公开(公告)号：US08285530B2

公开(公告)日：2012-10-09

申请号：US12579645

申请日：2009-10-15

申请人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

发明人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

IPC分类号： G06G7/50

CPC分类号： G06G7/50 ,  G06F17/13 ,  G06F17/5018 ,  G06F2217/16

摘要： An embodiment of the present invention may be a system or method for simulating a physical process. The physical process being simulated may be in a droplet. The process being simulated may be the drying of a droplet on a substrate. Simulating the physical process may include using a finite difference scheme to approximate a differential of a function. The function may be dependent on a plurality of variables. The location in space at which one or more of the variables is evaluated may depend on the sign of one or more of the variables and upon which portion of the finite difference equation is being evaluated.

摘要翻译： 本发明的实施例可以是用于模拟物理过程的系统或方法。 正在模拟的物理过程可能是液滴。 正在模拟的过程可能是干燥基底上的液滴。 模拟物理过程可以包括使用有限差分方案来近似函数的微分。 该函数可以取决于多个变量。 评估一个或多个变量的空间中的位置可以取决于一个或多个变量的符号，并且有限差分方程的哪个部分正在被评估。

公开(公告)号：US08014986B2

公开(公告)日：2011-09-06

申请号：US12476588

申请日：2009-06-02

申请人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

发明人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

IPC分类号： G06G7/48 ,  G06F17/10

CPC分类号： G06G7/48 ,  G06F17/13 ,  G06F17/5018

摘要： A computer implemented method for simulating a final pattern of a droplet of a fluid having a plurality of fluid properties is disclosed. The method includes using lubrication equations to represent solute flow, diffusion and evaporation of a droplet on a substrate. The method further includes solving the lubrication equations through temporal discretization and spatial discretization; and deriving the final pattern of the droplet from results of the solving. The final pattern is stored on a computer readable medium.

摘要翻译： 公开了一种用于模拟具有多种流体性质的流体液滴的最终模式的计算机实现的方法。 该方法包括使用润滑方程来表示液滴在基底上的溶质流动，扩散和蒸发。 该方法还包括通过时间离散化和空间离散求解润滑方程; 并从求解的结果中得出液滴的最终模式。 最终模式存储在计算机可读介质上。

公开(公告)号：US20110093241A1

公开(公告)日：2011-04-21

申请号：US12579645

申请日：2009-10-15

申请人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

发明人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

IPC分类号： G06G7/50 ,  G06F17/17

CPC分类号： G06G7/50 ,  G06F17/13 ,  G06F17/5018 ,  G06F2217/16

摘要： An embodiment of the present invention may be a system or method for simulating a physical process. The physical process being simulated may be in a droplet. The process being simulated may be the drying of a droplet on a substrate. Simulating the physical process may include using a finite difference scheme to approximate a differential of a function. The function may be dependent on a plurality of variables. The location in space at which one or more of the variables is evaluated may depend on the sign of one or more of the variables and upon which portion of the finite difference equation is being evaluated.

摘要翻译： 本发明的实施例可以是用于模拟物理过程的系统或方法。 正在模拟的物理过程可能是一个液滴。 正在模拟的过程可能是干燥基底上的液滴。 模拟物理过程可以包括使用有限差分方案来近似函数的微分。 该函数可以取决于多个变量。 评估一个或多个变量的空间中的位置可以取决于一个或多个变量的符号，并且有限差分方程的哪一部分被评估。

公开(公告)号：US20100305914A1

公开(公告)日：2010-12-02

申请号：US12476588

申请日：2009-06-02

申请人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

发明人： Jie Zhang ,  Jiun-Der Yu ,  Shinri Sakai

IPC分类号： G06F17/10 ,  G06F19/00

CPC分类号： G06G7/48 ,  G06F17/13 ,  G06F17/5018

摘要： A computer implemented method for simulating a final pattern of a droplet of a fluid having a plurality of fluid properties is disclosed. The method includes using lubrication equations to represent solute flow, diffusion and evaporation of a droplet on a substrate. The method further includes solving the lubrication equations through temporal discretization and spatial discretization; and deriving the final pattern of the droplet from results of the solving. The final pattern is stored on a computer readable medium.

