Asymptotic-Preserving (AP) methods

Principles of AP methods

The concept of an Asymptotic-Preserving (AP) method makes a breakthrough in the numerical resolution of asymptotic perturbations of Partial-Differential Equations. The general principle of an Asymptotic-Preserving method is as follows. Consider a singular perturbation problem P^eps whose solutions converge to those of a limit problem P⁰ when the perturbation parameter 'eps' tends to zero. A scheme P^eps,h for problem P^eps with discretization parameters 'h' is called Asymptotic Preserving (or AP) if its stability requirement on h is independent of 'eps' and if its limit P^0,h when 'eps' tends to zero is consistent with the limit problem P⁰. This property is illustrated by the commutative diagram below:

AP schemes are extremely powerful tools as they permit the use of the same scheme to discretize a perturbation problem and its limit problem, with fixed discretization parameters.

Applications:

• Quasineutral limit in plasmas >>> read more

• Strongly anisotropic diffusion problems >>> read more

• Compressible fluids, multiphase flows and fluids with density constraints >>> read more

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