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  2. QUICK scheme - Wikipedia

    en.wikipedia.org/wiki/Quick_scheme

    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.

  3. 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 ...

  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. 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.

  6. Lax–Wendroff method - Wikipedia

    en.wikipedia.org/wiki/Lax–Wendroff_method

    What follows is the Richtmyer two-step Lax–Wendroff method. The first step in the Richtmyer two-step Lax–Wendroff method calculates values for f(u(x, t)) at half time steps, t n + 1/2 and half grid points, x i + 1/2.

  7. Hybrid difference scheme - Wikipedia

    en.wikipedia.org/wiki/Hybrid_difference_scheme

    Hybrid difference scheme is a method used in the numerical solution for convection-diffusion problems. These problems play important roles in computational fluid dynamics . It can be described by the general partial equation as follows: [ 6 ]

  8. Finite volume method for two dimensional diffusion problem

    en.wikipedia.org/wiki/Finite_volume_method_for...

    We obtain the distribution of the property i.e. a given two dimensional situation by writing discretized equations of the form of equation (3) at each grid node of the subdivided domain. At the boundaries where the temperature or fluxes are known the discretized equation are modified to incorporate the boundary conditions .

  9. Upwind differencing scheme for convection - Wikipedia

    en.wikipedia.org/wiki/Upwind_differencing_scheme...

    Lower case denotes the face and upper case denotes node; , , and refer to the "East," "West," and "Central" cell. (again, see Fig. 1 below). Defining variable F as convection mass flux and variable D as diffusion conductance = and =

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