In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides wi...In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides with conventional methods is obtained by means of integral identities techniques.展开更多
A new method is proposed for surface construction on irregular quad meshes as extensions to uniform B-spline surfaces. Given a number of control points, which form a regular or irregular quad mesh, a weight function i...A new method is proposed for surface construction on irregular quad meshes as extensions to uniform B-spline surfaces. Given a number of control points, which form a regular or irregular quad mesh, a weight function is constructed for each control point. The weight function is defined on a local domain and is C1 continuous. Then the whole surface is constructed by the weighted combination of all the control points. The property of the new method is that the surface is defined by piecewise Cl bi-cubic rational parametric polynomial with each quad face. It is an extension to uniform B-spline surfaces in the sense that its definition is an analogy of the B-spline surface, and it produces a uniform bi-cubic B-spline surface if the control mesh is a regular quad mesh. Examples produced by the new method are also included.展开更多
In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flow...In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flows because the regions near to the boundaries generally play an important role on the defined solutions. Using the vorticity-stream function form of the N-S equations as governing equations in the flow field simulation with irregular mesh, the determining/calculating wall vorticity under irregular mesh is very important. In this paper, one first order formula of wall vorticity under irregular mesh was derived based on the 2-D Taylor expansion and was tested numerically through an example of a flow with the Z type, shape of boundaries. A satisfactory result was found which was compared with one obtained by FEM.展开更多
Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmi...Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.展开更多
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. D...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.展开更多
基金Foundation item: Supported by the NSF of China(10371113)Supported by the Foundation of Overseas Scholar of China(2001(119))Supported by the project of Creative Engineering of Province of China(2002(219))
文摘In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption. Meanwhile, the superclose result coincides with conventional methods is obtained by means of integral identities techniques.
基金Supported by National Nature Science Foundation of China(Nos.61103117,61202150,61303088)Shandong Province Natural Science Foundation(ZR2011FL028)Shandong Ji'nan College and Institute Independent Innovation Project(201303016)
文摘A new method is proposed for surface construction on irregular quad meshes as extensions to uniform B-spline surfaces. Given a number of control points, which form a regular or irregular quad mesh, a weight function is constructed for each control point. The weight function is defined on a local domain and is C1 continuous. Then the whole surface is constructed by the weighted combination of all the control points. The property of the new method is that the surface is defined by piecewise Cl bi-cubic rational parametric polynomial with each quad face. It is an extension to uniform B-spline surfaces in the sense that its definition is an analogy of the B-spline surface, and it produces a uniform bi-cubic B-spline surface if the control mesh is a regular quad mesh. Examples produced by the new method are also included.
文摘In the engineering applications, flow problems with complicated geometrical shape of boundaries are of ten happen. Their boundary conditions should be given in precisely when doing the simulation of these type of flows because the regions near to the boundaries generally play an important role on the defined solutions. Using the vorticity-stream function form of the N-S equations as governing equations in the flow field simulation with irregular mesh, the determining/calculating wall vorticity under irregular mesh is very important. In this paper, one first order formula of wall vorticity under irregular mesh was derived based on the 2-D Taylor expansion and was tested numerically through an example of a flow with the Z type, shape of boundaries. A satisfactory result was found which was compared with one obtained by FEM.
文摘Adaptive higher-order finite element methods(hp-FEM)are well known for their potential of exceptionally fast(exponential)convergence.However,most hp-FEM codes remain in an academic setting due to an extreme algorithmic complexity of hp-adaptivity algorithms.This paper aims at simplifying hpadaptivity for H(curl)-conforming approximations by presenting a novel technique of arbitrary-level hanging nodes.The technique is described and it is demonstrated numerically that it makes adaptive hp-FEM more efficient compared to hp-FEM on regular meshes and meshes with one-level hanging nodes.
文摘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.
