Non-physical Phenomena Research Articles

K-e and Reynolds Stress Turbulence Model Comparisons for Two-Dimensional Injection Flows

Two-dimensional steady e owe elds generated by transverse injection into a supersonic e ow are numerically sim- ulated by integrating the Favre-averaged Navier -Stokes equations. Fine-scale turbulence effects are modeled with compressible K-≤ and second-order Reynolds-stress turbulence models. These numerical results are compared to numerical results of the Jones -Launder K-≤ model and experimental data. The credibility of the Reynolds-stress turbulence model relative to experimental data and other turbulence models is demonstrated by comparison of surface pressure proe les, boundary-layer separation location, jet plume height, and descriptions of recirculation zones and e ow structureupstream and downstream of the jet. Results indicate that theReynolds-stress turbulence model correctly predicts mean e ow conditions for low static pressure ratios. However, it is also observed that, as the static pressure ratio increases, the boundary-layer separation point moves farther upstream of the jet and pre- dictions become lessconsistent with experimental results. The K-≤ results are lessconsistentwith theexperimental resultsthanthoseassociatedwiththeReynolds-stressturbulencemodel.Finally,unlikethe K-≤results,nonphysical vorticity phenomena upstream of the jet plume are not observed in the Reynolds-stress turbulence model results. This phenomenon is shown to coincide with strong gradients in the wall functions used to compute πt.

An accurate and efficient scheme for wave propagation in linear viscoelastic media

The problem of wave propagation in a linear viscoelastic medium can be described mathematically as an exponential evolution operator of the form [Formula: see text] acting on a vector representing the initial conditions, where [Formula: see text] is a spatial operator matrix and t is the time variable. Techniques like finite difference, for instance, are based on a Taylor expansion of this evolution operator. We propose an optimal polynomial approximation of [Formula: see text] based on the powerful method of interpolation in the complex plane, in a domain which includes the eigenvalues of the matrix [Formula: see text]. The new time‐integration technique is implemented to solve the isotropic viscoacoustic equation of motion. The algorithm is tested for the problem of wave propagation in a homogeneous medium and compared with second‐order temporal differencing and the spectral Chebychev method. The algorithm solves efficiently, and with machine accuracy, the problem of seismic wave propagation with a dissipation mechanism in the sonic band, a characteristic of sedimentary rocks. The computational effort in forward modeling based on the new technique is half compared to that of temporal differencing when two‐digit precision is required. Accuracy is very important, particularly for propagating distances of several wavelengths, since the anelastic effects should not be confused with nonphysical phenomena, such as numerical dispersion in time‐stepping methods. Finally, we compute the seismic response to a single shot in a realistic geologic model which includes a gas‐cap zone in an anticlinal fold. The results clearly show the importance of the attenuation and dispersion effects for an appropriate interpretation of the seismic data. In particular, the gas‐cap response (a bright spot) suffers significant variations in amplitude, phase, and arrival time compared to the purely acoustic case.

Applicable Mathematics of Non-Physical Phenomena

Applicable Mathematics of Non-Physical Phenomena

Applicable Mathematics of Non-Physical Phenomena

Applicable Mathematics of Non-Physical Phenomena

Applicable Mathematics of Non-Physical Phenomena.

Applicable Mathematics of Non-Physical Phenomena.

Applicable Mathematics of Non-Physical Phenomena

"Applicable Mathematics of Non-Physical Phenomena." Journal of the Operational Research Society, 33(8), pp. 772–773

Applicable Mathematics of Non-Physical Phenomena

Applicable Mathematics of Non-Physical Phenomena

Applicable mathematics of non-physical phenomena

Applicable mathematics of non-physical phenomena