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QUICK Scheme
In computational fluid dynamics QUICK, which stands for Quadratic Upstream Interpolation for Convective Kinematics, is a higher- order differencing scheme that considers a three-point upstream weighted quadratic interpolation for the cell face values. In computational fluid dynamics there are many solution methods for solving the steady convection–diffusion equation. Some of the used methods are the central differencing scheme, upwind scheme, hybrid scheme, power law scheme and QUICK scheme. The QUICK scheme was presented by Brian P. Leonard – together with the QUICKEST (QUICK with Estimated Streaming Terms) scheme – in a 1979 paper. In order to find the cell face value a quadratic function passing through two bracketing or surrounding nodes and one node on the upstream side must be used. In central differencing scheme and second order upwind scheme the first order derivative is included and the second order derivative is ignored. These schemes are therefore considered seco ... [...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] |
Gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gradient of a function is non-zero at a point , the direction of the gradient is the direction in which the function increases most quickly from , and the magnitude of the gradient is the rate of increase in that direction, the greatest absolute directional derivative. Further, a point where the gradient is the zero vector is known as a stationary point. The gradient thus plays a fundamental role in optimization theory, where it is used to maximize a function by gradient ascent. In coordinate-free terms, the gradient of a function f(\bf) may be defined by: :df=\nabla f \cdot d\bf where ''df'' is the total infinitesimal change in ''f'' for an infinitesimal displacement d\bf, and is seen to be maximal when d\bf is in the direction of the gradi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite-volume Method
The finite volume method (FVM) is a method for representing and evaluating partial differential equations in the form of algebraic equations. In the finite volume method, volume integrals in a partial differential equation that contain a divergence term are converted to surface integrals, using the divergence theorem. These terms are then evaluated as fluxes at the surfaces of each finite volume. Because the flux entering a given volume is identical to that leaving the adjacent volume, these methods are conservative. Another advantage of the finite volume method is that it is easily formulated to allow for unstructured meshes. The method is used in many computational fluid dynamics packages. "Finite volume" refers to the small volume surrounding each node point on a mesh. Finite volume methods can be compared and contrasted with the finite difference methods, which approximate derivatives using nodal values, or finite element methods, which create local approximations of a soluti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Power Law Scheme
The power law scheme was first used by Suhas Patankar (1980). It helps in achieving approximate solutions in computational fluid dynamics (CFD) and it is used for giving a more accurate approximation to the one-dimensional exact solution when compared to other schemes in computational fluid dynamics (CFD). This scheme is based on the analytical solution of the convection diffusion equation. This scheme is also very effective in removing False diffusion error. Working The power-law scheme interpolates the face value of a variable, \phi\,, using the exact solution to a one-dimensional convection-diffusion equation given below: :\frac(\rho u \phi)\,= \frac\Gamma\frac In the above equation Diffusion Coefficient, \Gamma and both the density \rho and velocity remains constant u across the interval of integration. Integrating the equation, with Boundary Conditions, :\phi_0\,= \phi , _ :\phi_L\,= \phi , _ Variation of face value with distance, x is given by the expression, \frac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upwind Scheme
In computational physics, the term upwind scheme (sometimes advection scheme) ''typically'' refers to a class of numerical discretization methods for solving hyperbolic partial differential equations, in which so-called upstream variables are used to calculate the derivatives in a flow field. That is, derivatives are estimated using a set of data points biased to be more "upwind" of the query point, with respect to the direction of the flow. Historically, the origin of upwind methods can be traced back to the work of Courant, Isaacson, and Rees who proposed the CIR method. Model equation To illustrate the method, consider the following one-dimensional linear advection equation : \frac + a \frac = 0 which describes a wave propagating along the x-axis with a velocity a. This equation is also a mathematical model for one-dimensional linear advection. Consider a typical grid point i in the domain. In a one-dimensional domain, there are only two directions associated with point i – l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
False Diffusion
False diffusion is a type of error observed when the upwind scheme is used to approximate the convection term in convection–diffusion equations. The more accurate central difference scheme can be used for the convection term, but for grids with cell Peclet number more than 2, the central difference scheme is unstable and the simpler upwind scheme is often used. The resulting error from the upwind differencing scheme has a diffusion-like appearance in two- or three-dimensional co-ordinate systems and is referred as "false diffusion". False-diffusion errors in numerical solutions of convection-diffusion problems, in two- and three-dimensions, arise from the numerical approximations of the convection term in the conservation equations. Over the past 20 years many numerical techniques have been developed to solve convection-diffusion equations and none are problem-free, but false diffusion is one of the most serious problems and a major topic of controversy and confusion among num ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and at times conflated with the latter. Definition Maximum overshoot is defined in Katsuhiko Ogata's ''Discrete-time control systems'' as "the maximum peak value of the response curve measured from the desired response of the system." Control theory In control theory, overshoot refers to an output exceeding its final, steady-state value. For a step input, the ''percentage overshoot'' (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the ''overshoot'' is just the maximum value of the step response minus one. Also see the definition of ''overshoot'' in an electronics context. For second-order system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is the occurrence of a signal or function exceeding its target. Undershoot is the same phenomenon in the opposite direction. It arises especially in the step response of bandlimited systems such as low-pass filters. It is often followed by ringing, and at times conflated with the latter. Definition Maximum overshoot is defined in Katsuhiko Ogata's ''Discrete-time control systems'' as "the maximum peak value of the response curve measured from the desired response of the system." Control theory In control theory, overshoot refers to an output exceeding its final, steady-state value. For a step input, the ''percentage overshoot'' (PO) is the maximum value minus the step value divided by the step value. In the case of the unit step, the ''overshoot'' is just the maximum value of the step response minus one. Also see the definition of ''overshoot'' in an electronics context. For second-order system ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convective
Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow. Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see Convection cell). The convection may be due to gravitational, electromagnetic or fictitious body forces. Heat transfer by natural convection plays a role in the structure of Earth's atmosphere, its oceans, and its mantle. Discrete convective cells in the atmosphere can be identified by clouds, with stronger convection resulting in thunderstorms. Natural convection also plays a role in stellar physics. Convection is often categorised or des ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discretized
In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification). Discretization is also related to discrete mathematics, and is an important component of granular computing. In this context, ''discretization'' may also refer to modification of variable or category ''granularity'', as when multiple discrete variables are aggregated or multiple discrete categories fused. Whenever continuous data is discretized, there is always some amount of discretization error. The goal is to reduce the amount to a level considere ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
