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  2. 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.

  3. Beam and Warming scheme - Wikipedia

    en.wikipedia.org/wiki/Beam_and_Warming_scheme

    In numerical mathematics, Beam and Warming scheme or Beam–Warming implicit scheme introduced in 1978 by Richard M. Beam and R. F. Warming, [1] [2] is a second order accurate implicit scheme, mainly used for solving non-linear hyperbolic equations. It is not used much nowadays.

  4. 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 ...

  5. Lax–Friedrichs method - Wikipedia

    en.wikipedia.org/wiki/Lax–Friedrichs_method

    This method is conservative and first order accurate, hence quite dissipative. It can, however be used as a building block for building high-order numerical schemes for solving hyperbolic partial differential equations, much like Euler time steps can be used as a building block for creating high-order numerical integrators for ordinary ...

  6. 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.

  7. 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.

  8. 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.

  9. MUSCL scheme - Wikipedia

    en.wikipedia.org/wiki/MUSCL_scheme

    Thus, the accuracy of a TVD discretization degrades to first order at local extrema, but tends to second order over smooth parts of the domain. The algorithm is straight forward to implement. Once a suitable scheme for F i + 1 / 2 ∗ {\displaystyle F_{i+1/2}^{*}} has been chosen, such as the Kurganov and Tadmor scheme (see below), the solution ...

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