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searching for Governing equation 81 found (88 total)

Lax–Wendroff method (1,017 words) [view diff] exact match in snippet view article find links to article

of explicit time integration where the function that defines the governing equation is evaluated at the current time. Suppose one has an equation of the

Vortex shedding (842 words) [view diff] no match in snippet view article find links to article

In fluid dynamics, vortex shedding is an oscillating flow that takes place when a fluid such as air or water flows past a bluff (as opposed to streamlined)

Method of fundamental solutions (1,175 words) [view diff] exact match in snippet view article find links to article

method (BEM) which also uses the fundamental solution to satisfy the governing equation. Consequently, both the MFS and the BEM are of a boundary discretization

Flow distribution in manifolds (1,450 words) [view diff] exact match in snippet view article find links to article

loss is described using the Darcy–Weisbach equation. One obtains a governing equation of dividing flow as follows: where W {\displaystyle W\,} is the velocity

Kansa method (1,964 words) [view diff] exact match in snippet view article find links to article

kernel function, satisfy the governing equation and are often fundamental solution or general solution of governing equation. Consequently, only boundary

Annular fin (685 words) [view diff] exact match in snippet view article find links to article

heat exchange in liquid–gas heat exchanger systems. To derive the governing equation of an annular fin, certain assumptions must be made. The fin must

Finite volume method for unsteady flow (2,115 words) [view diff] exact match in snippet view article find links to article

absent in case of steady flows. The finite volume integration of the governing equation is carried out over a control volume and also over a finite time step

Kernel function for solving integral equation of surface radiation exchanges (1,330 words) [view diff] exact match in snippet view article find links to article

media. Because media neither absorb, emit, nor scatter radiation. Governing equation of heat transfer between two surface Ai and Aj q ( r i ) = ∫ λ = 0

Von Neumann stability analysis (1,427 words) [view diff] exact match in snippet view article find links to article

example of explicit time integration where the function that defines governing equation is evaluated at the current time. Later, the method was given a more

Hele-Shaw flow (1,327 words) [view diff] exact match in snippet view article find links to article

R e l ( h / l ) 2 ≪ 1. {\displaystyle Re_{l}(h/l)^{2}\ll 1.} The governing equation of Hele-Shaw flows is identical to that of the inviscid potential

Vorticity equation (1,693 words) [view diff] exact match in snippet view article find links to article

terms of vector calculus this is the curl of the flow velocity). The governing equation is: D ω D t = ∂ ω ∂ t + ( u ⋅ ∇ ) ω = ( ω ⋅ ∇ ) u − ω ( ∇ ⋅ u ) +

Singular boundary method (1,161 words) [view diff] exact match in snippet view article find links to article

problems with boundary nodes, in which a fundamental solution of the governing equation is explicitly known. The salient feature of the SBM is to overcome

Analytic element method (1,279 words) [view diff] exact match in snippet view article find links to article

domain, and the governing equation is satisfied everywhere exactly except along the border of the element, where the governing equation is not strictly

Bending of plates (8,494 words) [view diff] exact match in snippet view article find links to article

function. The bending of circular plates can be examined by solving the governing equation with appropriate boundary conditions. These solutions were first found

Astronautics (776 words) [view diff] exact match in snippet view article find links to article

Russian cosmist Konstantin Tsiolkovsky derived the rocket equation, the governing equation for a rocket-based propulsion, enabling computation of the final velocity

Kelvin's circulation theorem (1,031 words) [view diff] exact match in snippet view article find links to article

velocity vector, and ds is an element along the closed contour. The governing equation for an inviscid fluid with a conservative body force is D u D t =

SVFlux (418 words) [view diff] exact match in snippet view article find links to article

the flow regime through waste rock piles. Several forms of the flow governing equation are implemented in the software which provides greater flexibility

Kirchhoff–Love plate theory (4,012 words) [view diff] exact match in snippet view article find links to article

x 3 {\displaystyle x_{3}} direction is applied to the plate, the governing equation is M α β , α β = − q {\displaystyle M_{\alpha \beta ,\alpha \beta

Vibration of plates (3,653 words) [view diff] exact match in snippet view article find links to article

drum. For free vibrations, the external force q is zero, and the governing equation of an isotropic plate reduces to D ∇ 2 ∇ 2 w = − 2 ρ h w ¨ {\displaystyle

Forward osmosis (3,154 words) [view diff] exact match in snippet view article find links to article

concentration differential for the solute. It is clear from this governing equation that a solute will diffuse from an area of high concentration to an

Groundwater flow equation (1,998 words) [view diff] exact match in snippet view article find links to article

is also an unknown. This is a non-linear problem, even though the governing equation is linear. An alternative formulation of the groundwater flow equation

Plate theory (6,056 words) [view diff] exact match in snippet view article find links to article

conditions. For an isotropic, homogeneous plate under pure bending the governing equation is ∂ 4 w ∂ x 1 4 + 2 ∂ 4 w ∂ x 1 2 ∂ x 2 2 + ∂ 4 w ∂ x 2 4 = 0 where

Unified methods for computing incompressible and compressible flow (1,813 words) [view diff] exact match in snippet view article find links to article

{}T\right)+\Phi {}} One way to fix this problem is to change the governing equation; known as preconditioning; which can also increases the accuracy.

