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The difficulties include long simulation times, large computer memory requirements, and computational instability.
Steps taken to avoid computational instability are described.
It has been discovered that although central difference approximations are locally second-order accurate, they often suffer from computational instability and the resulting solutions exhibit non-physical oscillations.
The present model is constructed with fixed model parameters, so that it does not suffer from computational instability with the dynamic model.
It is shown that the derived form of the finite difference Jacobian prevents nonlinear computational instability and thereby permits long-term numerical integrations.
The discretization errors of metrics and Jacobian may cause serious computational instability and inaccuracy in numerical results, especially for high-order finite difference schemes.
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Its inherent lack of shock-capturing capability often results in spurious oscillations and computational instabilities.
The latter application required high spatial and temporal resolutions, with computational cells of 0.2 × 0.2 m and time steps as short as 0.6 s to avoid computational instabilities.
Computational instabilities inherent in the solution of inviscid, incompressible free-surface flow have been apparent for some time and different techniques have been used to overcome them.
Molecular surface (MS) contains non-smooth geometric singularities, such as cusps, tips and self-intersecting facets, which often lead to computational instabilities in molecular simulations, and violate the physical principle of surface free energy minimization.
All simulations ran to convergence with no computational instabilities.
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