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Upwind Scheme
In computational physics, the term advection scheme refers to a class of numerical discretization methods for solving hyperbolic partial differential equations. In the so-called upwind schemes ''typically'', the 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 Richard Courant, 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Physics
Computational physics is the study and implementation of numerical analysis to solve problems in physics. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science. It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics — an area of study which supplements both theory and experiment. Overview In physics, different theories based on mathematical models provide very precise predictions on how systems behave. Unfortunately, it is often the case that solving the mathematical model for a particular system in order to produce a useful prediction is not feasible. This can occur, for instance, when the solution does not have a closed-form expression, or is too complicated. In such cases, numerical approximations are required. Computational physics is the subject that deals with these ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley & Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American Multinational corporation, multinational Publishing, publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, Academic journal, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, Technology, technical, and engineering subject areas, abandoning its literary interests. Wiley's son Joh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Godunov's Scheme
In numerical analysis and computational fluid dynamics, Godunov's scheme is a conservative numerical scheme, suggested by Sergei Godunov in 1959, for solving partial differential equations. One can think of this method as a conservative finite volume method which solves exact, or approximate Riemann problems at each inter-cell boundary. In its basic form, Godunov's method is first order accurate in both space and time, yet can be used as a base scheme for developing higher-order methods. Basic scheme Following the classical finite volume method framework, we seek to track a finite set of discrete unknowns, Q^_i = \frac \int_ ^ q(t^n, x)\, dx where the x_ = x_ + \left( i - 1/2 \right) \Delta x and t^n = n \Delta t form a discrete set of points for the hyperbolic problem: q_t + ( f( q ) )_x = 0, where the indices t and x indicate the derivatives in time and space, respectively. If we integrate the hyperbolic problem over a control volume _, x_ we obtain a method of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Upwind Differencing Scheme For Convection
The upwind differencing scheme is a method used in numerical methods in computational fluid dynamics for convection–diffusion problems. This scheme is specific for Peclet number greater than 2 or less than −2 Description By taking into account the direction of the Fluid dynamics, flow, the upwind differencing scheme overcomes that inability of the central differencing scheme. This scheme is developed for strong convective flows with suppressed diffusion effects. Also known as ‘Donor Cell’ Differencing Scheme, the convected value of property \phi at the cell face is adopted from the upstream node. It can be described by Steady convection-diffusion partial Differential Equation: \frac(\rho\phi)+\nabla \cdot (\rho \mathbf \phi)\,= \nabla \cdot (\Gamma \nabla \phi) + S_ Continuity equation: \left(\rho u A \right)_ - \left(\rho u A \right)_w = 0 \, where \rho is density, \Gamma is the diffusion coefficient, \mathbf is the velocity vector, \phi is the property to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
