THE EXISTENCE OF GLOBAL SOLUTIONS FOR THE FULL NAVIER-STOKES-KORTEWEG SYSTEM OF VAN DER WAALS GAS

The aim of this work is to prove the existence for the global solution of a nonisothermal or non-isentropic model of capillary compressible fluids derived by J.E.Dunn and J.Serrin(1985),in the case of van der Waals gas.Under the small initial perturbation,the proof of the global existence is based on an elementary energy method using the continuation argument of local solution.Moreover,the uniqueness of global solutions and large time behavior of the density are given.It is one of the main difficulties that the pressure p is not the increasing function of the densityρ.

Simplifi ed traditional bubble-motion equation and air-gun wavelet simulation based on a Van der Waals gas model

An air-gun source is the most commonly used excitation method in off shore seismic exploration.The excitation characteristics of an air-gun source aff ect seismic data quality.Far-field wavelet simulation is an important approach to study these characteristics.Compared to the measured wavelet,far-field wavelet simulation based on a traditional bubble-motion equation and ideal gas wavelet model has some disadvantages,such as a greater amplitude and smaller pulse attenuation velocity.Here,we start from the linear acoustic wave equation in the spherical coordinate system to deduce an improved,simpler bubble-motion equation and develop a Van der Waals gas wavelet model based on this equation.Unlike the existing methods,our method considers the high-pressure environment during actual excitation,heat exchange between the bubble and outside water,and change in the air fl ow at the muzzle.The results show that the far-fi eld wavelet simulated using this model is closer to the measured wavelet than that of the ideal gas wavelet model.At the same time,our method has a more succinct equation and a higher calculation effi ciency.

Centered Waves for the Two-dimensional Pseudo-Steady van der Waals Gas Satisfied Maxwell's Law Around a Sharp Corner

In this paper,the authors study the centered waves for the two-dimensional(2D for short)pseudo-steady supersonic flow with van der Waals gas satisfied Maxwell's law around a sharp corner.In view of the initial value of the specific volume and the properties of van der Waals gas,the centered waves at the sharp corner are constructed by classification.It is shown that the supersonic incoming flow turns the sharp corner by a centered simple wave or a centered simple wave with right-contact discontinuity or a composite wave(jump-fan,fan-jump or fan-jump-fan),or a combination of waves and constant state.Moreover,the critical angle of the sharp corner corresponding to the appearance of the vacuum phenomenon is obtained.

Simulating the signature produced by a single airgun under real gas conditions

Models that simulate the signature of single airguns form the basis for modeling the signals of airgun arrays. Most of the existing models assume that the air inside the produced bubble is ideal gas, which may lead to errors because of the high operating pressure of the airguns. In this study, we propose a model that precisely simulates the signals of single airguns by applying the Van der Waals equation based on the Ziolkowski algorithm. We also consider a thermodynamically open quasistatic system, the heat transition between water and gas, the throttling effect of the port and the bubble rise, and the effect of the sea surface. Modeling experiments show that(1) the energy of the source increases and the signal-tonoise ratio of the signature wavelet decreases with increasing seawater temperature,(2) the reflection coefficient of the sea surface under the actual state and depth of the source affects the notch caused by the surface reflection,(3) the computed signature with the proposed model is very close to the actual data, and(4) the proposed model accurately simulates the signature of single airguns.