Pseudo Arc-length Numerical Algorithm For Explosion And Shock Problem And The Verification And Validation Of The Programs

The explosion phenomenon is one of the unavoidable disasters in human life,bringing a lot of threat to people's life safety and property safety.With the development of science and technology,researchers are increasingly using numerical calculation to study explosion and impact problems.The inner mechanism of the explosion shock problems can be described by partial differential equations,and solutions of these equations(system)based on continuum mechanics usually have singularities,such as rarefaction wave,shock wave,etc.A sum of theoretical and computational methods have been developed in recent years,and solve some numerical problems of the partial differential equations from various angle,such as numerical oscillation and dissipation.However,it takes a great computational cost to overcome these problems.Hence,to solve these problems efficiently while keeping a high resolution has been the main research directions.In this paper,we present the pseudo arc-length method(PALM)for solving detonation wave problems with strong discontinuity.The main work of this paper is as follows:(1)Briefly summarize the development of numerical format and computational grid,especially the research progress of adaptive mesh technique.Based on the finite volume method and r-adaptive grid method,we put forward a pseudo arc-length method,and demonstrate the basic idea and principle of the method.The necessity and methods of verification and validation is also outlined,and we mainly give an introduction of the method of manufactured solution.(2)Make a study of the basic idea and theory of pseudo arc-length method.For one-dimensional hyperbolic system of conservations,we transform the control equations into arc-length space,then update physics quantities combined with perturbation theory.After that we get the grid movement speed according to the moving grid method,and develop the control equations with the finite volume method.Finally we return the computation space back to physical space and get the new grid points and their physical quantities.We demonstrate the numerical discrete of pseudo arc-length method,including time discrete and space discrete,and deduce the particular form of shock wave propagation speed.By the numerical simulation of one step chemical reaction model and branched chain reaction model,we compare the pseudo arc-length method and the finite volume method on the degree of approximation to the exact solution,and the grid distribution effect of the pseudo arc-length algorithm,and then we draw a conclusion about the advantage of the pseudo arc-length method.(3)For two-dimensional hyperbolic system of conservation,we replace the grid node coordinates through the Gauss-Seidel iteration formula,and update the physical quantities following the laws of conservation of physical quantities in the process of transforming calculation space.Finally we promote the physical quantities using the finite volume method.We describe the selection of arc-length control function in detail,then we take the method of the manufactured solution to make a verification of the programs,and prove whether the pseudo arc-length method will help improving the precision via error analysis.Through the numerical simulation of detonation wave diffraction problem,we further illustrate that our algorithm will solve the detonation wave propagation problems effectively and will capture the detonation front reliably.(4)To illustrate the applicability of the pseudo arc-length method in actual physical problems,we apply the pseudo arc-length algorithm to the gas detonation wave propagation problems in 2D pipeline.We study the process about the interaction of the shear wave,the incident shock wave and Mach wave and they form three wave structures eventually.Meanwhile,the simulation about detonation wave propagation in different expansion pipes have been conducted and we focus on the capture effect of the detonation front.At last we study the formation and change of detonation cell in a straight pipeline.(5)We carry out a series of shock tube experiments to confirm the correctness of the pseudo arc-length method.Based on the principle of safety,air tightness and easy extensibility,we state the shock tube experimental platform construction method and experimental test methods detailedly.We get the cellular structures of the detonation wave in the experiment and make qualitative analysis of them.Finally we make a comparison of the numerical results and the classic experimental results.(6)Summarize the work of this paper,and discuss the later research direction and possible problem solutions.