摘要翻译： 公开了一种用于模拟具有多种流体性质的流体液滴的最终模式的计算机实现的方法。 该方法包括使用润滑方程来表示液滴在基底上的溶质流动，扩散和蒸发。 该方法还包括通过时间离散化和空间离散求解润滑方程; 并从求解结果中得出液滴的最终模式。 最终模式存储在计算机可读介质上。

公开(公告)号：US08285526B2

公开(公告)日：2012-10-09

申请号：US12629273

申请日：2009-12-02

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06F7/60 ,  G06F17/10

CPC分类号： G06F7/60 ,  G06F17/5018

摘要： A system and method for simulating a droplet on a substrate with a moving contact line. The height of the droplet above the substrate is represented as a height function. A height evolution equation represents how the height of a droplet with moving contact line varies over time. The height function at a first point in space and a first point in time is calculated. An extrapolated height value at the first point in time is based on the height function at the first point in space and the first point in time, and the contact line at the first point in time. The extrapolated height value is at a second point in space below the substrate. The height evolution equation is used to calculate the height function at a second point in time based upon the extrapolated height value at the first point in time.

摘要翻译： 一种用于利用移动接触线模拟基底上的液滴的系统和方法。 衬底上方的液滴的高度表示为高度函数。 高度演化方程式表示具有移动接触线的液滴的高度随时间而变化。 计算空间中的第一点和第一时间点的高度函数。 第一时间点的外推高度值基于空间第一点和第一时间点的高度函数，以及第一时间点的接触线。 外推高度值位于衬底下方的空间的第二点。 高度演化方程用于基于第一时间点的外推高度值计算第二时间点的高度函数。

公开(公告)号：US07930155B2

公开(公告)日：2011-04-19

申请号：US12107674

申请日：2008-04-22

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06G7/50

CPC分类号： G06F17/5018 ,  G06F2217/16

摘要： The present invention is directed towards systems and methods for simulating and analyzing a change in concentration of solute in a solution. The solution being simulated is encompassed by an interface. The concentration at a first point in time is determined at a set of nodes encompassed by the interface. A spatial cell is associated with each node. An extended concentration is calculated at an extended node. The extended node is not encompassed by the interface. The concentration is calculated at a second point in time at a set of nodes encompassed by the interface, based upon the concentration at the set of nodes encompassed by the interface at the first point in time and the extended concentration.

摘要翻译： 本发明涉及用于模拟和分析溶液中溶质浓度变化的系统和方法。 被模拟的解决方案被界面包围。 在第一时间点处的浓度在由界面包围的一组节点上确定。 空间单元与每个节点相关联。 在扩展节点处计算扩展浓度。 扩展节点不包含在接口中。 基于在第一时间点处的界面包围的节点集合和扩展浓度，在由界面包围的一组节点处的第二时间点计算浓度。

公开(公告)号：US07899654B2

公开(公告)日：2011-03-01

申请号：US12043867

申请日：2008-03-06

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06F17/50 ,  G06F13/00

CPC分类号： G06F17/5018 ,  G06F2217/16

摘要： A computer implemented method for simulating a final pattern of a droplet of a fluid having a plurality of fluid properties is disclosed. The method includes representing a position of a moving fluid boundary at a first point in time with a plurality of fluid markers, wherein the moving fluid boundary provides a boundary for a single-phase fluid. The moving fluid boundary separates a simulation space into a fluid space and a vacuum space, and the single-phase fluid inhabits the fluid space. The method further includes evaluating a plurality of indicator function defined on a quadrilateral grid for a velocity field, a pressure, and the plurality of fluid markers. The quadrilateral grid is formed by a plurality of points inside the fluid space and the vacuum space. The method also includes calculating surface tension at the moving fluid boundary through a level set method, solving a plurality of flow equations through a projection method for a surface location on the boundary, and representing the position of the moving fluid boundary at a second point in time by updating the positions of the fluid markers based on the plurality of velocity values. The fluid properties and the shape of the final pattern is then stored on a computer readable media.

摘要翻译： 公开了一种用于模拟具有多种流体性质的流体液滴的最终模式的计算机实现的方法。 该方法包括用多个流体标记物在第一时间点表示运动流体边界的位置，其中移动流体边界为单相流体提供边界。 运动流体界面将模拟空间分成流体空间和真空空间，单相流体居住在流体空间中。 该方法还包括评估用于速度场，压力和多个流体标记的在四边形网格上定义的多个指示符函数。 四边形网格由流体空间和真空空间内的多个点形成。 该方法还包括通过水平集方法计算移动流体边界处的表面张力，通过用于边界上的表面位置的投影方法求解多个流动方程，并且在第二点处表示运动流体边界的位置 基于多个速度值更新流体标记的位置。 然后将流体性质和最终图案的形状存储在计算机可读介质上。

