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Smoothed Particle Hydrodynamics
Smoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method (where the co-ordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as density. Method Advantages * By construction, SPH is a meshfree method, which makes it ideally suited to simulate problems dominated by complex boundary dynamics, like free surface flows, or large boundary displacement. * The lack of a mesh significantly simplifies the model implementation and its parallelization, even for many-core architectures. * SPH can be easily extended to a wide variety of fields, and hybridized with some other mod ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), density function, or density of an absolutely continuous random variable, is a Function (mathematics), function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be equal to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. More precisely, the PDF is used to specify the probability of the random variable falling ''within ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Order Of Magnitude
In a ratio scale based on powers of ten, the order of magnitude is a measure of the nearness of two figures. Two numbers are "within an order of magnitude" of each other if their ratio is between 1/10 and 10. In other words, the two numbers are within about a factor of 10 of each other. For example, 1 and 1.02 are within an order of magnitude. So are 1 and 2, 1 and 9, or 1 and 0.2. However, 1 and 15 are not within an order of magnitude, since their ratio is 15/1 = 15 > 10. The reciprocal ratio, 1/15, is less than 0.1, so the same result is obtained. Differences in order of magnitude can be measured on a base-10 logarithmic scale in " decades" (i.e., factors of ten). For example, there is one order of magnitude between 2 and 20, and two orders of magnitude between 2 and 200. Each division or multiplication by 10 is called an order of magnitude. This phrasing helps quickly express the difference in scale between 2 and 2,000,000: they differ by 6 orders of magnitude. Examples o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Journal Of Tribology
A journal, from the Old French ''journal'' (meaning "daily"), may refer to: *Bullet journal, a method of personal organization *Diary, a record of personal secretive thoughts and as open book to personal therapy or used to feel connected to oneself. A record of what happened over the course of a day or other period *Daybook, also known as a general journal, a daily record of financial transactions *Logbook, a record of events important to the operation of a vehicle, facility, or otherwise *Transaction log, a chronological record of data processing *Travel journal, a record of the traveller's experience during the course of their journey In publishing, ''journal'' can refer to various periodicals or serials: *Academic journal, an academic or scholarly periodical **Scientific journal, an academic journal focusing on science **Medical journal, an academic journal focusing on medicine **Law review, a professional journal focusing on legal interpretation *Magazine, non-academic or scho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Simulation
Fluid animation refers to computer graphics techniques for generating realistic animations of fluids such as water and smoke. Fluid animations are typically focused on emulating the qualitative visual behavior of a fluid, with less emphasis placed on rigorously correct physical results, although they often still rely on approximate solutions to the Euler equations (fluid dynamics), Euler equations or Navier–Stokes equations that govern real fluid physics. Fluid animation can be performed with different levels of complexity, ranging from time-consuming, high-quality animations for films, or visual effects, to simple and fast animations for real-time computer graphics, real-time animations like computer games. Relationship to computational fluid dynamics Fluid animation differs from computational fluid dynamics (CFD) in that fluid animation is used primarily for visual effects, whereas computational fluid dynamics is used to study the behavior of fluids in a scientifically rigo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Incompressible Flow
In fluid mechanics, or more generally continuum mechanics, incompressible flow is a flow in which the material density does not vary over time. Equivalently, the divergence of an incompressible flow velocity is zero. Under certain conditions, the flow of compressible fluids can be modelled as incompressible flow to a good approximation. Derivation The fundamental requirement for incompressible flow is that the density, \rho , is constant within a small element volume, ''dV'', which moves at the flow velocity u. Mathematically, this constraint implies that the material derivative (discussed below) of the density must vanish to ensure incompressible flow. Before introducing this constraint, we must apply the conservation of mass to generate the necessary relations. The mass is calculated by a volume integral of the density, \rho : : = . The conservation of mass requires that the time derivative of the mass inside a control volume be equal to the mass flux, J, acro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voxels
In computing, a voxel is a representation of a value on a three-dimensional regular grid, akin to the two-dimensional pixel. Voxels are frequently used in the visualization and analysis of medical and scientific data (e.g. geographic information systems (GIS)). Voxels also have technical and artistic applications in video games, largely originating with surface rendering in '' Outcast'' (1999). ''Minecraft'' (2011) makes use of an entirely voxelated world to allow for a fully destructable and constructable environment. Voxel art, of the sort used in ''Minecraft'' and elsewhere, is a style and format of 3D art analogous to pixel art. As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. Instead, rendering systems infer the position of a voxel based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). Some volumetric ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structured Grid
A regular grid is a tessellation of ''n''-dimensional Euclidean space by congruent parallelotopes (e.g. bricks). Its opposite is irregular grid. Grids of this type appear on graph paper and may be used in finite element analysis, finite volume methods, finite difference methods, and in general for discretization of parameter spaces. Since the derivatives of field variables can be conveniently expressed as finite differences, structured grids mainly appear in finite difference methods. Unstructured grids offer more flexibility than structured grids and hence are very useful in finite element and finite volume methods. Each cell in the grid can be addressed by index (i, j) in two dimensions or (i, j, k) in three dimensions, and each vertex has coordinates (i\cdot dx, j\cdot dy) in 2D or (i\cdot dx, j\cdot dy, k\cdot dz) in 3D for some real numbers ''dx'', ''dy'', and ''dz'' representing the grid spacing. Related grids A Cartesian grid is a special case where the elements are un ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Rendering
In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field. A typical 3D data set is a group of 2D slice images acquired by a CT, MRI, or MicroCT scanner. Usually these are acquired in a regular pattern (e.g., one slice for each millimeter of depth) and usually have a regular number of image pixels in a regular pattern. This is an example of a regular volumetric grid, with each volume element, or voxel represented by a single value that is obtained by sampling the immediate area surrounding the voxel. To render a 2D projection of the 3D data set, one first needs to define a camera in space relative to the volume. Also, one needs to define the opacity and color of every voxel. This is usually defined using an RGBA (for red, green, blue, alpha) transfer function that defines the RGBA value for every possible voxel value. For example, a volu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Cubes
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional discrete scalar field (the elements of which are sometimes called voxels). The applications of this algorithm are mainly concerned with medical visualizations such as CT and MRI scan data images, and special effects or 3-D modelling with what is usually called metaballs or other metasurfaces. The marching cubes algorithm is meant to be used for 3-D; the 2-D version of this algorithm is called the marching squares algorithm. History The algorithm was developed by William E. Lorensen (1946-2019) and Harvey E. Cline as a result of their research for General Electric General Electric Company (GE) was an American Multinational corporation, multinational Conglomerate (company), conglomerate founded in 1892, incorporated in the New York (state), state of New York and headquartere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metaballs
In computer graphics, metaballs, also known as blobby objects, are organic-looking ''n''-dimensional isosurfaces, characterised by their ability to meld together when in close proximity to create single, contiguous objects. In solid modelling, polygon meshes are commonly used. In certain instances, however, metaballs are superior. A metaball's "blobby" appearance makes them versatile tools, often used to model organic objects and also to create base meshes for sculpting. The technique for rendering metaballs was invented by Jim Blinn in the early 1980s to model atom interactions for Carl Sagan's 1980 TV series ''Cosmos''. It is also referred to colloquially as the "jelly effect" in the motion and UX design community, commonly appearing in UI elements such as navigations and buttons. Metaball behavior corresponds to mitosis in cell biology, where chromosomes generate identical copies of themselves through cell division. Definition Each metaball is defined as a funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Motion
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale geophysical flows involving oceans/atmosphere and modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
