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The numerical time step is set to 0.1 km divided by the P-wave velocity.
When Δt is taken smaller, the error in the numerical time integration will be reduced.
For the numerical time integration in the SGM we use an embedded explicit RKM of order 4 ( 3 ).
The Newmark-β method is employed for the numerical time integration of the dynamic problem.
This formulation avoids the numerical time differentiation with respect to the observer time, which is computationally more efficient.
Thus it is not possible in the numerical time integration approach to find time instant when restoring force vector becomes a null vector.
Similar(43)
To simplify the numerical time-integration of the Vlasov equation, we adopt an operator splitting technique (e.g., Cheng and Knorr, 1976; Ghizzo et al., 2003).
It may then be necessary to control the error by coupling the numerical time-integration method with an adaptive time step control.
The propagation of capillary waves on material interfaces between two fluids imposes a strict constraint on the numerical time-step applied to solve the equations governing this problem and is directly associated with the stability of interfacial flow simulations.
The PAIRS formulation can consistently represent dynamics that are both fast and slow relative to the numerical time-step.
Numerical integration is performed using a semi-implicit scheme and the adaptive numerical time step required for stability ranges in the free-run between 3 and 11 days.
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