In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bell...In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bellman equation.We prove the convergence of the method and outline the relationships to other numerical methods.The case of vanishing diffusion is treated by introducing an artificial diffusion term.We illustrate the superiority of our method to the standardly used implicit finite difference method on two numerical examples from finance.展开更多
针对自由界面问题,构建了拉格朗日粒子和流体体积(volume of fluid,VOF)耦合算法.拉格朗日粒子方法可以准确追踪运动界面,但是一般很难保证流体的质量守恒性.VOF方法可以保证很好的质量守恒性,但是不容易计算界面的几何信息.因此,本文...针对自由界面问题,构建了拉格朗日粒子和流体体积(volume of fluid,VOF)耦合算法.拉格朗日粒子方法可以准确追踪运动界面,但是一般很难保证流体的质量守恒性.VOF方法可以保证很好的质量守恒性,但是不容易计算界面的几何信息.因此,本文构造了一种耦合算法,吸收两种方法的优点.耦合算法中还引入了四叉树自适应网格技术,可以在大变形区域提高界面的分辨率,并能减少计算量.利用耦合算法模拟经典的Zalesak旋转盘问题和单涡剪切流动,数值结果和文献已有结果吻合较好,验证了耦合算法的稳定性、有效性和准确性.展开更多
在大地形三维多分辨率显示中,针对裂缝消除问题提出了一种基于LOD(Level of Detail)控制和裂缝可视性的改进算法。证明在四叉树网格可视距离/尺寸比>3时,必然满足限制四叉树约束;基于裂缝的可见性,在预处理阶段通过区分地形上升裂缝...在大地形三维多分辨率显示中,针对裂缝消除问题提出了一种基于LOD(Level of Detail)控制和裂缝可视性的改进算法。证明在四叉树网格可视距离/尺寸比>3时,必然满足限制四叉树约束;基于裂缝的可见性,在预处理阶段通过区分地形上升裂缝和地形下降裂缝,为后者添加与裂缝大小一致的几何图形来生成裂缝消除补丁;在实时渲染过程中,既不需要通过CPU计算来控制网格的层次差,也不需要通过CPU来识别相邻网格层次差和消除裂缝。实验测试表明:该算法简单有效,附加网格数据比裙边算法减少约75%,且完全能够避免地形裂缝的显示。展开更多
A 2D depth-averaged flow-pollutant coupled model based on quad-tree meshes was established to accurately simulate flows in water areas with irregular natural boundaries in this paper. The grids were generated by recur...A 2D depth-averaged flow-pollutant coupled model based on quad-tree meshes was established to accurately simulate flows in water areas with irregular natural boundaries in this paper. The grids were generated by recursive subdivision about seeding points. A new neighbor-finding algorithm was presented. The governing equations were discrctized in collocated conservative variables by using the finite volume method, and the normal flux of mass, momentum and pollutants across the interlace between cells were computed by a Godunov-type Flux Difference Splitting （FDS） scheme. The model was applied to simulate flow fields around a groin. The computed values are in agreement with observed data. The results indicate that quad-tree meshes have fine local resolution, high efficiency and easy local refinement. It is clear that the quad-tree grid model can offer gains in efficiency when applied to complex flow domains or strong shear flows. Finally the model is applied to flow fields and concentration fields simulation in Jiangsu Haizhou Bay. The simulated polluted area is matched well with observations. Therefore, this model can be used to predict flow and concentration fields of actual water area with irregular natural land boundaries.展开更多
基金supported by the European Union in the FP7-PEOPLE-2012-ITN Program under Grant Agreement Number 304617(FP7 Marie Curie Action,Project Multi-ITN STRIKE-Novel Methods in Computational Finance).
文摘In this work we introduce a new unconditionally convergent explicit Tree-Grid Method for solving stochastic control problems with one space and one time dimension or equivalently,the corresponding Hamilton-Jacobi-Bellman equation.We prove the convergence of the method and outline the relationships to other numerical methods.The case of vanishing diffusion is treated by introducing an artificial diffusion term.We illustrate the superiority of our method to the standardly used implicit finite difference method on two numerical examples from finance.
文摘针对自由界面问题,构建了拉格朗日粒子和流体体积(volume of fluid,VOF)耦合算法.拉格朗日粒子方法可以准确追踪运动界面,但是一般很难保证流体的质量守恒性.VOF方法可以保证很好的质量守恒性,但是不容易计算界面的几何信息.因此,本文构造了一种耦合算法,吸收两种方法的优点.耦合算法中还引入了四叉树自适应网格技术,可以在大变形区域提高界面的分辨率,并能减少计算量.利用耦合算法模拟经典的Zalesak旋转盘问题和单涡剪切流动,数值结果和文献已有结果吻合较好,验证了耦合算法的稳定性、有效性和准确性.
文摘在大地形三维多分辨率显示中,针对裂缝消除问题提出了一种基于LOD(Level of Detail)控制和裂缝可视性的改进算法。证明在四叉树网格可视距离/尺寸比>3时,必然满足限制四叉树约束;基于裂缝的可见性,在预处理阶段通过区分地形上升裂缝和地形下降裂缝,为后者添加与裂缝大小一致的几何图形来生成裂缝消除补丁;在实时渲染过程中,既不需要通过CPU计算来控制网格的层次差,也不需要通过CPU来识别相邻网格层次差和消除裂缝。实验测试表明:该算法简单有效,附加网格数据比裙边算法减少约75%,且完全能够避免地形裂缝的显示。
基金Project supported by State Key Laboratory Science Foundation (Grant No: 2005406811), National Natural Science Foundation of China (Grant No: 50009001) and Natural Science Foundation of Jiangsu Province (Grant No: BK2000004).
文摘A 2D depth-averaged flow-pollutant coupled model based on quad-tree meshes was established to accurately simulate flows in water areas with irregular natural boundaries in this paper. The grids were generated by recursive subdivision about seeding points. A new neighbor-finding algorithm was presented. The governing equations were discrctized in collocated conservative variables by using the finite volume method, and the normal flux of mass, momentum and pollutants across the interlace between cells were computed by a Godunov-type Flux Difference Splitting （FDS） scheme. The model was applied to simulate flow fields around a groin. The computed values are in agreement with observed data. The results indicate that quad-tree meshes have fine local resolution, high efficiency and easy local refinement. It is clear that the quad-tree grid model can offer gains in efficiency when applied to complex flow domains or strong shear flows. Finally the model is applied to flow fields and concentration fields simulation in Jiangsu Haizhou Bay. The simulated polluted area is matched well with observations. Therefore, this model can be used to predict flow and concentration fields of actual water area with irregular natural land boundaries.
