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.

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 prior simulation of a velocity field and a temperature field is carried out, and snapshot data of the velocity field and that of the temperature field are collected during the prior simulation. Then principal component analysis on the collected snapshot data obtains velocity-field and temperature field dimension transformation matrixes, on the based on which the analysis models of the velocity field and temperature field having respective first degrees of freedom are converted into reduced degree-of-freedom models. Consequently, a simulation of the velocity field and the temperature field is carried out using models having respective reduced degrees of freedom (i.e., second degrees of freedom).

Abstract: The present invention relates to a method for airborne particle contamination control, comprising: creating a simulation by modeling a turbulent airflow in an environment that includes an equipment of interest; plotting a flow parameter on the simulation to visualize a flow field of air according to a current design; creating an injection point on the simulation for particles in the environment; determining a particle concentration of the particles; determining, by a computing device and from the particle concentration, whether the current design provides contamination control; in response to determining that the current design does not provide contamination control, creating a modified design; and providing the modified design for implementation. The present invention further relates to a computing device for airborne particle contamination control. The present invention still further relates to a non-transitory computer-readable medium for airborne particle contamination control.

Abstract: A fluid-flow simulation over a computer-generated surface is generated using a quasi-simultaneous technique. The simulation includes a fluid-flow mesh of inviscid and boundary-layer fluid cells. An initial fluid property for an inviscid fluid cell is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. An initial boundary-layer fluid property a boundary-layer fluid cell is determined using the initial fluid property and a viscous fluid simulation that simulates fluid viscous effects. An updated boundary-layer fluid property is determined for the boundary-layer fluid cell using the initial fluid property, initial boundary-layer fluid property, and an interaction law. The interaction law approximates the inviscid fluid simulation using a matrix of aerodynamic influence coefficients computed using a two-dimensional surface panel technique and a fluid-property vector.

Abstract: A prediction of whether a point on a computer-generated surface is adjacent to laminar or turbulent flow is made using a transition prediction technique. A plurality of boundary-layer properties at the point are obtained from a steady-state solution of a fluid flow in a region adjacent to the point. A plurality of instability modes are obtained, each defined by one or more mode parameters. A vector of regressor weights is obtained for the known instability growth rates in a training dataset. For each instability mode in the plurality of instability modes, a covariance vector is determined, which is the covariance of a predicted local growth rate with the known instability growth rates. Each covariance vector is used with the vector of regressor weights to determine a predicted local growth rate at the point. Based on the predicted local growth rates, an n-factor envelope at the point is determined.

Abstract: Methods of estimating human insulin absorption for use in an insulin pump are disclosed. A method includes prompting a user to select between a first insulin absorption model and a second insulin absorption model. The method also includes prompting a user to provide at least one model parameter. The method further includes forming an applied insulin absorption model from the selected insulin absorption model and the at least one model parameter.

Abstract: The present invention is directed to simulating evaporation of 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 solves equations, which may represent an approximation of evaporation of the droplet on a domain whose size is varying over time. The boundaries of saturation regions are tracked and updated over time, and the equations are iteratively solved with the new boundaries of the saturation regions.

Abstract: Methods and systems for modeling a reservoir system are described. The method includes constructing a reservoir model of a reservoir system. The reservoir model includes a reservoir and a plurality of wells. Also, one or more material balance groups are constructed with each material balance group having a portion of at least one of the plurality of wells, a portion of the reservoir, and at least one well management algorithm to track material balance within the respective material balance group. Then, fluid flow through the reservoir model is simulated based on the material balance groups by a simulator and the results are reported.

Abstract: A method includes identifying a simulated input flow stream associated with a chemical processing facility. The input flow stream includes an input component basis with multiple components having one or more properties that differ. The method also includes converting the input flow stream into a simulated output flow stream, which includes an output component basis that differs from the input component basis and comprises a single, active group of oil components and zero or more pure components. A pure component property of a pure component in the input flow stream could be combined with an oil component property of an oil component in the input flow stream. A pure component property of a pure component in the input flow stream could also be transferred to a pure component in the output flow stream without combination. An oil component property of an oil component in the input flow stream could further be mapped to an oil component property of the single output oil component.