公开(公告)号：US20090228258A1

公开(公告)日：2009-09-10

申请号：US12043867

申请日：2008-03-06

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06G7/48

CPC分类号： G06F17/5018 ,  G06F2217/16

摘要： A computer implemented method for simulating a final pattern of a droplet of a fluid having a plurality of fluid properties is disclosed. The method includes representing a position of a moving fluid boundary at a first point in time with a plurality of fluid markers, wherein the moving fluid boundary provides a boundary for a single-phase fluid. The moving fluid boundary separates a simulation space into a fluid space and a vacuum space, and the single-phase fluid inhabits the fluid space. The method further includes evaluating a plurality of indicator function defined on a quadrilateral grid for a velocity field, a pressure, and the plurality of fluid markers. The quadrilateral grid is formed by a plurality of points inside the fluid space and the vacuum space. The method also includes calculating surface tension at the moving fluid boundary through a level set method, solving a plurality of flow equations through a projection method for a surface location on the boundary, and representing the position of the moving fluid boundary at a second point in time by updating the positions of the fluid markers based on the plurality of velocity values. The fluid properties and the shape of the final pattern is then stored on a computer readable media.

摘要翻译： 公开了一种用于模拟具有多种流体性质的流体液滴的最终模式的计算机实现的方法。 该方法包括用多个流体标记物在第一时间点表示运动流体边界的位置，其中移动流体边界为单相流体提供边界。 运动流体界面将模拟空间分成流体空间和真空空间，单相流体居住在流体空间中。 该方法还包括评估用于速度场，压力和多个流体标记的在四边形网格上定义的多个指示符函数。 四边形网格由流体空间和真空空间内的多个点形成。 该方法还包括通过水平集方法计算移动流体边界处的表面张力，通过用于边界上的表面位置的投影方法求解多个流动方程，并且在第二点处表示运动流体边界的位置 基于多个速度值更新流体标记的位置。 然后将流体性质和最终图案的形状存储在计算机可读介质上。

公开(公告)号：US07813907B2

公开(公告)日：2010-10-12

申请号：US11777076

申请日：2007-07-12

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06G7/50

CPC分类号： G06F17/5018 ,  G06F2217/16

摘要： An embodiment of the present invention may be a system or method for simulating the flow of a single-phase fluid flow. Markers represent a moving fluid boundary of the single-phase fluid at a first point in time. The moving fluid boundary separates a simulation space into a fluid space and a non-fluid space. The single-phase fluid inhabits the fluid space. A signed distance function is evaluated at points surrounding the moving fluid boundary based upon markers. The curvature of the moving fluid boundary based on the signed distance function is evaluated near the markers in the non-fluid space. The curvature is not evaluated at the moving fluid boundary. The velocity of the fluid is calculated based upon the curvature of the level set in the non-fluid space. Update the position of the moving fluid boundary at a second point in time based on the velocity of the fluid.

摘要翻译： 本发明的实施例可以是用于模拟单相流体流的流动的系统或方法。 标记表示在第一时间点的单相流体的运动流体边界。 运动流体边界将模拟空间分成流体空间和非流体空间。 单相流体居住在流体空间。 基于标记在运动流体边界周围的点处评估带符号距离函数。 基于有符号距离函数的运动流体边界的曲率在非流体空间中的标记附近进行评估。 在运动流体边界处不评估曲率。 基于在非流体空间中设定的水平面的曲率来计算流体的速度。 基于流体的速度在第二时间点更新移动流体边界的位置。

公开(公告)号：US20100250203A1

公开(公告)日：2010-09-30

申请号：US12411810

申请日：2009-03-26

申请人： Jie Zhang ,  Jiun-Der Yu

发明人： Jie Zhang ,  Jiun-Der Yu

IPC分类号： G06F17/10 ,  G06F19/00

CPC分类号： G06F17/5018

摘要： The present invention is directed towards systems, methods and a computer-readable medium for simulating the evolution of a height of an evaporating droplet. The simulation includes a simulation space with boundary conditions. The simulation includes generating a height function that is representative of the height of the droplet at a first point in time at a plurality of points in the simulation space based upon a lubrication equation that is a differential function describing variation of the height function over time. The simulation determines the height function at a second point in time by finding an approximate solution that satisfies the lubrication equations and boundary conditions.

摘要翻译： 本发明涉及用于模拟蒸发液滴的高度演变的系统，方法和计算机可读介质。 模拟包括具有边界条件的模拟空间。 模拟包括基于作为描述高度函数随时间的变化的差分函数的润滑方程来生成代表在模拟空间中的多个点处的第一时间点处的液滴的高度的高度函数。 模拟通过找到满足润滑方程和边界条件的近似解决方案来确定第二时间点的高度函数。