Abstract: Computer based CAE models for simulating the physical behavior of disposable articles during manufacturing processes.

Abstract: A method includes initiating a first reservoir simulation on a first simulator for a first set of physical parameters of a first reservoir. The first reservoir simulator uses a first set of components for a compositional reservoir model. A second reservoir simulation is initiated on a second simulator. A network simulation is initiated on a network simulator to model a network for coupling the first reservoir and the second reservoir to a surface facility. The network simulator uses a second set of components for a compositional network model. The method further includes translating each of a first hydrocarbon fluid stream of the first reservoir simulator and a second hydrocarbon fluid stream of the second reservoir simulator to a common fluid model. Further, network balancing is initiated among the simulators at a corresponding point in each controller time step.

Abstract: A general, computational-mathematical modeling method for the solution of large, boundary-coupled transport problems involving the flow of mass, momentum, energy or subatomic particles is disclosed. The method employs a modeling processor that extracts a matrix operator equation (or set of equations) from a numerical transport code (NTC). The outputs of software codes, available for modeling physical problems governed by conservation laws in the form of differential equations, can be processed into closed-form operator equations with the method. Included is a numerical transport code functionalization (NTCF) model which can be determined numerically, based on a system of solutions of an NTC, evaluating outputs for a given set of inputs. The NTCF model is a linear or nonlinear, multi-variable operator equation or set of such equations. The NTCF model defines relationships between general, time-variable inputs and outputs, some known and some unknown, considered as boundary values.

Abstract: A particle behavior analysis system includes a calculation section that, regarding a decomposition portion decomposed in accordance with a decomposition method in a range to be analyzed, considers interaction force with another substance that acts on a particle and calculates behavior of the particle, while performing information communication with other devices; and an output processing section that switches output advisability of an analysis result obtained by the calculation section based on priority of the decomposition portion corresponding to the advisability of output processing of the analysis result.

Abstract: Embodiments include a system for determining cardiovascular information for a patient. The system may include at least one computer system configured to receive patient-specific data regarding a geometry of the patient's heart, and create a three-dimensional model representing at least a portion of the patient's heart based on the patient-specific data. The at least one computer system may be further configured to create a physics-based model relating to a blood flow characteristic of the patient's heart and determine a fractional flow reserve within the patient's heart based on the three-dimensional model and the physics-based model.

Abstract: Systems and methods for generating transfer functions associated with calculating local stresses on pipe elements by post processing forces and moments of a pipe model representing the piping system. The transfer functions are reusable and allow recalculation with different sets of user data without requiring regeneration of the transfer functions.

Abstract: A method for simulating the stretching and wiggling of liquids is provided. The complex phase-interface dynamics is effectively simulated by introducing the Eulerian vortex sheet method, which focuses on the vorticity at the interface and is extended to provide user control for the production of visual effects. The generated fluid flow creates complex surface details, such as thin and wiggling fluid sheets. To capture such high-frequency features efficiently, a denser grid is used for surface tracking in addition to coarser simulation grid. A filter, called the liquid-biased filter, is used to downsample the surface in the high-resolution grid into the coarse grid without unrealistic volume loss resulting from aliasing error.

Abstract: A system and method is provided for controlling the operation of notifying drivers of the fluid level. Primary and secondary keys are adapted to be associated to primary and secondary drivers. A key ignition device is positioned on the primary and secondary keys and generates driver status signals. A fluid level sensing device is operable to generate a fluid level signal indicative of the fluid level. A controller is coupled to the fluid level sensing device and the key ignition device. The controller determines whether the driver of the vehicle is the primary or secondary driver in response to the driver status signals. The controller notifies the primary or secondary driver of the fluid level in response to the fluid level signal. The controller selectively controls the operation of notifying the primary or the secondary driver based on whether the driver is the primary or secondary driver.

Abstract: A numerical analysis device executes: Step 102 of selecting a fluidic device model and a pipe model used for transient analysis from among fluidic device models and pipe models that are located between a start point and an end point set in the pipeline network model constructed as a 3D model of a pipeline network that includes fluidic devices and pipes; Step 104 of dividing the selected fluidic device model and pipe model into volume elements and into junction elements; Step 106 of deriving volumes of the respective volume elements obtained and pressure loss coefficients corresponding to the respective junction elements, based on the shape of the fluidic device model, a shape of the pipe model, and a physical quantities of the fluid, of associating the volumes with the volume elements, and of associating the pressure loss coefficients with the junction elements.

