Sean Vitousek and Oliver B. Fringer Stability and consistency of nonhydrostatic free-surface models using the semi-implicit θ-method International Journal for Numerical Methods in Fluids 72
This paper demonstrates unconditional stability of nonhydrostatic free-surface models by using the semi-implicit method. The form of numerical damping induced by the method is examined, and hydrostatic and nonhydrostatic models are found to exhibit significantly different damping behavior that is dependent on wavenumber. The numerical stability, damping, and order of accuracy of a numerical model can be determined analytically from eigenvalue analysis.
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