Heat generation in integrated circuits (263 words) [view diff] exact match in snippet view article find links to article

generation in integrated circuits and is an undesired effect. The governing equation of the physics of the problem to be analyzed is the heat diffusion

Navier–Stokes equations (15,692 words) [view diff] exact match in snippet view article find links to article

theorem of vector calculus). The first equation is a pressureless governing equation for the velocity, while the second equation for the pressure is a

Euler–Bernoulli beam theory (7,372 words) [view diff] exact match in snippet view article find links to article

approximated by a shear force applied at the free end. In that case the governing equation and boundary conditions are: E I d 4 w d x 4 = 0 w | x = 0 = 0 ; d

Electro Thermal Dynamic Stripping Process (1,520 words) [view diff] exact match in snippet view article find links to article

difference between ERH and ET-DSP is shown in the governing equations. The governing equation for electrical resistance heating (ERH) is given by, ρ c ¯ ( ∂ T ∂

Zeldovich–Taylor flow (1,990 words) [view diff] exact match in snippet view article find links to article

between the weak discontinuity and the detonation front. The second governing equation implies that at this point v ′ {\displaystyle v'} must be infinite

Pressure-correction method (868 words) [view diff] exact match in snippet view article find links to article

)\end{aligned}}} ( ∗ ) {\displaystyle (\ast )} then provides the governing equation for pressure computation. The idea of pressure-correction also exists

Kuramoto model (3,919 words) [view diff] exact match in snippet view article find links to article

oscillators is zero (i.e. ψ = 0 {\displaystyle \psi =0} ). Finally, the governing equation becomes d θ i d t = ω i − K r sin ⁡ ( θ i ) {\displaystyle {\frac

Finite volume method for one-dimensional steady state diffusion (1,348 words) [view diff] exact match in snippet view article find links to article

Discretization The crux of Finite volume method is to integrate the governing equation over each control volume. Nodal points are used to discretize equations

Boundary particle method (763 words) [view diff] exact match in snippet view article find links to article

Laplacian operators to eliminate a number of nonhomogeneous terms in the governing equation. The RC-MRM uses the recursive structures of the MRM interpolation

Ginzburg–Landau equation (1,117 words) [view diff] exact match in snippet view article find links to article

part of A {\displaystyle A} ). The Ginzburg–Landau equation is the governing equation for A {\displaystyle A} . The unstable modes can either be non-oscillatory

Taylor dispersion (2,761 words) [view diff] exact match in snippet view article find links to article

}}c_{1}+\epsilon c_{2}+\cdots } Substituting this series into the governing equation and collecting terms of different orders will lead to series of equations

Conformal map (2,511 words) [view diff] exact match in snippet view article find links to article

provide a useful check on the accuracy of numerical simulations of the governing equation. For example, in the case of very viscous free-surface flow around

Mixing (physics) (617 words) [view diff] exact match in snippet view article

diffusion as in spinodal decomposition. The convective portion of the governing equation contains fluid motion terms that are governed by the Navier–Stokes

Gold sink (1,090 words) [view diff] exact match in snippet view article find links to article

but essentially it's the same. A strong linked system would have a governing equation for NPC vendors to follow. NPCs would be restricted to craft with

Fractional calculus (7,500 words) [view diff] exact match in snippet view article find links to article

derivative for diffusion nonlocality. The time-space fractional diffusion governing equation can be written as ∂ α u ∂ t α = − K ( − Δ ) β u . {\displaystyle {\frac

Jeffery–Hamel flow (2,773 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F=a} at θ = 0 {\displaystyle \theta =0} , integration of governing equation gives θ = 3 2 ∫ F a d F ( a − F ) ( F − b ) ( F − c ) ) {\displaystyle

Self-similar solution (1,423 words) [view diff] exact match in snippet view article find links to article

self-similar solutions can be found for semi-infinite solids. The governing equation when heat conduction is the primary heat transfer mechanism is the

Liñán's diffusion flame theory (764 words) [view diff] exact match in snippet view article find links to article

and transport properties and with unity Lewis number reactants, the governing equation for the non-dimensional temperature field T ( y ) {\displaystyle T(y)}

