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Here finite difference preconditioning with central differences leads to instability.
We solve this using a Gauss-Seidel method with central differences for the and.
The strategy for estimating the time step length is illustrated in Section 5. Examples compare the efficiency of AVI with central differences in Section 6.
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In order to compare the effects of different numerical integration algorithms, the stabilities and accuracies of STAH tests with Central Difference Method, Linear Acceleration Method and Chang Method are studied.
High-resolution upwind discretization scheme was used for solving convection terms with central difference schemes for diffusion terms.
The numerical scheme is a Crank-Nicolson implicit treatment of all terms of the equations with central differencing for space derivatives.
In this study, the Chebyshev spectral collocation method was used to discretize in η and finite differences with central differencing for derivatives was used to discretize in ξ.
For both phases, the convective terms have been discretized using the quadratic upstream interpolation for convective kinematics (QUICK) scheme, and diffusive and non-Newtonian terms with central differencing scheme.
It is observed that the improved finite difference scheme with second order central differences produces the natural frequencies and characteristic functions with a rapid convergence as compared to the conventional approach of using the first order central differences.
Conclusions concerning individual and collective effects of warping, pretwist, tension-torsion coupling and tennis racket effect (twist-rotational coupling) terms on the natural frequencies are drawn from numerical results obtained by using a finite difference procedure with first order central differences.
Contrary to standard finite-differences (FD) schemes, the Green's function formulation incorporates domain curvature effects by weighting the central differences with non-linear metrics, indeed, logarithmic distance for cylindrical and inverse distance for spherical coordinates.
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