Abstract: One embodiment of the present invention sets forth a geometric multi-grid technique which enables accurate simulations of three dimensional (3D) fluid volumes. A model of the fluid to be simulated is represented using a cubic cell grid. The geometric multi-grid is generated to provide a hierarchy of increasingly coarser representations of the model that are used by a fluid pressure solver. During fluid simulations, the linear complementarity problem (LCP) resulting from discretizing the Poisson equation, subject to separating solid boundary conditions, is solved using the geometric multi-grid. Visual artifacts such as liquid sticking to a bounding surface are minimized and the computations performed to solve the LCP are simplified.

Abstract: One embodiment of the present invention sets forth an Eulerian fluid simulation technique which enables real-time simulations of large scale three dimensional fluid volumes that include free surface water. A hybrid grid representation composed of regular cubic cells on top of a layer of tall cells is used to reduce computation time. Water above an arbitrary terrain can be represented without consuming an excessive amount of memory and compute power, while focusing simulation effort on the area near the surface of the water to produce accurate results. Additionally, the grid representation may be optimized for a graphics processor implementation of the fluid solver.

Abstract: The invention is a method of modeling a hydrocarbon reservoir. A parameter value in a set of equations is adjusted so that the output of the equations accurately matches observed sediment erosion and deposition behavior for sediment sizes throughout a range of about 10 microns to about 10 centimeters. An initial condition of a sediment bed in the hydrocarbon reservoir is defined. The equations are applied to the initial condition, wherein outputs of the equations express how a fluid flow affects erosion and deposition of sediments at the initial condition. The initial condition is adjusted based on the equation outputs to create a subsequent sediment bed condition. The equations are re-applied to the subsequent sediment bed condition a pre-determined number of times. The subsequent sediment bed condition is re-adjusted after each re-application of the equations. The model of the hydrocarbon reservoir is created and outputted.

Abstract: A system generates a state diagram model in a graphical modeling system, where the state diagram model includes at least one state. A condition statement is associated with the at least one state, and defines a condition upon which one or more actions associated with the at least one state are executed.

Abstract: A method and apparatus for describing the statistical orientation distribution of nonspherical particles in a simulation of a process wherein a mold cavity is filled with a suspension that contains a large number of nonspherical particles. The method and apparatus may be applied to the analysis of an injection molding process for producing a fiber reinforced molded polymer component or of a metal casting process for producing a fiber reinforced metal product. The results of these analyses may be used to determine tension and warping aspects of the component, and to optimize the process conditions used in the production process.

Abstract: A method, program and computer system for changing scale of reservoir model permeabilities (for example a hydrocarbon reservoir) are provided. Mini-models of reservoirs are defined (S100) with a number of meshes and cells in these meshes. For each model mesh, a scaling of the permeability values KH of the meshes is carried out (S400-800) via a mean power formula KH?H??kHi?H relating the mesh permeability KH to the local permeabilities kH,i of the cells. According to the invention, the power coefficient ?H appearing therein is analytically modified, relatively to its expression given by the Noetinger-Haas relationship, in order to correct a non-ergodicity bias.

Abstract: A computer system analyzes data from giant subsurface hydrocarbon reservoirs which are organized into a number of component cells and simulates the conditions in the reservoirs based on determination of thermodynamic phase equilibrium using equation of state (EOS) modeling. The computer system takes the form of a heterogeneous (hybrid) computer environment which includes computer processor units (or CPU's) and graphical processing units (or GPU's). The system takes advantage of computational acceleration capabilities of the graphical processing units while utilizing the computer processing units for execution control, input/output of data and memory. Processing time requirements are reduced by more than an order of magnitude speed improvement over existing methods.