Temporal discretization (883 words) [view diff] exact match in snippet view article find links to article

variable. The following equation is obtained when applied to the governing equation, including full discretized diffusion, convection, and source terms

Polymer physics (3,237 words) [view diff] exact match in snippet view article find links to article

chain were independent of the chain chemistry. What is more, the governing equation turns out to be a random walk, or diffusive walk, in space. Indeed

Moffatt eddies (818 words) [view diff] exact match in snippet view article find links to article

\theta }},\quad u_{\theta }=-{\frac {\partial \psi }{\partial r}}} the governing equation can be shown to be simply the biharmonic equation ∇ 4 ψ = 0 {\displaystyle

Numerical solution of the convection–diffusion equation (1,140 words) [view diff] exact match in snippet view article find links to article

convection–diffusion equation has to deal with the convection part of the governing equation in addition to diffusion. When the Péclet number (Pe) exceeds a critical

Cosmological perturbation theory (2,050 words) [view diff] exact match in snippet view article find links to article

{\displaystyle u\ll c~,} so we are in the non-relativistic regime. The first governing equation follows from matter conservation – the continuity equation ∂ ρ ∂ t

Homotopy analysis method (2,128 words) [view diff] exact match in snippet view article find links to article

the zeroth-order deformation equation, one can directly derive the governing equation of um(x) L [ u m ( x ) − χ m u m − 1 ( x ) ] = c 0 R m [ u 0 , u 1

Buckling (5,405 words) [view diff] exact match in snippet view article find links to article

loaded with a uniform compressive force per unit length, the derived governing equation can be stated by: ∂ 4 w ∂ x 4 + 2 ∂ 4 w ∂ x 2 ∂ y 2 + ∂ 4 w ∂ y 4

Taylor–Maccoll flow (1,657 words) [view diff] exact match in snippet view article find links to article

Substituting the above assumed form for the velocity field, into the governing equation, we obtain the general Taylor–Maccoll equation ( c 2 − f ′ 2 ) f ″

Precipitation hardening (5,467 words) [view diff] exact match in snippet view article find links to article

and r {\displaystyle r} is the second phase particle radius. This governing equation shows that for dislocation bowing the strength is inversely proportional

Hagen–Poiseuille equation (6,109 words) [view diff] exact match in snippet view article find links to article

cross-section u(y,z) satisfies the condition that u = 0 on the walls. The governing equation reduces to ∂ 2 u ∂ y 2 + ∂ 2 u ∂ z 2 = − G μ . {\displaystyle {\frac

Korteweg–De Vries equation (3,135 words) [view diff] exact match in snippet view article find links to article

several connections to physical problems. In addition to being the governing equation of the string in the Fermi–Pasta–Ulam–Tsingou problem in the continuum

Hydrodynamic stability (2,875 words) [view diff] exact match in snippet view article find links to article

disturbances of different wavelengths evolve independently. (A nonlinear governing equation will allow disturbances of different wavelengths to interact with

Meshfree methods (4,421 words) [view diff] exact match in snippet view article find links to article

(November 2008). "A gradient smoothing method (GSM) based on strong form governing equation for adaptive analysis of solid mechanics problems". Finite Elements

Standard step method (1,658 words) [view diff] exact match in snippet view article find links to article

Reach (yn<yc). The above surface water profiles are based on the governing equation for gradually varied flow (seen below) d y d x = S 0 − S f 1 − F n

Chandrasekhar's white dwarf equation (1,430 words) [view diff] exact match in snippet view article find links to article

\infty } or equivalently C → 0 {\displaystyle C\rightarrow 0} , the governing equation reduces to 1 η 2 d d η ( η 2 d φ d η ) = − φ 3 {\displaystyle {\frac

Dirac delta function (14,099 words) [view diff] exact match in snippet view article find links to article

describe transient loads or point loads acting on structures. The governing equation of a simple mass–spring system excited by a sudden force impulse I

Wind-turbine aerodynamics (5,153 words) [view diff] exact match in snippet view article find links to article

because of its robustness and simplicity to build and maintain. The governing equation for power extraction is: where P is the power, F is the force vector

Thermal simulations for integrated circuits (2,063 words) [view diff] exact match in snippet view article find links to article

{\displaystyle Q} is the generated heat per unit volume in [W·m−3]. The governing equation of the physics of the heat transfer problem relates the flux of heat

Electromigration (4,598 words) [view diff] exact match in snippet view article find links to article

Localized increase of current density is known as current crowding. A governing equation which describes the atom concentration evolution throughout some interconnect

Pressure measurement (9,894 words) [view diff] exact match in snippet view article find links to article

of pressure measurement instruments Physical phenomena Instrument Governing equation Limiting factors Practical pressure range Ideal accuracy Response

