Numerical Simulation Study Of Explosion And Shock Problem Based On Pseudo Arc-length Algorithm

Numerical simulation of explosion and shock phenomena has very important theoretical significance and engineering practical value.The key problem of numerical simulation of explosion and shock phenomena is reducing the singularity of strong impact discontinuity and capturing the wave-front of explosive shock wave efficient accurately.Based on the pseudo arc-length algorithm,the numerical problems of explosion and shock problem are studied.The main contents of this thesis are described as follows:(1)By introducing pseudo arc-length parameter,the original physical model becomes a coupling system of governing equations and adaptive mesh equations.The governing equations are discrete by finite volume algorithm,which can deal with the large distorted mesh.Adaptive mesh equations are discrete by Gaussian iteration.Then amount of grid movements and inflow and outflow of gird values are computed to obtain the conservation interpolation of grid values.Finally the discretization of pseudo arc-length numerical algorithm is realized.(2)By introducing the Newton iteration method,the limit differential dynamic system of hyperbolic conservation equation and adaptive mesh equations is analyzed.The nonlinear problem is converted into linear problem,and then linear problem is analyzed by regularization reduction method.Finally the stability theory of pseudo arc-length numerical algorithm is established.(3)Since the grids are distorted,the numerical algorithm is non-convergence in three-dimensional space.Then the combination of block reconstruction and integral calculation strategy is adopted in the algorithm design process: the hexahedron units divided into multiple tri-prisms respectively in the reconstruction of physical values;the whole area calculation is taken in the grid movement and control equations evolutionary process.Finally the pseudo arc-length numerical algorithm for explosion and shock problem is obtained.(4)By modifying the inhomogeneous term of the governing equations,the governing equations meet a known solution(usually a periodic function).Take the known solution into the governing equations,and then pseudo arc-length method is used for iterative solution.Then numerical error norms and convergent orders for pseudo arc-length algorithm are obtained,which imply the pseudo arc-length numerical algorithm is convergent.(5)By constructing conservative higher order interpolation,the pseudo arc-length algorithm and high-order discontinuous Galerkin method are combined.So the purpose of combination of pseudo arc-length algorithm and high-order algorithm to solve the singular strong discontinuity problems of shock wave is realized.(6)Aiming at the negative problems of density,pressure and chemical reaction degree in the calculation process due to the rigid problem of chemical reaction source term,or the interaction of shock wave and rarefaction wave,the positive conditions and complement algorithms are added into the original algorithm to improve pseudo arc-length numerical algorithm for the numerical simulation of the explosion and shock reaction flow problem.(7)The interaction of shock waves and rarefaction wave in the explosive shock wave of multi-material problem can lead to complex geometrical topology of fluid interface.Aiming at this problem,the pseudo arc-length algorithm is combined with the five equation model to deal with the multi-material problem.Then the geometric details of fluid interface are not needed to consider.Thus the numerical simulation of the explosive shock wave for multi-material problem is realized.(8)Based on the message passing model,the parallel program of pseudo arc-length algorithm is developed.The algorithm flow chart of calculating program is established,and the pseudo codes of important computing steps for mathematical calculation expressions are given.Base on this,the parallel computing programs of pseudo arc-length numerical algorithm for explosion and shock problem are developed.(9)With a variety of explosive shock reaction kinetics model,and five-equation model for multi-medium flow in multi-dimensional space,pseudo arc-length numerical algorithm is applied to physical problems of explosive shock wave,such as explosion on the ground,explosion on the front step,detonation of obstacle diffraction,explosion in box,explosion shock retaining wall,double underwater explosion,solid explosive initiation,air explosion and so on.Then physical phenomena,which are shock wave reflection,shock wave diffraction,interference of explosive shock waves and rarefaction wave,superposition of explosive shock wave and so on,are studied in numerical simulations.Then the analysis of physical problem is carried out to get conclusions.