Abstract: A method for computing or estimating fractional, multi-phase/multi-component flow through a porous medium employing a 3D digital representation of a porous medium and a computational fluid dynamics method to calculate flow rates, pressures, saturations, internal velocity vectors and other flow parameters is described. The method employs a unique method of introducing non-wetting and wetting fluids into the pores at the inlet face of the 3D digital representation of a porous medium and a novel process control application to achieve quasi-steady state flow at low inlet concentrations of non-wetting fluid. In addition, the method of the present invention reduces the time required to simulate to complete the fluid dynamic calculations. The resulting values of flow of non-wetting fluid, wetting fluid, saturation, and other parameters are used to generate plots of relative permeability imbibition and drainage curves. Computerized systems and programs for performing the method are also provided.

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: Methods, systems, and computer readable media are provided for real-time oil and gas field production optimization using a proxy simulator. A base model of a reservoir, well, pipeline network, or processing system is established in one or more physical simulators. A decision management system is used to define control parameters, such as valve settings, for matching with observed data. A proxy model is used to fit the control parameters to outputs of the physical simulators, determine sensitivities of the control parameters, and compute correlations between the control parameters and output data from the simulators. Control parameters for which the sensitivities are below a threshold are eliminated. The decision management system validates control parameters which are output from the proxy model in the simulators. The proxy model may be used for predicting future control settings for the control parameters.

Abstract: Disclosed herein are improved systems and methods for right sizing grid models for performing, for example, reservoir simulations. Implementations in accordance with the present disclosure may begin with a relatively fine scale grid model. Successive coarsening and resampling operations may be repeated until one or more characteristics of the coarsened grid model begin to unacceptably diverge from those of the fine scale model. Similarly, successive coarsening and upscaling operations may be performed until one or more characteristics of the coarsened grid model begin to unacceptably diverge from those of the previously-coarsened grid model. The resulting coarsened grid model may be suitably sized for reservoir simulations.

Abstract: A system and method for evaluating cooling performance of equipment in a data center, the equipment including a plurality of equipment racks and at least one cooling provider.

Abstract: A method of determining the feasibility of a proposed structure analysis process is disclosed. The process involved the electron beam excitation of x-rays from a multi-layered structure. The method comprises generating predicted x-ray data represents the x-ray excitation response of the multi-layered structure according to one or more sets of process conditions. The x-ray data are generated using structure data defining the structure and composition of the layers. The effects upon the x-ray data of changes to the structure data are then analyzed in accordance with one or more predetermined feasibility criteria, so as to determine the feasibility of performing the proposed structure analysis process upon the multi-layered structure.

Abstract: The embodiments of the present invention provide novel techniques for visualizing parameter values, such as parameter values measured in an industrial measurement process. In particular, the disclosed embodiments provide visualization techniques for re-scaling a representation of a target parameter range with respect to an overall parameter range for a parameter value. Re-scaling the representation of the target parameter range effectively provides continuous dynamic zooming for the measured parameter value. This allows for better visualization as well as providing continuous feedback to an operator of the industrial measurement process regarding the current measured parameter value, thereby facilitating faster and more accurate operation of the industrial measurement process.

Abstract: Simulating a physical process includes storing, in a computer-accessible memory, state vectors for voxels, where the state vectors correspond to a model and include entries that correspond to particular momentum states of possible momentum states at a voxel. Interaction operations are performed on the state vectors. The interaction operations model interactions between elements of different momentum states according to the model. Move operations performed on the state vectors reflect movement of elements to new voxels according to the model. The model is adapted to simulate a high-Knudsen number flow that has a Knudsen number greater than 0.1.

Abstract: A method of assisting failure mode and effects analysis of a system having a plurality of components includes obtaining data associated with a component, or a group of components, of the system. The component or the group is associated with component type data or group type data, respectively, that includes data relating to at least one failure feature common to all components or groups, respectively, of that type. The component/group data and the component/group type data can then be stored and/or transferred for use in a failure mode and effects analysis of the system.

Abstract: Disclosed herein are improved coarsening and splitting techniques for preparing grids for performing simulations. In some implementations, methods in accordance with the present disclosure may include providing a grid having a plurality of grid pillars; and performing one or more splitting operations on at least a portion of the grid to increase a grid density within the portion of the grid, the plurality of grid pillars within the portion of the grid being forced to remain fixed in position during the one or more splitting operations.

