Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs:Applications to Compressible Euler Equations and Granular Hydrodynamics

We introduce adaptive moving mesh central-upwind schemes for one-and two-dimensional hyperbolic systems of conservation and balance laws.The proposed methods consist of three steps.First,the solution is evolved by solving the studied system by the second-order semi-discrete central-upwind scheme on either the one-dimensional nonuniform grid or the two-dimensional structured quadrilateral mesh.When the evolution step is complete,the grid points are redistributed according to the moving mesh differential equation.Finally,the evolved solution is projected onto the new mesh in a conservative manner.The resulting adaptive moving mesh methods are applied to the one-and two-dimensional Euler equations of gas dynamics and granular hydrodynamics systems.Our numerical results demonstrate that in both cases,the adaptive moving mesh central-upwind schemes outperform their uniform mesh counterparts.

THE ASYMPTOTIC PRESERVING UNIFIED GAS KINETIC SCHEME FOR GRAY RADIATIVE TRANSFER EQUATIONS ON DISTORTED QUADRILATERAL MESHES

In this paper,we consider the multi-dimensional asymptotic preserving unified gas kinetic scheme for gray radiative transfer equations on distorted quadrilateral meshes.Different from the former scheme [J.Comput.Phys.285（2015）,265-279] on uniform meshes,in this paper,in order to obtain the boundary fluxes based on the framework of unified gas kinetic scheme（UGKS）,we use the real multi-dimensional reconstruction for the initial data and the macro-terms in the equation of the gray transfer equations.We can prove that the scheme is asymptotic preserving,and especially for the distorted quadrilateral meshes,a nine-point scheme [SIAM J.SCI.COMPUT.30（2008）,1341-1361] for the diffusion limit equations is obtained,which is naturally reduced to standard five-point scheme for the orthogonal meshes.The numerical examples on distorted meshes are included to validate the current approach.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

QUANTITATIVE APPROACH TO INFLUENCES OF HIGH SEDIMENT LADEN INUNDATION FLOWS ON THE MORPHOLOGICAL VARIATION OF FLOODPLAINS

This article mainly aims at developing an integrated 2-D numerical simulation model on inundation, sediment transportation and the morphological variations of floodplains due to high sediment-laden inundation flows. Due to the complexity of inner and outer boundaries and the arbitrary structures within the computational domain of floodplains, an unstructured Finite-Volume Method （FVM） based on an irregular polygon mesh was worked out so that the influences of complex boundaries can be integrated into the simulation. A case study was conducted in the Lower Yellow River Basin, in which a dike-break at the Huayuankou Hydrological Station was assumed to happen when a flood scale of 1982 was suffered in the region. The simulated spatial distribution of sediment deposition and erosion can be used to reasonably explain the natural phenomena of ＂suspended river＂ of the lower part of the Yellow River. It is concluded that the inundation process of water is similar to a variable-river-bed condition during the simulation because the sediment deposition and erosion are modified by new values at the end of each time step. The mass and momentum conservation were strictly followed during the simulation. Therefore, the prediction of floodplain evolutions by the integrated simulation model, proposed in this study, can be adequately and accurately given if the real condition of an floodplain can be obtained in detail.