Abstract: A system for optimizing a rate-of-penetration of a drill string includes a plurality of sensors in operable communication with the drill string; and a controller in operable communication with the plurality of sensors. The controller is connectable to a drill string motivator and capable of outputting a signal to the drill string motivator for optimizing the rate-of-penetration of the drill string, and the signal is configured to provide at least one of weight on bit, an amount of speed to rotate the drill string, an amount of torque to be applied to the drill string, and an amount of mudflow to the drill string.

Abstract: A method and system for modeling a three-dimensional smoke propagation animation system. The animation system can be configured to include a particle system manager, a compartment manager, a state variable manager, a three-dimensional space outline rendering module, and a three-dimensional smoke animation rendering module. The particle system manager creates and updates an existing particle system based on an input script and data from the state variable manager. The state variable manager loads smoke propagation data and provides smoke information to the particle system manager to create and update the particle system and space outline. The compartment manager creates a three-dimensional outline with respect to each compartment space from a compartment data and updates the status of the existing three-dimensional outlines based on information from the state variable manager. A final three-dimensional smoke propagation animation can then be rendered by the three-dimensional smoke animation rendering module.

Abstract: The invention concerns a method and a system for predicting the apparent flow conductivity of a heterogeneous medium. According to the invention, the following steps are implemented:—choosing a flow conductivity element type with a given set of characteristic parameters;—determining equations for said flow in said element type;—determining a network statistics for said given set of characteristic parameters; and—performing a stochastic homogenisation of said equations, for said network statistics. The invention applies more particularly to the predicting of the apparent viscosity of non-Newtonian fluids in a heterogeneous porous medium.

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: A catheterization device that may be designed by use of an adaptive genetic algorithm computational fluid dynamics approach, as well as other Global Optimization methods that may include simulated annealing, multistart and interval methods, continuous branch and bound methods, evolutionary algorithms, and tabu search and scatter search methods, as well as other available Global Optimization methods that is able to maximize/optimize the dwell time of an infused agent in the vicinity of a vascular lesion. The device may have an internal by-pass channel that allows the blood upstream of the lesion to continue its pulsatile flow through the vessel in the part of it occluded by the lesion, while simultaneously allowing the disbursement and maximal dwell time of an antithrombolytic or other diagnostic or therapeutic agent needed to treat the lesion. Different embodiments of the catheterization device are disclosed and indications for the use of these devices in the treatment of vascular diseases are discussed.

Abstract: A method for generating data indicative of lung function of a subject. The method comprises receiving first data which has been obtained from the subject, and inputting said first data to a model of lung function to generate said data indicative of lung function. The model of lung function comprises a first model component modelling transfer of gaseous oxygen from a gaseous space within the lung to biological material within the lung based upon quantitative data indicative of oxygen content in the inhaled gases and oxygen content in the biological material and a second model component modelling the transfer of oxygen from the lungs by oxygenation of venous blood to create oxygenated blood based upon quantitative data indicative of oxygen content in the venous blood.

Abstract: This invention presents a method to simulate how blood flows through the heart, using the reconstructed 4D motion of the endocardial surface of the left ventricle. The reconstruction, utilizing a computing device, captures the motion of the full 3D surfaces of the complex features, such as the papillary muscles and the ventricular trabeculae. By visualizing the flow field, the capability of viewing the interactions between the blood and the trabeculae in far more detail has been achieved.

Abstract: A method for black oil delumping is disclosed which comprises: converting a black oil wellstream into a compositional wellstream thereby enabling the composition and component molar rates of a production well in a black oil reservoir simulation to be reconstituted.

Abstract: The present invention relates generally to polyolefin production and to reducing volatile organic content (VOC) associated with the polyolefin. Techniques include the construction and implementation of a purge column model to calculate or estimate the VOC content in the polyolefin exiting the purge column. The techniques facilitate the design and operation of the polyolefin manufacturing process.

