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
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
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 conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local different...In the conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.展开更多
基于全程波波动方程的逆时偏移(Reverse Time Migration)可以对回转波、多次反射波成像,不受横向速度变化影响,没有倾角限制,随着计算机软硬件技术的进步,再次成为偏移方法研究热点.本文将格子法用于叠前逆时深度偏移成像.格子法作为波...基于全程波波动方程的逆时偏移(Reverse Time Migration)可以对回转波、多次反射波成像,不受横向速度变化影响,没有倾角限制,随着计算机软硬件技术的进步,再次成为偏移方法研究热点.本文将格子法用于叠前逆时深度偏移成像.格子法作为波场延拓方法,处理起伏地表边界条件容易,可用于含起伏地表边界条件的逆时波场延拓;可利用变尺度非规则对计算域进行离散,因此可根据速度模型调整网格尺度来降低存储量,放大时间步长,降低计算量.采用光滑的曲人工边界,也可避免常规的PML吸收边界存在的角点区域需特别处理的麻烦.本方法通过事先计算和存储边界单元的局部几何参数,与直边界PML方法相比不增加任何计算量.格子法还具有容易实现并行计算的特点,非常适用于叠前逆时偏移.本文给出了二维问题算例.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.
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.
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 conventional differential quadrature （DQ） method the functional values along a mesh line are used to approximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature （LDQ） method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in the new approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directly approximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature is still kept. Numerical examples are provided to validate the LDQ method.
文摘基于全程波波动方程的逆时偏移(Reverse Time Migration)可以对回转波、多次反射波成像,不受横向速度变化影响,没有倾角限制,随着计算机软硬件技术的进步,再次成为偏移方法研究热点.本文将格子法用于叠前逆时深度偏移成像.格子法作为波场延拓方法,处理起伏地表边界条件容易,可用于含起伏地表边界条件的逆时波场延拓;可利用变尺度非规则对计算域进行离散,因此可根据速度模型调整网格尺度来降低存储量,放大时间步长,降低计算量.采用光滑的曲人工边界,也可避免常规的PML吸收边界存在的角点区域需特别处理的麻烦.本方法通过事先计算和存储边界单元的局部几何参数,与直边界PML方法相比不增加任何计算量.格子法还具有容易实现并行计算的特点,非常适用于叠前逆时偏移.本文给出了二维问题算例.
