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In this paper, we develop a family of high order asymptotic preserving schemes for some discrete-velocity kinetic equations under a diffusive scaling, that in the asymptotic limit lead to macroscopic models such as the heat equation, the porous media equation, the advection-diffusion equation, and the viscous Burgers' equation. Our approach is based on the… (More)

- Research Showcase, Cmu, Juhi Jang, Ian Tice, Yanjin Wang
- 2015

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The… (More)

- Juhi Jang, Nader Masmoudi
- 2008

An important problem in the theory of compressible gas flows is to understand the singular behavior of vacuum states. The main difficulty lies in the fact that the system becomes degenerate at the vacuum boundary, where the characteristics coincide and have unbounded derivative. In this paper, we overcome this difficulty by presenting a new formulation and… (More)

- Research Showcase, Cmu, Juhi Jang, Ian Tice, Yanjin Wang
- 2015

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The… (More)

In this paper, some theoretical aspects will be addressed for the asymptotic preserving DG-IMEX schemes recently proposed in [10] for kinetic transport equations under a diffusive scaling. We will focus on the methods that are based on discontinuous Galerkin (DG) spatial discretizations with the P k polynomial space and a first order IMEX temporal… (More)

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The… (More)

We study the evolution of passive scalars in both rigid and moving slab-like domains , in both horizontally periodic and infinite contexts. The scalar is required to satisfy Robin-type boundary conditions corresponding to Newton's law of cooling, which lead to non-trivial equilibrium configurations. We study the equilibration rate of the passive scalar in… (More)

In this paper, we develop high-order asymptotic preserving (AP) schemes for the BGK equation in a hyperbolic scaling, which leads to the macroscopic models such as the Euler and compressible Navier-Stokes equations in the asymptotic limit. Our approaches are based on the so-called micro-macro formulation of the kinetic equation which involves a natural… (More)

- Juhi Jang, Nader Masmoudi
- 2010

An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of vacuum. In particular , physical vacuum, in which the boundary moves with a nontrivial finite normal acceleration, naturally arises in the study of the motion of gaseous stars or shallow water. Despite its… (More)

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