Abstract: A method for predicting aerodynamic impact for small appendages on aircraft, wherein the improvement comprises using an adaptable computational fluid dynamic model of airflow adjacent the appendage by isolating a patch surrounding the small appendage, measuring the load on the patch without the appendage in place and with the appendage in a place and subtracting the two for increasing computational accuracy of the load predictions for the small appendage to be able to measure the effect of the small appendage.

Abstract: A computerized tool for assessing conditions in a room includes a data extraction module for at least one of modeling and extracting environmental condition data of a room and a layout module for calculating a layout of the room from the environmental condition data. The computerized tool may also include a temperature module for at least one of modeling and extracting temperature data in the room and a thermal profile module for calculating a thermal profile of the room from the temperature data. The thermal profile may be overlayed on the calculated layout to thus enable the relationship between the thermal profile and the room layout to be visualized.

Abstract: A method and system for monitoring lens material residence within a conduit to improve the quality of molded products by reducing defects arising from entrapped lens material. According to the method a finite element mesh representative of a conduit is stored in a digital storage device. A simulation is run on a digital computer in which one type of lens material sequentially flows through the conduit in discrete batches temporal history of the batches within the conduit is tracked. The simulation is useful for analyzing material delivery conduits in injection molding and casting systems, for example, for lens manufacturing. According to the system, a digital storage device stores a finite element mesh representative of a conduit. A digital computer is coupled to the digital storage device for executing a set of instructions to run a simulation and track the temporal history of the batches within the conduit.

Abstract: The invention relates to a method of performing an oilfield operation of an oilfield having at least one wellsite, each wellsite having a wellbore penetrating a subterranean formation for extracting fluid from an underground reservoir therein. The method steps include obtaining a plurality of real-time parameters from a plurality of sensors disposed about the oilfield, wherein the plurality of real-time parameters comprise at least one selected from a group consisting of real-time flow rate data and real-time pressure data of the wellbore, configuring a gridless analytical simulator for simulating the underground reservoir based on the plurality of real-time parameters, generating real-time simulation results of the underground reservoir and the at least one wellsite in real-time using the gridless analytical simulator, and performing the oilfield operation based on the real-time simulation results.

Abstract: A system and method enable testing of a plurality of well-logging tools on a common, realistic earth model. To enable this testing, a model of a synthetic virtual geologic volume of interest is generated. From the synthetic virtual geologic volume of interest, a plurality of test properties are determined as a function of position within the virtual geologic volume of interest, wherein the test properties are measurable in actual geologic volumes of interest by a well-logging instruments. The individual test properties are then distributed to well-logging instrument developers with the model of the synthetic virtual geologic volume of interest to enable modeling and/or benchmarking of different well-logging instruments on the synthetic virtual geologic volume of interest and the ability to derive the original formation properties regardless of the method used (inversion, analytical solution, etc.).

Abstract: A method and system for patient-specific computational modeling and simulation for coupled hemodynamic analysis of cerebral vessels is disclosed. An anatomical model of a cerebral vessel is extracted from 3D medical image data. The anatomical model of the cerebral vessel includes an inner wall and an outer wall of the cerebral vessel. Blood flow in the cerebral vessel and deformation of the cerebral vessel wall are simulated using coupled computational fluid dynamics (CFD) and computational solid mechanics (CSM) simulations based on the anatomical model of the cerebral vessel.

Abstract: Methods for determining fluid rheology, the methods including determining a first discharged volume or weight of a fluid at a first time, determining at least a second discharged volume or weight of the fluid at a second time, and calculating fluid rheology based on the determined first and at least second discharged fluid volumes or weights at the first and second times.

Abstract: This present invention relates to a device for the measurement of the amount of oxygen in a gas mixture, or other gas with significantly different magnetic susceptibility than the background gas mixture, by the use of a suspended test body in a magnetic field that experiences force due to the magnetic susceptibility of the measurand gas. In order to enable a fast time response for the system with a change in oxygen concentration, a flow regime is presented which allows a fast sweep of the measurement volume combined with adjustable, balanced pressure drops via a flow balancing element (or elements) within the flow channels to independently minimise flow related uncertainties.

