Modeling of shear wave velocity in limestone by soft computing methods

The main purpose of current study is development of an intelligent model for estimation of shear wave velocity in limestone. Shear wave velocity is one of the most important rock dynamic parameters. Because rocks have complicated structure, direct determination of this parameter takes time, spends expenditure and requires accuracy. On the other hand, there are no precise equations for indirect determination of it; most of them are empirical. By using data sets of several dams of Iran and neuro-genetic, adaptive neuro-fuzzy inference system （ANFIS）, and gene expression programming （GEP） methods, models are rendered for prediction of shear wave velocity in limestone. Totally, 516 sets of data has been used for modeling. From these data sets, 413 ones have been utilized for building the intelligent model, and 103 have been used for their performance evaluation. Compressional wave velocity （Vp）, density （7） and porosity （.n）, were considered as input parameters. Respectively, the amount of R for neuro-genetic and ANFIS networks was 0.959 and 0.963. In addition, by using GEP, three equations are obtained; the best of them has 0.958R. ANFIS shows the best prediction results, whereas GEP indicates proper equations. Because these equations have accuracy, they could be used for prediction of shear wave velocity for limestone in the future.

LATTICE-BOLTZMANN MODEL FOR COMPRESSIBLE PERFECT GASES

We present an adaptive lattice Boltzmann model to simulate super- sonic flows.The particle velocities are determined by the mean velocity and internal energy.The adaptive nature of particle velocities permits the mean flow to have high Mach number.A particle potential energy is introduced so that the model is suitable for the perfect gas with arbitrary specific heat ratio.The Navier-Stokes equations are derived by the Chapman-Enskog method from the BGK Boltzmann equation. As preliminary tests,two kinds of simulations have been performed on hexagonal lattices.One is the one-dimensional simulation for sinusoidal velocity distributions. The velocity distributions are compared with the analytical solution and the mea- sured viscosity is compared with the theoretical values.The agreements are basically good.However,the discretion error may cause some non-isotropic effects.The other simulation is the 29 degree shock reflection.

Adaptive Lattice Boltzmann Model for Compressible Flows

A new lattice Boltzmann model for compressible flows is presented. The main difference from the standard lattice Boltzmann model is that the particle velocities are no longer constant, but vary with the mean velocity and internal energy. The adaptive nature of the particle velocities permits the mean flow to have a high Mach number. The introduction of a particle potential energy makes the model suitable for a perfect gas with arbitrary specific heat ratio. The Navier Stokes (N\|S) equations are derived by the Chapman Enskog method from the BGK Boltzmann equation. Two kinds of simulations have been carried out on the hexagonal lattice to test the proposed model. One is the Sod shock tube simulation. The other is a strong shock of Mach number 5 09 diffracting around a corner.