The control of the numerical divergence of the magnetic field in combination with the explicit/implicit time stepping scheme is also discussed.
It is found that for the fixed-grid method, numerical divergence occurs when the moving boundary moves across any of the neighboring nodes.
By using this method, the clearance between two screw rotors can be attained via the normal rack generation computation and then eliminated by proportionally distribute the normal compensation onto the measured rotor profiles to obtain the "ideal" rotor profiles to avoid numerical divergence in the following compressor performance computation.
Free surface and absorbing boundary conditions are employed for the top surface (z = 0 km) and the other three boundaries of the computation area, respectively; these conditions avoid numerical divergence and numerical dispersion.
However, it is computationally involved, makes the simulation process more time-consuming and sometimes leads to computational difficulties such as numerical oscillations, divergence in solution especially, when the process operates over a wide thermodynamic region and is constituted of many components.
In time, the numerical solution diverges from the true solution and this error due to divergence will become more dominant.
Next we discuss how both of these issues can be addressed in practice, the first by defining a form of mutual information that is naturally continuous and therefore does not require an ad hoc discretisation step and the other addresses the case where, in a naturally discrete system numerical artefacts resulting in divergences can be avoided.
When the divergence cleaning method introducing auxiliary scalar field ψ is applied to the base numerical schemes for imposing divergence-free condition to the magnetic field in a MHD equation, the approximations to derivatives of ψ require the neighboring points.
We also show that these numerical methods preserve the divergence.
In the applications of the method to general fluid simulations, the growth of small structures can be sufficiently reproduced, while the divergence of numerical solutions can be suppressed.
