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Asynchronous numerical scheme for modeling hyperbolic systems
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We present an asynchronous method for the explicit integration of multi-scale partial differential equations. This method is restricted by a local CFL condition rather than the traditional global CFL condition. First, we developed an upwind asynchronous forward Euler scheme for the transport equation and we proved that the asynchronous scheme is first order convergent. To improve the convergence rate of the asynchronous scheme, we derived an asynchronous Runge–Kutta 2 scheme from a standard explicit Runge–Kutta method.
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Title: Asynchronous numerical scheme for modeling hyperbolic systems
Description:
We present an asynchronous method for the explicit integration of multi-scale partial differential equations.
This method is restricted by a local CFL condition rather than the traditional global CFL condition.
First, we developed an upwind asynchronous forward Euler scheme for the transport equation and we proved that the asynchronous scheme is first order convergent.
To improve the convergence rate of the asynchronous scheme, we derived an asynchronous Runge–Kutta 2 scheme from a standard explicit Runge–Kutta method.
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