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The implicit treatment of the constraint directions gives us improved stability over velocity based methods.
The implicit treatment of the acoustic part allows the time-step to be independent of the Mach number.
The non-Darcy flow implementation is based on an implicit treatment with relaxation of the non-Darcy control parameter.
The implicit treatment of the parallel-gradient terms permits the use of a relatively large time step.
The use of Krylov techniques allows the implicit treatment of the Coriolis term with low storage requirements.
An implicit treatment of both topography and friction source terms is also exhibited to improve the scheme while dealing with vanishing water heights.
The main difficulty in the implicit treatment of the nonlocal boundary value problems is the nonclassical form of the resulting matrix of the system of linear algebraic equations.
In the present study, an implicit treatment of interface conditions is presented to eliminate the interface conditions from the original system.
We present an implicit treatment of the pressure term in MPM to mitigate the numerical instabilities and small time steps in incompressible material problems.
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The effects of the semi-implicit treatment on linear waves in a cylinder are shown both through a detailed analysis and numerical tests.
When the semi-implicit treatment of the waves is used, the semi-implicit operator must be applied in the predictor step as well as in the corrector step.
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