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  2. 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.

  3. FTCS scheme - Wikipedia

    en.wikipedia.org/wiki/FTCS_scheme

    It is a first-order method in time, explicit in time, and is conditionally stable when applied to the heat equation. When used as a method for advection equations, or more generally hyperbolic partial differential equations, it is unstable unless artificial viscosity is included. The abbreviation FTCS was first used by Patrick Roache.

  4. 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}}}

  5. Heat equation - Wikipedia

    en.wikipedia.org/wiki/Heat_equation

    Animated plot of the evolution of the temperature in a square metal plate as predicted by the heat equation. The height and redness indicate the temperature at each point. The initial state has a uniformly hot hoof-shaped region (red) surrounded by uniformly cold region (yellow). As time passes the heat diffuses into the cold region.

  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. Convection (heat transfer) - Wikipedia

    en.wikipedia.org/wiki/Convection_(Heat_transfer)

    In many real-life applications (e.g. heat losses at solar central receivers or cooling of photovoltaic panels), natural and forced convection occur at the same time (mixed convection). [4] Internal and external flow can also classify convection. Internal flow occurs when a fluid is enclosed by a solid boundary such as when flowing through a pipe.

  8. Flux limiter - Wikipedia

    en.wikipedia.org/wiki/Flux_limiter

    Admissible limiter region for second-order TVD schemes. Unless indicated to the contrary, the above limiter functions are second order TVD. This means that they are designed such that they pass through a certain region of the solution, known as the TVD region, in order to guarantee stability of the scheme.

  9. Combined forced and natural convection - Wikipedia

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

    The second case is when natural convection acts in the opposite way of the forced convection. Consider a fan forcing air upward over a cold plate. [5] In this case, the buoyant force of the cold air naturally causes it to fall, but the air being forced upward opposes this natural motion.