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Under-Relaxation

Under-Relaxation reduces solution oscillations and helps to keep the computation stable. After each iteration, at each cell, a new value for variable $ \color{white} U$ in cell $ \color{white} i$ is then updated using following equation:
4 3
where $ \color{white} \alpha$ is under-relaxation factor. The choice $ \color{white} \alpha$ $ \color{white} =$ $ \color{white} 1$ corresponds to no under-relaxation. The choice $ \color{white} \alpha$ $ \color{white} <$ $ \color{white} 1$ is under-relaxation. This may slow down speed of convergence but increases the stability of the computation, i.e. it decreases the possibility of divergence or oscillations in the solution. For more details see e.g. [3].

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