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  2. Numerical solution of the convection–diffusion equation

    en.wikipedia.org/wiki/Numerical_solution_of_the...

    The convection–diffusion equation describes the flow of heat, particles, or other physical quantities in situations where there is both diffusion and convection or advection. For information about the equation, its derivation, and its conceptual importance and consequences, see the main article convection–diffusion equation. This article ...

  3. Crank–Nicolson method - Wikipedia

    en.wikipedia.org/wiki/Crank–Nicolson_method

    The Crank–Nicolson stencil for a 1D problem. The Crank–Nicolson method is based on the trapezoidal rule, giving second-order convergence in time.For linear equations, the trapezoidal rule is equivalent to the implicit midpoint method [citation needed] —the simplest example of a Gauss–Legendre implicit Runge–Kutta method—which also has the property of being a geometric integrator.

  4. Convection–diffusion equation - Wikipedia

    en.wikipedia.org/wiki/Convection–diffusion...

    The convection–diffusion equation can be derived in a straightforward way [4] from the continuity equation, which states that the rate of change for a scalar quantity in a differential control volume is given by flow and diffusion into and out of that part of the system along with any generation or consumption inside the control volume: + =, where j is the total flux and R is a net ...

  5. Upwind scheme - Wikipedia

    en.wikipedia.org/wiki/Upwind_scheme

    For the second-order upwind scheme, becomes the 3-point backward difference in equation and is defined as u x − = 3 u i n − 4 u i − 1 n + u i − 2 n 2 Δ x {\displaystyle u_{x}^{-}={\frac {3u_{i}^{n}-4u_{i-1}^{n}+u_{i-2}^{n}}{2\Delta x}}}

  6. False diffusion - Wikipedia

    en.wikipedia.org/wiki/False_diffusion

    Fig 1:Flow domain illustrating false diffusion. In figure 1, u = 2 and v = 2 m/s everywhere so the velocity field is uniform and perpendicular to the diagonal (XX). The boundary conditions for temperature on north and west wall is 100 ̊C and for east and south wall is 0 ̊C.

  7. Fourier number - Wikipedia

    en.wikipedia.org/wiki/Fourier_number

    A second parameter, the Biot number arises in nondimensionalization when convective boundary conditions are applied to the heat equation. [2] Together, the Fourier number and the Biot number determine the temperature response of a solid subjected to convective heating or cooling.

  8. Material derivative - Wikipedia

    en.wikipedia.org/wiki/Material_derivative

    The material derivative is defined for any tensor field y that is macroscopic, with the sense that it depends only on position and time coordinates, y = y(x, t): +, where ∇y is the covariant derivative of the tensor, and u(x, t) is the flow velocity.

  9. Combined forced and natural convection - Wikipedia

    en.wikipedia.org/wiki/Combined_forced_and...

    The first case is when natural convection aids forced convection. This is seen when the buoyant motion is in the same direction as the forced motion, thus accelerating the boundary layer and enhancing the heat transfer. [5] Transition to turbulence, however, can be delayed. [6] An example of this would be a fan blowing upward on a hot plate.