On Conditions for L2-Dissipativity of an Explicit Finite-Difference Scheme for Linearized 2D and 3D Barotropic Gas Dynamics System of Equations with Regularizations

We deal with 2D and 3D barotropic gas dynamics system of equations with two viscous regularizations: so-called quasi-gas dynamics (QGD) and quasi-hydrodynamics (QHD) ones. The system is linearized on a constant solution with any velocity, and an explicit two-level in time and symmetric three-point in each spatial direction finite-difference scheme on the uniform rectangular mesh is considered for the linearized system. We study L2-dissipativity of solutions to the Cauchy problem for this scheme by the spectral method and present a criterion in the form of a matrix inequality containing symbols of symmetric matrices of convective and regularizing terms. Analyzing these inequality and matrices, we also derive explicit sufficient conditions and necessary conditions in the Courant-type form which are rather close to each other. For the QHD regularization, such conditions are derived for the first time in 2D and 3D cases, whereas, for the QGD regularization, they improve those that have recently been obtained. Explicit formulas for a scheme parameter that guarantee taking the maximal time step are given for these conditions. An important moment is a new choice of an “average” spatial mesh step ensuring the independence of the conditions from the ratios of the spatial mesh steps and, for the QGD regularization, from the Mach number as well.

Reverse Time Migration Based on the Pseudo-Space-Domain First-Order Velocity-Stress Acoustic Wave Equation

Reverse time migration (RTM) is an ideal seismic imaging method for complex structures. However, in conventional RTM based on rectangular mesh discretization, the medium interfaces are usually distorted. Besides, reflected waves generated by the two-way wave equation can cause artifacts during imaging. To overcome these problems, a high-order finite-difference (FD) scheme and stability condition for the pseudo-space-domain first-order velocity-stress acoustic wave equation were derived, and based on the staggered-grid FD scheme, the RTM of the pseudo-space-domain acoustic wave equation was implemented. Model experiments showed that the proposed RTM of the pseudo-space-domain acoustic wave equation could systematically avoid the interface distortion problem when the velocity interfaces were considered to compute the pseudo-space-domain intervals. Moreover, this method could effectively suppress the false scattering of dipping interfaces and reflections during wavefield extrapolation, thereby reducing migration artifacts on the profile and significantly improving the quality of migration imaging.

Methodical procedure of virtual manufacturing for analysing WAAM distortion along with experimental verification

This paper deals with a principal development of virtual manufacturing (VM) procedure to predict substrate distortion induced by Wire Arc Additive Manufacturing (WAAM) process. In this procedure, a hollow shape is designed in a thin-walled form made of stainless steel. The procedure starts with geometrical modelling of WAAM component consisting of twenty-five deposited layers with austenitic stainless-steel wire SS316L as feedstock and SS304 as substrate material. The hollow shape is modelled based on simplified rectangular mesh geometry with identical specimen dimensions during the experiment. Material model to be defined can be retrieved directly from a database or by conducting a basic experiment to obtain the evolution of material composition, characterized using Scanning Electron Microscopy (SEM) with Energy Dispersive X-ray (EDX) analysis, and generated using advanced modelling software JMATPRO for creating new properties including the flow curves. Further, a coupled thermomechanical solution is adopted, including phase-change phenomena defined in latent heat, whereby temperature history due to successive layer deposition is simulated by coupling the heat transfer and mechanical analysis. Transient thermal distribution is calibrated from an experiment obtained from thermocouple analysis at two reference measurement locations. New heat transfer coefficients are to be adjusted to reflect actual temperature change. As the following procedure prior to simulation execution, a sensitivity analysis was conducted to find the optimal number of elements or mesh size towards temperature distribution. The last procedure executes the thermomechanical numerical simulation and analysis the post-processing results. Based on all aspects in VM procedures and boundary conditions, WAAM distortion is verified using a robotic welding system equipped with a pulsed power source. The experimental substrate distortion is measured at various points before and after the process. It can be concluded based on the adjusted model and experimental verification that using nonlinear numerical computation, the prediction of substrate distortion with evolved material property of component yields far better result which has the relative error less than 11% in a comparison to database material which has 22%, almost doubled the inaccuracy.