Abstract: Methods and systems for simulating and visualizing a flowing fluid when interacting with an intersecting object are provided. The simulating of falling fluid as a two-dimensional plan and rendering first and second depth buffers corresponding to current depth information for, respectively, a top surface and a bottom surface of an object is rendered. The values of first and second current simulation textures are rendered for the top and bottom surfaces of the object, where for a given frame each of the first and second current simulation texture values is set to either a corresponding value of the first and second current simulation texture values is set to either a corresponding value of each or second depth buffer or a corresponding, velocity-offset value of the previous frame's first or second simulation texture respectively. A visible fluid mesh is rendered in the two-dimensional plane based on the current simulation textures.

Abstract: Provided is an atmospheric flow simulation method for reducing a simulation error of wind speed caused due to an influence of different terrain resolutions using a numerical simulation; and, more particularly, an atmospheric flow simulation method which can compensate the wind speed of the atmospheric flow field using low-resolution terrain data by introducing an influence of different terrain resolutions as a terrain roughness and adding it to the terrain condition.

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 method for modelling a saturation dependant property in a sample by obtaining a spatially resolved measurement of fluid saturation in the sample; determining a measured value of a saturation dependant property from the measurement; fitting a model to the measured value to obtain a model value for the measured value; and optimising the fit of the model to the measured value by minimizing an error between the model and the measured value where the error is a distance between the measured value and the model value.

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 computing device includes a host application and an analytical tool. The host application is configured to present an interface to a user and allow the user to modify a component model. The component model includes a three-dimensional representation of at least a portion of a vehicle component and has a virtual housing at least partially defining an internal cavity. The analytical tool is configured to generate a solid body representing the internal cavity and calculate a volume of the solid body. The analytical tool is further configured to determine whether the internal cavity is bounded by the virtual housing of the component model.

Abstract: A method, system, and computer-readable storage medium are disclosed for simulating shallow viscoelastic flows. In one embodiment, input representing a deposition of a fluid in a shallow bed may be received. The fluid may have a set of fluid properties including a viscoelastic property. In one embodiment, a motion of the fluid in the shallow bed may be simulated. The motion may be simulated based on the set of fluid properties including the viscoelastic property. The simulation of the motion may comprise determining a viscoelastic force acting on the fluid based on the viscoelastic property.

Abstract: Fluid-flow simulation over a computer-generated aircraft surface is generated using inviscid and viscous simulations. A fluid-flow mesh of fluid cells is obtained. At least one inviscid fluid property for the fluid cells is determined using an inviscid fluid simulation that does not simulate fluid viscous effects. A set of intersecting fluid cells that intersects the aircraft surface are identified. One surface mesh polygon of the surface mesh is identified for each intersecting fluid cell. A boundary-layer prediction point for each identified surface mesh polygon is determined. At least one boundary-layer fluid property for each boundary-layer prediction point is determined using the at least one inviscid fluid property of the corresponding intersecting fluid cell and a boundary-layer simulation that simulates fluid viscous effects. At least one updated fluid property for at least one fluid cell is determined using the at least one boundary-layer fluid property and the inviscid fluid simulation.

Abstract: A method for performing oilfield operations for an oilfield. The method includes receiving modeling data and user instructions from a graphical user interface, selectively adjusting at least a portion of the modeling data to generate adjusted modeling data, obtaining an oilfield model based on the user instructions, instantiating first and second simulator instances based on the user instructions for performing a simulation using the adjusted modeling data and the oilfield model, passing interim simulation results between the first and second simulator instances for performing the simulation, displaying a result of the simulation using the graphical user interface, and performing the oilfield operations based on the result of the simulation. Further, the oilfield operations include a gas lift operation of the oilfield and the graphical user interface is configured to emulate the gas lift operation using a wellbore simulator.

