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Streamline diffusion, given an advection-diffusion equation, refers to all diffusion going on along the advection direction. [1]
In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is also a fluid. The properties that are carried with the advected substance are conserved properties such as energy. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy. Here the fluid may be any material that contains thermal energy, such as water or air. In general, any substance or conserved, extensive quantity can be advected by a fluid that can hold or contain the quantity or substance.
In probability theory and statistics, diffusion processes are a class of continuous-time Markov process with almost surely continuous sample paths. Brownian motion, reflected Brownian motion and Ornstein–Uhlenbeck processes are examples of diffusion processes.
The magnetic Reynolds number (Rm) is the magnetic analogue of the Reynolds number, a fundamental dimensionless group that occurs in magnetohydrodynamics. It gives an estimate of the relative effects of advection or induction of a magnetic field by the motion of a conducting medium, often a fluid, to magnetic diffusion. It is typically defined by:
Forced convection is a mechanism, or type of transport, in which fluid motion is generated by an external source. Alongside natural convection, thermal radiation, and thermal conduction it is one of the methods of heat transfer and allows significant amounts of heat energy to be transported very efficiently.
CLaMS is a modular chemistry transport model (CTM) system developed at Forschungszentrum Jülich, Germany. CLaMS was first described by McKenna et al. (2000a,b) and was expanded into three dimensions by Konopka et al. (2004). CLaMS has been employed in recent European field campaigns THESEO, EUPLEX, TROCCINOX SCOUT-O3, and RECONCILE with a focus on simulating ozone depletion and water vapour transport.
The Nernst–Planck equation is a conservation of mass equation used to describe the motion of a charged chemical species in a fluid medium. It extends Fick's law of diffusion for the case where the diffusing particles are also moved with respect to the fluid by electrostatic forces. It is named after Walther Nernst and Max Planck.
Flow visualization or flow visualisation in fluid dynamics is used to make the flow patterns visible, in order to get qualitative or quantitative information on them.
AUSM stands for Advection Upstream Splitting Method. It is developed as a numerical inviscid flux function for solving a general system of conservation equations. It is based on the upwind concept and was motivated to provide an alternative approach to other upwind methods, such as the Godunov method, flux difference splitting methods by Roe, and Solomon and Osher, flux vector splitting methods by Van Leer, and Steger and Warming. The AUSM first recognizes that the inviscid flux consist of two physically distinct parts, i.e., convective and pressure fluxes. The former is associated with the flow (advection) speed, while the latter with the acoustic speed; or respectively classified as the linear and nonlinear fields. Currently, the convective and pressure fluxes are formulated using the eigenvalues of the flux Jacobian matrices. The method was originally proposed by Liou and Steffen for the typical compressible aerodynamic flows, and later substantially improved in to yield a more accurate and robust version. To extend its capabilities, it has been further developed in for all speed-regimes and multiphase flow. Its variants have also been proposed.
The National Atmospheric Release Advisory Center (NARAC) is located at the University of California's Lawrence Livermore National Laboratory. It is a national support and resource center for planning, real-time assessment, emergency response, and detailed studies of incidents involving a wide variety of hazards, including nuclear, radiological, chemical, biological, and natural emissions.
Bram van Leer is Arthur B. Modine Emeritus Professor of aerospace engineering at the University of Michigan, in Ann Arbor. He specializes in Computational fluid dynamics (CFD), fluid dynamics, and numerical analysis. His most influential work lies in CFD, a field he helped modernize from 1970 onwards. An appraisal of his early work has been given by C. Hirsch (1979)
In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factored form. It is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. It is an example of an operator splitting method.
A complementarity problem is a type of mathematical optimization problem. It is the problem of optimizing a function of two vector variables subject to certain requirements (constraints) which include: that the inner product of the two vectors must equal zero, i.e. they are orthogonal. In particular for finite-dimensional real vector spaces this means that, if one has vectors X and Y with all nonnegative components, then for each pair of components xi and yi one of the pair must be zero, hence the name complementarity. e.g. X = (1, 0) and Y = (0, 2) are complementary, but X = (1, 1) and Y = (2, 0) are not. A complementarity problem is a special case of a variational inequality.
The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.
Diffusion is the net movement of anything generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical potential. It is possible to diffuse "uphill" from a region of lower concentration to a region of higher concentration, like in spinodal decomposition.
In chaos theory and fluid dynamics, chaotic mixing is a process by which flow tracers develop into complex fractals under the action of a fluid flow. The flow is characterized by an exponential growth of fluid filaments. Even very simple flows, such as the blinking vortex, or finitely resolved wind fields can generate exceptionally complex patterns from initially simple tracer fields.
Theodore Seio Chihara is a mathematician working on orthogonal polynomials who introduced Al-Salam–Chihara polynomials, Brenke–Chihara polynomials, and Chihara–Ismail polynomials. His brother is composer Paul Chihara.
In scientific visualization, texture advection is a family of methods to densely visualize vector fields or flows. Scientists can use the created images and animations to better understand these flows and reason about them. In comparison to techniques that visualise streamlines, streaklines, or timelines, methods of this family don't need any seed points and can produce a whole image at every step.
Truncated Newton methods, also known as Hessian-free optimization, are a family of optimization algorithms designed for optimizing non-linear functions with large numbers of independent variables. A truncated Newton method consists of repeated application of an iterative optimization algorithm to approximately solve Newton's equations, to determine an update to the function's parameters. The inner solver is truncated, i.e., run for only a limited number of iterations. It follows that, for truncated Newton methods to work, the inner solver needs to produce a good approximation in a finite number of iterations; conjugate gradient has been suggested and evaluated as a candidate inner loop. Another prerequisite is good preconditioning for the inner algorithm.
Christoph Schwab is a German applied mathematician, specializing in numerical analysis of partial differential equations and boundary integral equations.
In mathematics, leximin order is a total preorder on finite-dimensional vectors. A more accurate, but less common term is leximin preorder. The leximin order is particularly important in social choice theory and fair division.
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