High resolution schemes for hyperbolic conservation laws

Maximum-entropy meshfree method for compressible and near-incompressible elasticity

Numerical integration errors and volumetric locking in the near-incompressible limit are two outstanding issues in Galerkin-based meshfree computations. In this paper, we present a modified Gaussian integration scheme on background cells for meshfree methods that alleviates errors in numerical integration and ensures patch test satisfaction to machine precision. Secondly, a lockingfree small-strain elasticity formulation for meshfree methods is proposed, which draws on developments in assumed strain methods and nodal integration techniques. In this study, maximum-entropy basis functions are used; however, the generality of our approach permits the use of any meshfree approximation. Various benchmark problems in two-dimensional compressible and near-incompressible small strain elasticity are presented to demonstrate the accuracy and optimal convergence in the energy norm of the maximum

/pdf/maximum-entropy-meshfree-method-for-compressible-and-near-16ichzmee2.pdf

Maximum-Entropy Meshfree Method for Compressible and Near-Incompressible Elasticity

The results on theoretical and numerical modeling of resonant piezoelectric devices in China are reviewed. Solutions to dynamic problems of the propagation of bulk acoustic waves (BAW), surface acoustic waves (SAW), vibrations of finite bodies, and analyses of specific devices are discussed. Results from both the ultrasonics community and mechanics researchers are included. It is hoped that the paper will be useful for the understanding, communication and collaboration between Chinese and foreign scholars. The paper may also be helpful for bridging the gap between ultrasonics and mechanics researchers on piezoelectricity research. The paper contains 316 references.

https://rd.springer.com/content/pdf/10.1007%2Fs11433-008-0188-1.pdf

Analytical and numerical modeling of resonant piezoelectric devices in China-A review

Physics-constrained deep learning for solving seepage equation

Well test analysis for polymer flooding is different from traditional well test analysis because of the non-Newtonian properties of underground flow and other mechanisms involved in polymer flooding. Few of the present works have proposed a numerical approach of pressure transient analysis which fully considers the non-Newtonian effect of real polymer solution and interprets the polymer rheology from details of pressure transient response. In this study, a two-phase four-component fully implicit numerical model incorporating shear thinning effect for polymer flooding based on PEBI (Perpendicular Bisection) grid is developed to study transient pressure responses in polymer flooding reservoirs. Parametric studies are conducted to quantify the effect of shear thinning and polymer concentration on the pressure transient response. Results show that shear thinning effect leads to obvious and characteristic nonsmoothness on pressure derivative curves, and the oscillation amplitude of the shear-thinning-induced nonsmoothness is related to the viscosity change decided by shear thinning effect and polymer concentration. Practical applications are carried out with shut-in data obtained in Daqing oil field, which validates our findings. The proposed method and the findings in this paper show significant importance for well test analysis for polymer flooding and the determination of the polymer in situ rheology.

https://downloads.hindawi.com/journals/jchem/2015/107625.pdf

Numerical Well Test Analysis for Polymer Flooding considering the Non-Newtonian Behavior

Numerical quadrature is an important ingredient of Galerkin meshless methods. A new numerical quadrature technique, partition of unity quadrature (PUQ), for Galerkin meshless methods was presented. The technique is based on finite covering and partition of unity. There is no need to decompose the physical domain into small cell. It possesses remarkable integration accuracy. Using Element-free Galerkin methods as example, Galerkin meshless methods based on PUQ were studied in detail. Meshing is always not required in the procedure of constitution of approximate function or numerical quadrature, so Galerkin meshless methods based on PUQ are “truly” meshless methods.

Galerkin meshless methods based on partition of unity quadrature

The shape-preserving quadratic spline interpolations introduced by Schumaker need users to adjust the slopes to satisfy monotone condition, We study carefully the reasons of requiring users to adjust the slopes and introduce a new method that does not need the users to adjust the slopes. The new method first finds out the intervals that do not satisfy monotone conditions, then chooses additional split points that are given suitable slopes to satisfying monotone conditions, at last constructs shape preserving polynomial interpolation based on the method of Schumaker. Examples are given to illustrate the efficiency of the interpolation.

An Improved Method on Shape Preserving Quadratic Spline Interpolation

A modified physics-based method is adopted to control the water waves, and the discretization of the governing 2D N-S equation is taken as the interaction between the variables in spaces, based on the idea of spreading though the neighboring regions. Meshing model of the water surface is based on a terrain LOD scheme called Tiled Quad-tree. With that the region of water surface can be extended unboundedly. A new controlling strategy is used, that the driving parameters of the water movement is taken separately, so it's easy to change parameters in real time while generating various water waves. Reflection and refraction of rays in water is simulated to improve the visual impression. It is shown that these methods can efficiently produce realistic movement of various water waves in real-time.

Lu Detang

Papers

Numerical Well Test Analysis for Polymer Flooding considering the Non-Newtonian Behavior

Galerkin meshless methods based on partition of unity quadrature

An Improved Method on Shape Preserving Quadratic Spline Interpolation

Realistic and real-time simulation of water

Implicit Surfaces Based on BP Neural Networks