arXiv subjects

Zhonghua Qiao

Publications and source records attributed to Zhonghua Qiao.

57 records · Page 4Linked to original sources

arXiv2015

Convergence of a Fast Explicit Operator Splitting Method for the Molecular Beam Epitaxy Model

A fast explicit operator splitting (FEOS) method for the molecular beam epitaxy model has been presented in [Cheng, et al., Fast and stable explicit operator splitting methods for phase-field models, J. Comput. Phys., submitted]. The original problem is split into linear and nonlinear subproblems. For the linear part, the pseudo-spectral method is adopted; for the nonlinear part, a 33-point difference scheme is constructed. Here, we give a compact center-difference scheme involving fewer points for the nonlinear subproblem. Besides, we analyze the convergence rate of the algorithm. The global error order $\mathcal{O}(τ^2+h^4)$ in discrete $L^2$-norm is proved theoretically and verified numerically. Some numerical experiments show the robustness of the algorithm for small coefficients of the fourth-order term for the one-dimensional case. Besides, coarsening dynamics are simulated in large domains and the $1/3$ power laws are observed for the two-dimensional case.

math.NA↗

arXiv2015

An unconditionally energy stable finite difference scheme for a stochastic Cahn-Hilliard equation

In this work, the MMC-TDGL equation, a stochastic Cahn-Hilliard equation is solved numerically by using the finite difference method in combination with a convex splitting technique of the energy functional. For the non-stochastic case, we develop an unconditionally energy stable difference scheme which is proved to be uniquely solvable. For the stochastic case, by adopting the same splitting of the energy functional, we construct a similar and uniquely solvable difference scheme with the discretized stochastic term. The resulted schemes are nonlinear and solved by Newton iteration. For the long time simulation, an adaptive time stepping strategy is developed based on both first- and second-order derivatives of the energy. Numerical experiments are carried out to verify the energy stability, the efficiency of the adaptive time stepping and the effect of the stochastic term.

math.NA↗

arXiv2011

NRxx Simulation of Microflows with Shakhov Model

In this paper, we propose a method to simulate the microflows with Shakhov model using the NRxx method developed in [4, 5, 6]. The equation under consideration is the Boltzmann equation with force terms and the Shakhov model is adopted to achieve the correct Prandtl number. As the focus of this paper, we derive a uniform framework for different order moment systems on the wall boundary conditions, which is a major difficulty in the moment methods. Numerical examples for both steady and unsteady problems are presented to show the convergence in the number of moments.

math-ph↗