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

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

set linear_system true

to speed up the computation.

Accuracy Analysis

tchamwa-0.0

tchamwa-0.5

tchamwa-1.0