Jian-Hu Feng

A CWENO-type central-upwind scheme for ideal MHD equations

A simple fourth-order, central-upwind scheme based on central weighted essentially non-oscillatory (CWENO) reconstruction is proposed in this paper for computing the approximate solutions of one- and two-dimensional ideal magnetohydrodynamics (MHD) equations with high-resolution. Since the non-uniform width of the different local Riemann fans is calculated more accurately, the central-upwind schemes enjoy a much smaller numerical viscosity as well as the staggering between two neighboring sets of grids is avoided. Due to the central-upwind scheme is combined with the fourth-order CWENO reconstruction, the scheme we present has the non-oscillatory behavior. The numerical results show the desired accuracy, high-resolution, and robustness of our method.

Computations of shallow water equations with high-order central-upwind schemes on triangular meshes

New high-order central-upwind schemes on triangular meshes are proposed to approximate the solutions of shallow water equations. The nonuniform width of the different local Riemann fans is calculated more accurately, and the new central-upwind schemes are of simplicity, universality and robustness. At the same time, due to the central-upwind schemes are combined with new reconstructions based on adaptive least squares, the schemes have the almost non-oscillatory behavior. The numerical results show the desired accuracy, high-resolution, and robustness of our methods.

Numerical simulation for two-phase flows using hybrid scheme

The present paper is devoted to the computation of two-phase flows using two-fluid approach. Two difficulties arise for the model: one of the equations is written in non-conservative form; non-conservative terms exist in the momentum and energy equations. To deal with the aforementioned difficulties, the non-conservative volume fraction equation is discretized by WENO scheme, and the CWENO-type central-upwind scheme is applied to solve the mass, momentum and energy equations. Computational results are eventually provided and discussed.

Computations of steady and unsteady transport of pollutant in shallow water

We present new models for simulating the steady and unsteady transport of pollutant. Then the simple central-upwind schemes based on central weighted essentially non-oscillatory reconstructions are proposed in this paper for computing the one- and two-dimensional steady and unsteady models. Since the non-uniform width of the different local Riemann fans is calculated more accurately, the central-upwind schemes enjoy a much smaller numerical viscosity as well as the staggering between two neighboring sets of grids is avoided. Synchronously, due to the central-upwind schemes are combined with the fourth-order central weighted essentially non-oscillatory reconstructions, the schemes have the non-oscillatory behavior. The numerical results show the desired accuracy, high-resolution, and robustness of our methods.

FLUID SIMULATION USING AN ADAPTIVE SEMI-DISCRETE CENTRAL-UPWIND SCHEME

In this paper, we propose an adaptive semi-discrete central-upwind scheme on triangular meshes to approximate the solutions of hyperbolic conservation laws in gas dynamics: a local smoothness indicator is implemented to identify discontinuous solution regions; away from the discontinuities, a simple and computationally economical flux is used; near the discontinuities, an accurate but computationally uneconomical flux is used. Several numerical experiments, Euler equations and Kelvin–Helmholtz instability, are successfully simulated. The numerical results show the desired accuracy, high efficiency and robustness of the adaptive scheme.

AN EFFICIENT THIRD-ORDER SCHEME FOR THREE-DIMENSIONAL HYPERBOLIC CONSERVATION LAWS

In this paper, we present a third-order central weighted essentially nonoscillatory (CWENO) reconstruction for computations of hyperbolic conservation laws in three space dimensions. Simultaneously...