Consistency Analysis Of Smooth Paticle Hydrodynamics Method

Computer simulation has increasingly become a more and more important tool for solving practical and complicated problems in engineering and science.It plays avaluable role in providing tests and examinations for theories,offering in-sights to complex physics,and assisting in the interpretation and even the discovery of new phenomena. Grid or mesh based on numerical methods such as the finite difference methods (FDM)and the finite el-ement methods (FEM) have been widely applied to various areas of computational fluid dynamics (CFD) and computational solid mechanics (CSM). they are currently the dominant methods in numerical simulations for solving practical problems in engineering and science.Despite the great success, grid based numerical methods have some deficiencies,which limit their applications in many types of complicated problems. These methods also face the problem of grid generation, which have a direct impact on stability and accuracy of results. Hence, the use of grid/mesh can lead to various difficulties in dealing with problems with free surface deformable boundary,moving interface,and extremely large deformation and crack propagation. Over the past years, meshfree methods have been a major research focus, towards the next generation of more effec-tive computational methods for more complicated problems.It was first invented to solve astrophysical problems in three-dimensional open space.it has Has been extensively researched and extended and is applied with the material strength of the dynamic response and dynamic problems with large deformation.In theory, we discussed the continuous form of nuclear approximation and the discrete particle approximation, because these two methods constitute the basis of SPH method. We studied the regeneration of SPH approximation, and derive continuous and discrete form of consistency conditions, which provides a generalized way for the construction of a analytic smooth function, and play an important role in SPH form of the formula.discrete consistency conditions provide repair methods for the particles discontinuity in the traditional SPH method, thus, we forward some correction and improvement of methods used to repair conventional SPH consistency and improve its accuracy.For the shortcomings of SPH method, the methods of restoring paticle consistency and corrected smooth particle hydrodynamics is descussed which can improve the accuracy within problem area nd the border region. CSPM method does not change the traditional smooth function, because it can not be applied in the problem with discontinuous,thus,DSPH is proposed which is based on non-continuous regions on both sides of the Taylor series expansion the final nuclear particle approximation of Non-continuous function and its derivative consists of two parts, one part is similar to the CSPM, the other part is processed by non-continuous part of the amendment.Finally, to verify DSPH formula in the performance of a continuous phenomenon, first of all we use non-continuous function which is a piecewise continuous polynomialto approve the approximation accuracy and efficiency, then DSPH method is used to simulate the shock wave problem, The results showed that not only can solve the boundary DSPH defects, but also can simulate the possible function of field variables in the non-continuity. Similarly DSPH formula has also been very good results in the simulation of one-dimensional shock tube.