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Tchamwa

First order explicit time integration method using the Tchamwa scheme.

References:

  1. 10.1016/j.advengsoft.2004.10.011
  2. 10.1002/nme.6574

Syntax

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integrator Tchamwa (1) [2]
# (1) int, unique integrator tag
# [2] double, spectral radius, \rho_\infty, default: 0.5

Theory

The integration relationship is given by the following.

\[ u_{n+1}=u_n+\Delta{}tv_n+\phi\Delta{}t^2a_n, \]
\[ v_{n+1}=v_n+\Delta{}ta_n, \]

where

\[ \phi=\dfrac{2}{1+\rho_\infty}. \]

The Tchamwa scheme has a first order accuracy and controllable numerical dissipation.

Remarks

If the model is linear, it is possible to indicate using

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set linear_system true

to speed up the computation.

Accuracy Analysis

tchamwa-0.0 tchamwa-0.5 tchamwa-1.0