Live-cell imaging (3,419 words) [view diff] exact match in snippet view article find links to article

scattering theory. Both the X-ray CT and laser HT shares the same governing equation – Helmholtz equation, the wave equation for a monochromatic wavelength

Hybrid-propellant rocket (6,947 words) [view diff] exact match in snippet view article find links to article

fuel additives such as aluminium, lithium, or metal hydrides. The governing equation for hybrid rocket combustion shows that the regression rate is dependent

Sandwich theory (6,771 words) [view diff] exact match in snippet view article find links to article

homogeneous part of the governing equation exactly and for the particular part approximately. Recall that the governing equation for a sandwich beam is

Potential flow (5,220 words) [view diff] exact match in snippet view article find links to article

used to model irrotational compressible flow. The derivation of the governing equation for φ {\displaystyle \varphi } from Eulers equation is quite straightforward

Self-buckling (1,602 words) [view diff] exact match in snippet view article find links to article

x\\&=-qx{\mathrm {d} w \over \mathrm {d} x}\end{aligned}}} We get that the governing equation is the third order linear differential equation with a variable coefficient

Potential flow around a circular cylinder (2,580 words) [view diff] exact match in snippet view article find links to article

}}x\rightarrow -\infty \,,\end{aligned}}} where ε is the small parameter. The governing equation is ∇ 2 ψ = − ω ( ψ ) . {\displaystyle \nabla ^{2}\psi =-\omega (\psi

Moving heat source model for thin plates (1,513 words) [view diff] exact match in snippet view article find links to article

distributions, such as semi-ellipsoidal and double ellipsoidal. The governing equation for 3D transient heat transfer in a solid of semi-infinite dimensions

Holotomography (1,842 words) [view diff] exact match in snippet view article find links to article

scattering theory. Both the X-ray CT and laser HT shares the same governing equation – Helmholtz equation, the wave equation for a monochromatic wavelength

ZFK equation (1,861 words) [view diff] exact match in snippet view article find links to article

\Theta =\beta (1-\theta ).} Substituting these variables into the governing equation and collecting only the leading order terms, we obtain 2 d 2 Θ d η

Characteristic mode analysis (3,500 words) [view diff] exact match in snippet view article find links to article

{J}}\right)} is the one to be diagonalized via characteristic modes. The governing equation of the CM decomposition is X ( J n ) = λ n R ( J n ) ( 1 ) {\displaystyle

Degree of reaction (1,558 words) [view diff] exact match in snippet view article find links to article

different blade loading coefficient with the degree of reaction. The governing equation is written as R = 1 + Δ W 2 U 2 − C y 2 U {\displaystyle R=1+{\frac

Biomechanics of sprint running (2,337 words) [view diff] exact match in snippet view article find links to article

predicting a sprinter's velocity. This has yet to be integrated into the governing equation of sprinting. The kinetics of running describes the motion of a runner

Insect flight (8,499 words) [view diff] exact match in snippet view article find links to article

typically 1/300 and the wing frequency is about 10–103 Hz. Using the governing equation as the Navier-Stokes equation being subject to the no-slip boundary

Electrodynamic droplet deformation (2,155 words) [view diff] exact match in snippet view article find links to article

the droplet and outside the droplet as having no net charge, the governing equation for the electric stress sub-problem reduces to Gauss's law with a

Large eddy simulation (7,232 words) [view diff] exact match in snippet view article find links to article

scales, including filtered scales with unfiltered scales. The filtered governing equation for a passive scalar ϕ {\displaystyle \phi } , such as mixture fraction

Janzen–Rayleigh expansion (1,229 words) [view diff] exact match in snippet view article find links to article

_{0}+M^{2}\varphi _{1}+M^{4}\varphi _{2}+\cdots )} Substituting this governing equation and collecting terms of different orders of M a {\displaystyle Ma}

ANUGA Hydro (3,552 words) [view diff] exact match in snippet view article find links to article

size in order to capture detail where it is required. By solving the governing equation within each cell, water surface, bed elevation (hence depth) and horizontal

Frank-Kamenetskii theory (3,944 words) [view diff] exact match in snippet view article find links to article

{\displaystyle \theta } stays close to 1 {\displaystyle 1} into the governing equation and collect only the leading-order terms to find out δ c d ψ d ζ =

Bond graph (7,241 words) [view diff] exact match in snippet view article find links to article

Element type Bond Name Bond with causality Governing equation(s) Single-port elements Source/ Sink, S S e − − − ⇀ | {\displaystyle S_{e}\;{\overset {\textstyle

Lake metabolism (10,035 words) [view diff] exact match in snippet view article find links to article

fitting the high-frequency data to models of lake metabolism. The governing equation for estimating lake metabolism from a single sensor located in the