Abstract: The present invention comprises systems and methods for large eddy simulations using a scaled S-model, which may be scaled in both time and space. Prior large eddy simulation models require at least one special coefficient, which vary from case to case and need to be decided experimentally or empirically. In embodiments, the scaled S-model does not require any coefficient that varies case by case or needs to be decided experimentally or empirically.

Abstract: The present invention comprises systems and methods for large eddy simulations using a scaled S-model, which may be scaled in both time and space. Prior large eddy simulation models require at least one special coefficient, which vary from case to case and need to be decided experimentally or empirically. In embodiments, the scaled S-model does not require any coefficient that varies case by case or needs to be decided experimentally or empirically.

Abstract: A finite difference level set projection algorithm on multi-staged quadrilateral grids for simulation of a split liquid film between two rollers. From one stage to the next, the number of meshes in the vertical direction changes by a select factor to provide a good balance between resolution and number of meshes. Having fewer meshes at the nip (the smallest gap between the rollers), the multi-staged quadrilateral grid allows a much bigger time step and requires much less CPU time to reach the steady state.

Abstract: Systems and methods for simulating multi-phase incompressible immiscible fluid flows with non-uniform fluid properties in each of the phases are presented. In embodiments, finite-difference-based simulations enable more precise modeling of a two-phase system, such as by way of example and not limitation, an ink and air system. In embodiments, values of a property of one fluid in the fluid system exist in the region occupied by that fluid and not in the region occupied by the other fluid. To facilitate simulating the multi-phase fluid system, a set of artificial values of the property of the first fluid are assigned in the region of the second fluid thereby creating a “ghost region” of values.

Abstract: 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.

Abstract: 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.

Abstract: Systems and methods for simulating a droplet with a moving contact line are presented. In embodiments, a height profile of the droplet on a substrate may be simulated using a lubrication equation solution that includes an artificial fluid flux to account for fluid loss due to the contact line movement. Embodiments may include a solute convection/diffusion equation with slipping contact dynamics solution to simulate the shape of the solute deposit on a substrate. When the contact line moves, the convection-diffusion equation includes an artificial solute flux to conserve mass. In embodiments, the droplet may be modeled as being on a planar or on a non-planar surface.

Abstract: Systems and methods for simulating a droplet with a moving contact line are presented. In embodiments, a height profile of the droplet on a substrate may be simulated using a lubrication equation solution that includes an artificial fluid flux to account for fluid loss due to the contact line movement. Embodiments may include a solute convection/diffusion equation with slipping contact dynamics solution to simulate the shape of the solute deposit on a substrate. When the contact line moves, the convection-diffusion equation includes an artificial solute flux to conserve mass.

Abstract: A system and method for simulating a physical process in a simulation domain. Dividing the simulation domain into a first sub-domain and a gap region. The gap region defines a region of a specified width between a contact line of a droplet and the first sub-domain. Generating a mesh that represents the first sub-domain as a plurality of elements. The specification of each element includes an integer element number that represents an order of each element. The specified width of the gap region is on the order of half the width of an element in the first sub-domain adjoining the gap region divided by the integer element number. Using the finite element method and the mesh to calculate a state of the droplet at a first point in time. Using a plurality of evolution equations to calculate the state of the droplet at a second point in time.

Abstract: 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.

Abstract: A system and method for simulating the flow of a viscoelastic fluid through a channel. The simulation including a interface between a first fluid and a second fluid. The simulation including the formation of a droplet. The simulation includes solving equations governing the viscoelastic flow of the first fluid through the channel, including viscoelastic stress equations that include a normalized relaxation time greater than or equal to 5. The calculations simulate the flow of the first fluid through the channel. The simulation is stable over a period time in which a droplet is formed. The simulation including a level set function that describes the position of the interface between the first and second fluids, and the evolution of the level set function over time describes the shape and position of the interface.

Abstract: In updating particle information in a particulate fluid flow simulation, a 2D/3D collision scheme checks for the existence of any particle collision, and if so, calculates the collision force and torque on each colliding particle. Another 2D/3D collision scheme checks whether any particle is contacting a solid wall domain boundary, and if so, calculates the wall force and torque. Following collision, the particle location is updated according to the particle translational velocity, the collision force, and the domain wall reaction force. The particle orientation is updated according to the particle angular velocity, collision torque, and wall reaction torque.

Abstract: To update particle information in a particulate fluid flow simulation, the new positions of the particles are determined by the balance of all forces, and such forces are calculated by taking surface integrals along the particle-fluid interface to reduce CPU overhead. A 3-D collision scheme for ellipsoidal particles to determine whether two or more ellipsoidal particles in the fluid flow collide, and if so, determine the location of the collision point between two colliding particles is also disclosed. Other aspects involve predicting the new location and orientation of each of the colliding particles after collision.

Abstract: 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.

Abstract: Using a level set projection method improves simulation of particulate fluid flow. The level set values are used to identify the particle-fluid boundary. The level set function is also used to evaluate the particle linear and angular momenta for the rigid particle projection. Governing fluid equations are solved in the solution domain, including in the region occupied by the rigid solid particle. The obtained velocity is rendered incompressible in the solution domain by doing the projection. The incompressible velocity field in the region occupied by the particle is further corrected to represent rigid body motion. This technique is further extended to embrace a particle collision scheme in a particulate fluid flow simulation.

Abstract: Embodiments of the present invention provide a finite difference method, a finite element projection, and a non-finite-element implementation of the finite element projection for solving the incompressible continuity equation on quadrilateral grids to obtain pressure and fluid velocity. An exemplary apparatus for simulating and analyzing the flow of an incompressible fluid is also provided. More particularly, embodiments of the present invention provide a non-finite-element-method (non-FEM) to implement the finite element projection to obtain a linear system whose coefficient matrix has an average bandwidth of five, in comparison to the finite difference scheme using conventional finite element projection and implementation with a bandwidth of nine. A two-dimensional-five-point-stencil-based non-FEM discretization is formulated to enforce the incompressible continuity equation.

Abstract: A finite difference level set projection algorithm on multi-staged quadrilateral grids for simulation of a split liquid film between two rollers. From one stage to the next, the number of meshes in the vertical direction changes by a select factor to provide a good balance between resolution and number of meshes. Having fewer meshes at the nip (the smallest gap between the rollers), the multi-staged quadrilateral grid allows a much bigger time step and requires much less CPU time to reach the steady state.

Abstract: The present invention is directed to simulating a droplet of a fluid, and may be embodied in a system, method or a computer-readable medium encoded with instructions for a processor to carry out such simulation. The present invention may evaluate differential equations, which may represent an approximation of behavior over time of the droplet on a non-flat substrate. The behavior that the differential equations represent may include diffusion in the droplet and evaporation of the droplet.

Abstract: 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.

Abstract: A system and method for simulating a physical process in a simulation domain. Dividing the simulation domain into a first sub-domain and a gap region. The gap region defines a region of a specified width between a contact line of a droplet and the first sub-domain. Generating a mesh that represents the first sub-domain as a plurality of elements. The specification of each element includes an integer element number that represents an order of each element. The specified width of the gap region is on the order of half the width of an element in the first sub-domain adjoining the gap region divided by the integer element number. Using the finite element method and the mesh to calculate a state of the droplet at a first point in time. Using a plurality of evolution equations to calculate the state of the droplet at a second point in time.