Guoxian Chen

Wuhan University | WHU · School of Mathematics and Statistics

We present a high‐order accurate, positivity‐preserving and well‐balanced finite volume scheme for the shallow water equations with variable topography. An unlimited third‐order scheme is combined with the recent, second‐order accurate Bottom‐Surface‐Gradient Method (BSGM, [5]). This is monitored by an a‐posteriori MOOD (Multidimensional Optimal Or...

Due to the Riemann solver free and avoiding characteristic decomposition, the central scheme is a simple and efficient tool for numerical solution of hyperbolic conservation laws (Nessyahu and Tadmor, J. Comput. Phys., 87(2):314-329,1990). But the theoretical Courant number CFL in order to preserve the invariant region of the numerical solution is...

In this paper we introduce sharp stability conditions for the single-stage MUSCL-Hancock scheme: 1) the CFL number is (3−1)/2 which admits almost 73 percent of the time step of classical two-stage MUSCL scheme and hence yields a considerable speed-up; 2) The preliminary TVD reconstruction is modified when necessary by a bound-preserving slope limit...

We propose a new second-order accurate hydrostatic reconstruction scheme for the Saint-Venant system. Such a scheme needs to overcome several difficulties: besides the well-known issues of positivity and well-balancing there is also the difficulty of unphysical reflections from non-monotone bottom reconstructions. We address all of these problems a...

Developing a precise and reproducible bandgap tuning method that enables tailored design of materials is of crucial importance for optoelectronic devices. Towards this end, we report a sphere diameter engineering (SDE) technique to manipulate the bandgap of two-dimensional (2D) materials. A one-to-one correspondence with an ideal linear working cur...

A key diffculty in the analysis and numerical approximation of the shallow water equations is the nonconservative product of measures due to the gravitational force acting on a sloped bottom. Solutions may be nonunique, and numerical schemes are not only consistent discretizations of the shallow water equations, but they also determine how to model...

In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet-dry cells, which is presented in this paper for the one dimensional c...

We propose a well‐balanced stable generalized Riemann problem (GRP) scheme for the shallow water equations with irregular bottom topography based on moving, adaptive, unstructured, triangular meshes. In order to stabilize the computations near equilibria, we use the Rankine–Hugoniot condition to remove a singularity from the GRP solver. Moreover, w...

In this paper, we construct a well-balanced, positivity preserving finite volume scheme for the shallow water equations based on a continuous, piecewise linear discretization of the bottom topography. The main new technique is a special reconstruction of the flow variables in wet–dry cells, which is presented in this paper for the one dimensional c...

A new geometrical conservative interpolation on unstructured meshes is developed for preserving still water equilibrium and positivity of water depth at each iteration of mesh movement, leading to an adaptive moving finite volume (AMFV) scheme for modeling flood inundation over dry and complex topography. Unlike traditional schemes involving positi...

An enhanced-interval linear programming (EILP) model and its solution algorithm have been developed that incorporate enhanced-interval uncertainty (e.g., A±, B± and C±) in a linear optimization framework. As a new extension of linear programming, the EILP model has the following advantages. Its solution space is absolutely feasible compared to t...

This paper presents a second-order accurate adaptive Godunov method for two-dimensional (2D) compressible multicomponent flows, which is an extension of the previous adaptive moving mesh method of Tang et al. (SIAM J. Numer. Anal. 41:487–515, 2003) to unstructured triangular meshes in place of the structured quadrangular meshes. The current algorit...

This paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55(1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is...