference scheme for all Mach Euler equations with a gravitational source term. To obtain the asymptotic preserving property, we start from the conservative form of…
In this paper, we present and analyze an energy-conserving and linearly implicit scheme for solving the nonlinear wave equations. Optimal error estimates in time and superconvergent error estimates in space are established without time-step…
We present a non-diagonal phase field model for phase transformations with unequal but finite diffusivities in the two phases. This model allows to recover the desired boundary conditions at the interface, and especially the elimination of…
Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…
We consider the compressible Euler system with anelastic scaling, modeling isentropic flows under the influence of gravity. In the zero-Mach-number limit, the solution of the compressible Euler system converges to a variable density…
Chromatographic processes can be modeled by nonlinear, convection-dominated partial differential equations, together with nonlinear relations: the adsorption isotherms. In this paper we consider the nonlinear equilibrium dispersive (ED)…
Blind face restoration methods have shown remarkable performance, particularly when trained on large-scale synthetic datasets with supervised learning. These datasets are often generated by simulating low-quality face images with a…
We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form parabolic equations. Based on the Feynman-Kac formula, the solution is expressed as a conditional expectation of an associated diffusion process.…
In this work, we propose a new semi-Lagrangian (SL) finite difference scheme for nonlinear advection-diffusion problems. To ensure conservation, which is fundamental for achieving physically consistent solutions, the governing equations are…
A thermodynamic approach to rapid phase transformations within a diffuse interface in a binary system is developed. Assuming an extended set of independent thermodynamic variables formed by the union of the classic set of slow variables and…
A key property of the linear Boltzmann semiconductor model is that as the collision frequency tends to infinity, the phase space density $f = f(x,v,t)$ converges to an isotropic function $M(v)\rho(x,t)$, called the drift-diffusion limit,…
A kind of spatial fractional diffusion equations in this paper are studied. Firstly, an L1 formula is employed for the spatial discretization of the equations. Then, a second order scheme is derived based on the resulting semi-discrete…