Ming-Cheng Shiue

The Barotropic Mode for the Primitive Equations

The barotropic mode of the Primitive Equations is considered. The corresponding equations resemble the Euler equations of incompressible flows with marked differences. The existence and uniqueness of solutions for the linearized equations is proven; the proof is based on the study of a nonstandard boundary value problem. In the nonlinear case, several schemes inspired by the projection method are proposed and their stability is studied. Finally, numerical simulations are described using one of these schemes, closely related to the pressure correction projection scheme.

Time-periodic solutions of the primitive equations of large-scale moist atmosphere: existence and stability

This article is devoted to the study of the asymptotic stability of the three-dimensional viscous primitive equations for large-scale moist atmosphere in the pressure coordinate system. An asymptotic stability criterion for the solutions of such model with time-dependent forcing terms is obtained. In particular, under the assumptions that the associated forces are both time-periodic and small (in a suitable sense), we obtain the existence of the time-periodic solution for the primitive equations of large-scale moist atmosphere. Moreover, this time-periodic solution is asymptotically stable in sense.

Convergence of the MAC Scheme for the Stokes/Darcy Coupling Problem

In this paper, we extend the MAC scheme for Stokes problem to the Stokes/Darcy coupling problem. The interface conditions between two separate regions are discretized and well-incorporated into the MAC grid setting. We first perform the stability analysis of the scheme for the velocity in both Stokes and Darcy regions and establish the stability for the pressure in both regions by considering an analogue of discrete divergence problem. Following the similar analysis on stability, we perform the error estimates for the velocity and the pressure in both regions. The theoretical results show the first-order convergence of the scheme in discrete

A simple projection method for the coupled Navier-Stokes and Darcy flows

L^2

Boundary value problems for the shallow water equations with topography

L2 norms for both velocity and the pressure in both regions. Moreover, in fluid region, the first-order convergence for the x-derivative of velocity component u and the y-derivative of velocity component v is also obtained in discrete

Interior penalty discontinuous Galerkin methods with implicit time‐integration techniques for nonlinear parabolic equations

L^2