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Viscous Vortex Domains Method
The viscous vortex domains (VVD) method is a mesh-free method of computational fluid dynamics for directly numerically solving 2D Navier-Stokes equations in Lagrange coordinates. It doesn't implement any turbulence model and free of arbitrary parameters. The main idea of this method is to present vorticity field with discrete regions (domains), which travel with diffusive velocity relatively to fluid and conserve their circulation. The same approach was used in Diffusion Velocity method of Ogami and Akamatsu, but VVD uses other discrete formulas Features The VVD method deals with viscous incompressible fluid. The viscosity and density of fluid is considered to be constant. Method can be extended for simulation of heat conductive fluid flows ( viscous vortex-heat domains method) The main features are: * Direct solving Navier-Stokes equations (DNS) * Calculation of the friction force at the body surfaces * Proper description of the boundary layers (even turbulent) * Infinite comp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meshfree Methods
In the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort. The absence of a mesh allows Lagrangian simulations, in which the nodes can move according to the velocity field. Motivation Numerical methods such as the finite difference method, finite-volume method, and finite element method were originally defined on meshes of data points. In such a mesh, each point has a fixed number of predefined neighbors, and this connectivity between neighbors can be used to define mathematical operators like the derivative. These operators are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layers
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric boun ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculation Of Body Diffusion Speed In VVD Method
A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 6 is a simple algorithmic calculation. Extracting the square root or the cube root of a number using mathematical models is a more complex algorithmic calculation. Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To ''calculate'' means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calculation Of Diffusion Speed In VVD Method
A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to the vague heuristics of calculating a strategy in a competition, or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 6 is a simple algorithmic calculation. Extracting the square root or the cube root of a number using mathematical models is a more complex algorithmic calculation. Statistical estimations of the likely election results from opinion polls also involve algorithmic calculations, but produces ranges of possibilities rather than exact answers. To ''calculate'' means to determine mathematically in the case of a number or amount, or in the case of an abstract problem to deduce the answer using ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Initial Conditions
In mathematics and particularly in dynamic systems, an initial condition, in some contexts called a seed value, is a value of an evolving variable at some point in time designated as the initial time (typically denoted ''t'' = 0). For a system of order ''k'' (the number of time lags in discrete time, or the order of the largest derivative in continuous time) and dimension ''n'' (that is, with ''n'' different evolving variables, which together can be denoted by an ''n''-dimensional coordinate vector), generally ''nk'' initial conditions are needed in order to trace the system's variables forward through time. In both differential equations in continuous time and difference equations in discrete time, initial conditions affect the value of the dynamic variables (state variables) at any future time. In continuous time, the problem of finding a closed form solution for the state variables as a function of time and of the initial conditions is called the initial value prob ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Conditions
In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. A large class of important boundary value problems are the Sturm–Liouville problems. The analysis of these problems involves the eigenfunctions of a differential operator. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kelvin's Circulation Theorem
In fluid mechanics, Kelvin's circulation theorem (named after William Thomson, 1st Baron Kelvin who published it in 1869) states:In a barotropic, ideal fluid with conservative body forces, the circulation around a closed curve (which encloses the same fluid elements) moving with the fluid remains constant with time. Stated mathematically: :\frac = 0 where \Gamma is the circulation around a material contour C(t). Stated more simply, this theorem says that if one observes a closed contour at one instant, and follows the contour over time (by following the motion of all of its fluid elements), the circulation over the two locations of this contour are equal. This theorem does not hold in cases with viscous stresses, nonconservative body forces (for example the Coriolis force) or non-barotropic pressure-density relations. Mathematical proof The circulation \Gamma around a closed material contour C(t) is defined by: :\Gamma(t) = \oint_C \boldsymbol \cdot \mathrm\boldsymbol where ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kinematic Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's axis than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Notations In Method Of Viscous Vortex Domains (VVD)
''Notations'' is a book that was edited and compiled by American avant-garde composer John Cage (1912–1992) with Alison Knowles and first published in 1969 by Something Else Press. The book is made up of a large collection of graphical scores, facsimiles of holographs, from the Foundation for Contemporary Performance Arts, with text by 269 composer A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and Defi ...s, which are presented in alphabetical order, with each score allotted equal space, and in which the editor has no more authority than the reader in assigning value to the work. The book includes the manuscript for the Beatles song "The Word" (song lyrics, but no musical notation) from the ''Rubber Soul'' album (1965). The text of the book was created using chance procedures to determ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direct Numerical Simulation
A direct numerical simulation (DNS)Here the origin of the term ''direct numerical simulation'' (see e.g. p. 385 in ) owes to the fact that, at that time, there were considered to be just two principal ways of getting ''theoretical'' results regarding turbulence, namely via turbulence theories (like the direct interaction approximation) and ''directly'' from solution of the Navier–Stokes equations. is a simulation in computational fluid dynamics (CFD) in which the Navier–Stokes equations are numerically solved without any turbulence model. This means that the whole range of spatial and temporal scales of the turbulence must be resolved. All the spatial scales of the turbulence must be resolved in the computational mesh, from the smallest dissipative scales (Kolmogorov microscales), up to the integral scale L, associated with the motions containing most of the kinetic energy. The Kolmogorov scale, \eta, is given by :\eta=(\nu^/\varepsilon)^ where \nu is the kinematic visco ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Fluid Dynamics
Computational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid ( liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems. Ongoing research yields software that improves the accuracy and speed of complex simulation scenarios such as transonic or turbulent flows. Initial validation of such software is typically performed using experimental apparatus such as wind tunnels. In addition, previously performed analytical or empirical analysis of a particular problem can be used for comparison. A final validation is often performed using full-scale testing, such as flight tests. CFD is applied to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