Abstract: A method, system, and computer-readable storage medium are disclosed for simulating paint behavior. In one embodiment, input representing a deposition of a first type of paint and a second type of paint on a canvas may be received. The first type of paint has a first set of fluid properties, and the second type of paint has a second set of fluid properties differing from the first set. In one embodiment, a motion of the first type of paint and the second type of paint on the canvas may be simulated dependent on the respective sets of fluid properties. The simulated motion of the second type of paint differs from the simulated motion of the first type of paint. An effect of the deposition of the paint may be determined dependent on the simulation. An image representing the effect of the deposition of the paint may be displayed.

Abstract: A method for calculating a force acting on an interface between immiscible fluids in an SPH (Smoothed Particle Hydrodynamics) based fluid simulation includes: calculating a force caused by viscosities of the fluids; calculating a force caused by pressures of the fluids; calculating an external force applied to the fluids from outside; and calculating an interactive force caused by interaction between the fluids. The force acting on the interface between the immiscible fluids are obtained by using sum of the force caused by the viscosities, the force caused by the pressures, the external force and the interactive force. The interactive force is a surface tensional force calculated based on a pressure acting on the interface between the fluids.

Abstract: A method of performing production operations of an oilfield, including obtaining a sample of separator discharge fluid from a separator, performing gas chromatography on the separator discharge fluid to obtain gas molar composition, performing oil characterization on the separator discharge fluid to obtain oil density and oil molecular weight, performing a simulation of the separator based on the gas molar composition, the oil density, the oil molecular weight, and a gas oil ratio (GOR) of the separator discharge fluid to obtain a simulated composition of separator inlet fluid, and presenting the simulated composition of separator inlet fluid, when the difference between the actual composition of separator outlet fluid and the simulated composition of separator outlet fluid is less than a threshold value.

Abstract: In an EGR system, a quantity of exhaust gas passing through an EGR valve is computed by an EGR valve model simulating a behavior of the recirculated exhaust gas passing through the EGR valve. An exhaust gas quantity flowing into a cylinder is computed by an EGR-gas-delay model simulating a behavior of the exhaust gas passing through the EGR valve and the throttle valve and then flows into a cylinder. The EGR-gas-delay model includes a confluent-delay model simulating a behavior of EGR gas passing thorough the EGR valve and flowing into the intake passage upstream of the throttle valve; an intake-pipe-delay model simulating a behavior of EGR gas flowing in the intake passage and passing through the throttle valve; and an intake-manifold-delay model simulating a behavior of EGR gas which passes through the throttle valve and then flows into the intake passage downstream of the throttle valve.

Abstract: A hybrid computational fluid dynamics (CFD) approach for modeling a bounded domain, such as a data center, is disclosed. The CFD modeling approach divides the bounded domain into one or more viscous regions and one or more inviscid regions, and then performs a viscous domain solve for the viscous region(s) using a computational fluid dynamics model with turbulence equations (i.e., a turbulence model), and performs inviscid domain solve for the inviscid region(s) using a set of inviscid equations (or potential flow equations). After solving for the different regions, results of the viscous domain solve and the inviscid domain solve are provided as a model of the bounded domain.

Abstract: A system and method for automatic generation and usage of fluid flow loss coefficients for T-junctions is disclosed. In one embodiment, a list of possible T-junctions is created using given geometric and flow parameters. Further, journal files are created using the geometric and the flow parameters associated with each T-junction. The journal files associated with each T-junction are pre-processed for creating a volume mesh. Boundary conditions and material properties for the volume mesh associated with each T-junction are defined. Simulation is performed using the volume mesh, the boundary conditions and the material properties associated with each T-junction to determine flow characteristics. Fluid flow loss coefficients for each T-junction are computed using the flow characteristics.

Abstract: A three-dimensional fluid simulation method is disclosed wherein: a first mesh of a flow domain non-uniformly split with respect to each of three degrees of freedom is defined; a second mesh uniformly sprit with respect to only one of the three degrees of freedom but non-uniformly with respect to other two degrees is defined; an object model is set in the first mesh and a motion equation is formed and calculated to obtain fluid velocity; based on the fluid velocity, flow imbalance is computed for each cell; based on the flow imbalance, fluid pressure correction equation is formed; the flow imbalance is mapped onto the second mesh and the fluid pressure correction is computed; the fluid pressure correction is mapped onto the first mesh; and until the flow imbalance and motion equations are converged the computation is repeated.