SHP Assessment for a Run-of-River (RoR) Scheme Using a Rectangular Mesh Sweeping Approach (MSA) Based on GIS

This work proposed a base method for automated assessment of Small Hydro-Power (SHP) potential for a run-of-river (RoR) scheme using geographic information systems (GIS). The hydro-power potential (HP) was represented through a comprehensive methodology consisting of a structured raster database. A calibrated and validated hydrological model (Soil and Water Assessment Tool—SWAT) was used to estimate monthly streamflow as the Mesh Sweeping Approach (MSA) driver. The methodology was applied for the upper part of the Huazuntlan River Watershed in Los Tuxtlas Mountains, Mexico. The MSA divided the study area into a rectangular mesh. Then, at every location within the mesh, SHP was obtained. The main components of the MSA as a RoR scheme were the intake, the powerhouse, and the surge tank. The surge tank was located at cells where the hydro-power was calculated and used as a reference to later locate the intake and powerhouse by maximizing the discharge and head. SHP calculation was performed by sweeping under different values of the penstock’s length, and the headrace’s length. The maximum permissible lengths for these two variables represented potential hydro-power generation locations. Results showed that the headrace’s length represented the major contribution for hydro-power potential estimation. Additionally, values of 2000 m and 1500 m for the penstock and the headrace were considered potential thresholds as there is no significant increment in hydro-power after increasing any of these values. The availability of hydro-power on a raster representation has advantages for further hydro-power data analysis and processing.

Analytic formulas for complete and incomplete first-order TEM moments below ground in a conductive half-space

In the resistive limit, discrete conductors give rise to magnetic dipole fields. Magnetostatic modeling of time integrals, or moments, of transient electromagnetic (TEM) data therefore offers a means for fast approximate 3D modeling and inversion of TEM data sets. In our approximate inversion scheme, the net TEM moment response is represented as the combination of discrete conductor and uniform host responses. The inversion algorithm first estimates a homogeneous host conductivity, and then it subtracts the host response and fits the residual moment data by adjusting the conductivities of cells comprising a 3D rectangular mesh. To expedite calculation of the host response, we have derived analytic formulas for first-order TEM moments produced on and under the ground by a horizontal electric dipole on the surface of a homogeneous conductive half-space. We present analytic expressions for idealized all-time “complete” moments, or resistive limits, as well as for realizable finite-time “incomplete” moments. The moments produced by an arbitrary horizontal polygonal loop are determined by combining contributions from appropriately oriented electric dipoles. Downhole TEM moments computed with the new expressions reveal substantial differences between incomplete and complete moments when early time data are excluded and between step and impulse response incomplete moments. The role of the formulas in the first stage of our moment-based 3D inversion scheme is illustrated via analysis of downhole TEM data recorded at Santander, Peru. The host conductivity of best fit for early time B-field moments is 2.40 mS/m, consistent with apparent conductivities derived from ground TEM data recorded in the same area.

Modeling of Complex Geological Body and Computation of Geomagnetic Anomaly

Modeling plays an important role in engineering exploration. However, the traditional rectangular mesh cannot meet the requirement because the actual shape of the model may be very complex. Therefore, this paper chooses the Delaunay grid for modeling and applies this method to magnetic numerical simulation. At the same time, we make use of the advantages of the Delaunay grid and choose to use grid encryption technology in the boundary and complex area of the model. Then, the formula for calculating the magnetic anomaly of tetrahedron is deduced in detail, and the magnetic anomaly with surface fluctuation is calculated. For a synthetic data model, Delaunay grids with different densities are used to model and calculate surface anomalies. The two results are compared with the analytical solution of the model. The results show that the method has high accuracy. Then, the method is applied to the actual geological body modeling in the Jinchuan mining area. According to local needs, a three-dimensional model with inhomogeneous grid density is established and the surface magnetic field of the model is calculated. Finally, the simulation data are compared with the measured data. The results show that the Delaunay grid modeling method has strong applicability.