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: A process for redesigning a distressed component, such as a turbine blade in a gas turbine engine, in which the distressed component is under thermal and structural loads, for improving the life of the component. The process includes obtaining the operating conditions of the machine in which the distressed component is used, finding the boundary conditions under which the distressed component operates, producing a 3-dimensional model of the distressed component with such detail that the distress levels are accurately represented on the model, subjecting the model to a series of technical analysis to predict a life for the component, reiterating the technical analysis until the levels of distress on the model accurately represent the distress that appears on the actual component, and then predicting a remaining life of the component based on the analysis, or redesigning the model and reanalyzing the model until a maximum life for the component has been found.

Abstract: This method for evaluating fluid flows in a heterogeneous medium, uses a hybrid grid constructed from a CPG type structured grid and from a radial grid. The first stage includes locally deforming a CPG type grid into a non-uniform Cartesian grid. These local grid cell deformations correspond to the change from a “CPG” frame to a “Cartesian” frame defined by the deformation. These deformations are then quantified, by a deformation function ?, and applied to the radial grid so as to shift to the “Cartesian” frame. The second stage includes locally correcting the definition of this deformation function around the radial grid, so that the radial grid, in the “Cartesian” frame, keeps its geometrical characteristics. A hybrid grid is then generated in the “Cartesian” frame from the two grids thus deformed. Finally, this hybrid grid is deformed to return to the “CPG” frame, using the inverse of deformation function ?.

Abstract: A simulation method for evaluating the aerodynamic performance of a golf club head uses arithmetic operations executed by a computer to analyze air flow around the head of a golf club when the club is swung, and thereby estimates the aerodynamic forces which act on the club head. Because the aerodynamic properties of a golf club head are evaluated without relying on experimental evaluations using physical prototypes, this method enables the efficient development of golf clubs.

Abstract: A client-server based system for building and executing flows (i.e., interconnected systems of algorithms). The client allows a user to build a flow specification and send the flow specification to the server. The server assembles the flow from the flow spec and executes the flow. A flow may be configured to analyze the impact (e.g., the financial impact) of a number of uncertainties associated with a plurality of assets. Uncertainty variables are used to characterize the uncertainties associated with the assets. An uncertainty variable associated with one asset may be functionally dependent on an uncertainty variable associated with another asset.

Abstract: According to at least one embodiment, a computer-implemented method for modeling cooling performance is provided. The method includes acts of receiving, by a computer, input data from a storage device, the input data including data related to physical structures within at least one equipment rack, selecting, based on the data related to physical structures, at least one first equation of a plurality of predetermined equations that describe pressure values in a plurality of spaces within the at least one equipment rack, determining pressure values in identified spaces of the plurality of spaces by solving the at least one first equation using the input data, determining airflow values between identified spaces by calculating a difference between the pressure values and storing, on the storage device, the airflow values as equipment rack airflow values within the at least one equipment rack.

Abstract: A machine, method and computer-usable medium for modeling an average flow of a substance through a composite material. Such a modeling includes an analytical calculation of an effective tensor Kå suitable for use with a variety of media. The analytical calculation corresponds to an approximation to the tensor K, and follows by first computing the diagonal values, and then identifying symmetries of the heterogeneity distribution. Additional calculations include determining the center of mass of the heterogeneous cell and its angle according to a defined Cartesian system, and utilizing this angle into a rotation formula to compute the off-diagonal values and determining its sign.

Abstract: One embodiment of the present invention sets forth a technique for efficiently simulating breaking waves in real-time. A two-dimensional shallow water height field simulation generates height and velocity information used to generate a wave line for each wave within the height field that satisfies criteria for overturning. For each overturning wave, a wave sheet is created from particles generated relative to points on the respective wave line. Each wave sheet may move separately from an underlying wave that gave rise to the wave sheet, allowing the wave sheet to fall and break, creating a realistic appearance. As a falling wave sheet collides with the underlying wave or water surface, free particles may be generated to simulation spray visible on a real breaking wave.