Abstract: A method for simulating fluid flow includes: discretizing a space in which a fluid flows into a regular lattice; assuming that fluid particles repetitively move and collide in the lattice; deriving a univariate polynomial equation by comparing the n-th (n is a non-negative integer) order momentum of velocity between the Maxwell-Boltzmann distribution and the discretized Maxwell-Boltzmann distribution; calculating the weight coefficients corresponding to the discrete velocities of the fluid particles based on the univariate polynomial equation; and deriving a lattice Boltzmann model using the weight coefficients. A lattice Boltzmann model with superior stability and accuracy may be derived easily.

Abstract: A computer system and method of modeling a crystallization process includes representing a plurality of crystals in a solution by different subsets of the plurality, tracking increase of the respective characteristic length of each crystal group, and determining a crystal size distribution to output a model to a user. Each subset forms a respective crystal group characterized by group attributes of (i) a number of crystals and (ii) a characteristic length. Additionally, the system and method track generation of new crystal groups generated by seeding, nucleation and/or breakage.

Abstract: A bearing assembly comprising a frame; a rotating disc disposed in the frame, the rotating disc comprising a first set of inserts; and a fixed disc disposed in the frame, the fixed disc comprising a second set of inserts, the second set of inserts configured to interact with the first set of inserts, and a lip disposed adjacent the second set of inserts. Also, a bearing assembly comprising a frame; a rotating disc disposed in the frame, the rotating disc comprising a first set of inserts and at least one groove disposed axially above at least one of the inserts; and a fixed disc disposed in the frame, the fixed disc comprising a second set of inserts, the second set of inserts configured to interact with the first set of inserts.

Abstract: Methods for characterizing a sample of porous media using a measuring device along with a multipoint statistical (MPS) model. Retrieving a set of reflected measured data provided by the measuring device of a surface of the sample in order to produce a sample imaging log, wherein the retrieved set of measured data is communicated to a processor. Selecting depth-defined surface portions of the sample from the sample imaging log as a training image for inputting in the MPS model. Determining pattern based simulations from the training image using one of a pixel-based template which is applied to the training image. Constructing from the pattern based simulations a complete-sampling image log of surface portions of the sample. Repeat the above steps in order to construct three dimensional (3D) sample images from stacked successive pattern based simulations so as to construct at least one 3D model of the sample.

Abstract: A system and a method for analyzing and simulating a die swell and flow profile in polymer melt extrusion through a die. The system includes a mesh generator to generate a computational mesh; a pre-processor to obtain die parameters, boundary conditions, polymer melt parameters including rheological characterization and constitutive equations and to generate an input file; a simulator to receive the input file from the pre-processor and process the input data to simulate die swell; a mesh corrector means to analyze the die swell obtained from the simulator and to correct the motion of the computational mesh and polymer melt to converge the die swell; a post-processor to visualize the die swell and flow profiles for the polymer melt; and a database means to store the die swell corresponding to the die, mesh and polymer melt parameters.

Abstract: Provided is a method of designing a coaxial dual-tube type hot gas duct for a very-high-temperature reactor. When determining the outer diameter of an inner tube and the inner diameter of a pressure tube, both of which defines an annular part of the hot gas duct having a dual-tube shape, one selected from hydraulic heads, flow rates, and hydraulic heads of very-high-temperature helium gas flowing to a very-high-temperature region and low-temperature helium gas flowing to a low-temperature region is taken into consideration as well as is a relation of about heat balance model, so that it is possible to minimize flow induced vibrations caused by the flow of a fluid.

Abstract: In some embodiments, the Navier-Stokes matrix A may be developed on the fly using arrays of Dirichlet and von Neumann boundary conditions. As a result, the storage requirements are dramatically reduced and hardware accelerators or single instruction multiple data processors may be used to solve the Navier-Stokes equations.

Abstract: A method is provided for calculating flow performance characteristics of a body immersed in a fluid under a set of fluid flow conditions. The method comprises providing a geometrical description of a surface of the body and determining the set of fluid flow conditions. The set of fluid flow conditions includes a combination selected from the combination set consisting of angle of attack and leading edge stagnation point location, angle of attack and flow separation point location, and leading edge stagnation point location and flow separation point location. The method further comprises calculating a velocity flow field for the body using a critical point potential flow methodology and calculating flow performance characteristics.

