Finite difference method

Abstract: The effect of constant suction/blowing on steady two-dimensional laminar forced flow about a uniform heat flux wedge is numerically analyzed. The nonlinear boundary-layer equations were transformed and the resulting differential equations were solved by an implicit finite difference scheme (Keller box method). Numerical results for the velocity distribution, the temperature distribution, the local skin friction coefficient and the local Nusselt number are presented for various values of Prandtl number Pr, pressure gradient parameterm and suction/blowing parameter ξ. In general, it has been found that the local skin friction coeffcient and the local Nusselt number increase owing to suction of fluid. This trend reversed for blowing of fluid. In addition to, as the blowing effect is strong enough, i.e. ξ≦−0.65, the flow separation only occurred in the case ofm=0.0.

Abstract: A three-dimensional unconditionally-stable locally-one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed and is proved unconditionally stable analytically. In it, the number of equations to be computed is the same as that with the conventional three-dimensional alternating direction implicit FDTD (ADI-FDTD) but with reduced arithmetic operations. The reduction in arithmetic operations leads to approximately 20% less computational time in comparisons with the ADI-FDTD method.

Abstract: SUMMARY We present a seismic waveform inversion methodology based on the Gauss–Newton method from pre-stack seismic data. The inversion employs a staggered-grid finite difference solution of the 2-D elastic wave equation in the time domain, allowing accurate simulation of all possible waves in elastic media. The partial derivatives for the Gauss–Newton method are obtained from the differential equation of the wave equation in terms of model parameters. The resulting wave equation and virtual sources from the reciprocity principle allow us to apply the Gauss–Newton method to seismic waveform inversion. The partial derivative wavefields are explicitly computed by convolution of forward wavefields propagated from each source with reciprocal wavefields from each receiver. The Gauss–Newton method for seismic waveform inversion was proposed in the 1980s but has rarely been studied. Extensive computational and memory requirements have been principal difficulties which are addressed in this work. We used different sizes of grids for the inversion, temporal windowing, approximation of virtual sources, and parallelizing computations. With numerical experiments, we show that the Gauss–Newton method has significantly higher resolving power and convergence rate over the gradient method, and demonstrate potential applications to real seismic data.