Aiming at the isoparametric bilinear finite volume element scheme,we initially derive an asymptotic expansion and a high accuracy combination formula of the derivatives in the sense of pointwise by employing the energy-embedded method on uniform grids.Furthermore,we prove that the approximate derivatives are convergent of order two.Finally,numerical examples verify the theoretical results.
In this paper,a boundary condition-enforced IBM is introduced into the LBMin order to satisfy the non-slip and temperature boundary conditions,and natural convections in a concentric isothermal annulus between a square outer cylinder and a circular inner cylinder are simulated.The obtained results show that the boundary condition-enforced method gives a better solution for the flow field and the complicated physics of the natural convections in the selected case is correctly captured.The calculated average Nusselt numbers agree well with the previous studies.
Yang HuXiao-Dong NiuShi ShuHaizhuan YuanMingjun Li
In this study, we present a conservative local discontinuous Galerkin(LDG) method for numerically solving the two-dimensional nonlinear Schrdinger(NLS) equation. The NLS equation is rewritten as a firstorder system and then we construct the LDG formulation with appropriate numerical flux. The mass and energy conserving laws for the semi-discrete formulation can be proved based on different choices of numerical fluxes such as the central, alternative and upwind-based flux. We will propose two kinds of time discretization methods for the semi-discrete formulation. One is based on Crank-Nicolson method and can be proved to preserve the discrete mass and energy conservation. The other one is Krylov implicit integration factor(IIF) method which demands much less computational effort. Various numerical experiments are presented to demonstrate the conservation law of mass and energy, the optimal rates of convergence, and the blow-up phenomenon.