Abstract: A devolatilization performance prediction apparatus for a solution devolatilization process using a twin-screw extruder is described. The devolatilization performance prediction apparatus determines a flow state of the solution in the twin-screw extruder, simulates the solution devolatilization process based on the flow state, and predicts a performance of a devolatilization process conducted with the twin screw extruder based on the simulation.

Abstract: A method of modeling a nonlinear hysteresis response of reservoir media involves obtaining measurements of core samples from the reservoir to generate a multitude of bounding curves representing primary drainage and primary imbibition characteristics of a reservoir, generating, using a processor, a plurality of constitutive equations based on the multitude of bounding curves and a multitude of material functions, the multitude of material functions determined based on material properties associated with the reservoir, generating, using the processor, an output in a form of capillary-pressure scanning curves based on the multitude of constitutive equations, the capillary-pressure scanning curves representing drainage and imbibition behaviors of the reservoir during an oilfield operation, and storing the output.

Abstract: Methods and computing systems for hydrocarbon exploration are disclosed. In one embodiment, an integrated petroleum systems model is generated for an area of interest, wherein the integrated petroleum systems model is based on: a geological outline, a set of satellite remote sensing data, and a set of airborne remote sensing data.

Abstract: A system for a flow simulation using Moving Particle Semi-implicit method, includes a processor representing a target incompressible fluid by a plurality of particles grouped according to different particle sizes depending on a spatial resolution required at positions in a simulation domain; temporarily updating a velocity and a position coordinate of each particle to a first velocity and a first position coordinate by implicitly calculating a variation of the velocity of each particle due to a viscosity of the incompressible fluid in each of a plurality of time steps having a predetermined time interval; and updating the first velocity and the first position coordinate to a second velocity and a second position coordinate of each particle at a next time step of each time step by calculating a velocity correction of the first velocity due to a pressure gradient of the incompressible fluid using the first velocity.

Abstract: Simulating a physical process includes storing, in a computer-accessible memory, state vectors for voxels, where the state vectors correspond to a model and include entries that correspond to particular momentum states of possible momentum states at a voxel. Interaction operations are performed on the state vectors. The interaction operations model interactions between elements of different momentum states according to the model. Move operations performed on the state vectors reflect movement of elements to new voxels according to the model. The model is adapted to simulate a high-Knudsen number flow that has a Knudsen number greater than 0.1.

Abstract: A method can include providing, in a geological domain, a conformal mesh, conformal to geological discontinuities of a geological model, that includes depositional domain coordinates associated with a depositional domain; providing, in the depositional domain, an initial, at least vertically structured, multidimensional grid that includes initial nodes that define grid cells; referencing the conformal mesh to identify a set of grid cells of the initial grid traversed by the geological discontinuities; splitting each of the grid cells in the set to form sub cells, each of the sub cells defined at least in part by one or more new nodes; and assigning geological domain coordinates associated with the geological domain to at least the new nodes to generate a final grid that includes the initial nodes, the new nodes and geological domain coordinates associated with the geological domain. Various other apparatuses, systems, methods, etc., are also disclosed.

Abstract: A system includes a computing device that includes a memory for storing a three-dimensional model that represents particles of a coarse fire simulation. The computing device also includes a graphics refiner for producing two-dimensional simulation segments from the three-dimensional model that represents particles of a coarse fire simulation. The separation distance between two or more of the two-dimensional simulation segments is based upon a level of spatial detail provided by the coarse fire simulation. The graphics refiner is configured to separately process the two-dimensional simulation segments to produce a detailed fire simulation.

Abstract: A system is provided. The system comprises a computer system comprising at least one processor, a thermodynamic state solver application, and a thermodynamic system solver application. When executed by the at least one processor, the thermodynamic state solver application computes a flash equilibrium state solution for each of a plurality of nodes in a thermodynamic network and determines for each of the plurality of nodes at least one sensitivity of a first thermodynamic property with reference to at least one second thermodynamic property. When executed by the at least one processor, the thermodynamic system solver computes a pressure at each of the nodes and flows between the nodes based at least in part on the sensitivities, wherein a result based on the pressures and flows is determined.

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.