Pseudo Arc-length Numerical Algorithm For Explosion And Shock Problem

Numerical simulation of explosion and shock phenomena has very important theory and application background, and the key points for calculating the changes of physical variables on both sides of the wave-fornt and understanding the propagation laws of blast wave is to capture and track the wave-front of shock wave accurately. The most difficulty for numerical simulation is establishing and discreting the corresponding mathematical models of the shock wave propagation. For the general numerical method, it’s hard to simulate the propagation process with sufficient resolution while also keeping the computational cost within acceptable limits under the extreme conditions. In this thesis, an efficient pseudo arc-length method is proposed from the physical points for handing the strong discontinuous problem of explosion and shock phenomena, and some related theories and applications of this new method are systematic analysised and studied. The main contents of this thesis are described as follows:(1)Firstly, a pseudo arc-length numerical algorithm is proposed based on the simple mathematical model of hyperbolic conservation equation, and the basic concept of pseudo ar-length method is defined, then the moving mesh property of the proposed method is studied as well. Secondly, some related mathematical theories of pseudo arc-length method are analysised, including the space equidistribution principle, variational principle and error estimation. Then the study focused on the numerical discrete feasibility and effectiveness of pseudo ar-length method in the Sobolev space, and the boundedness and convergence of the numerical method are presented under different interpolation approximation. Finally, the numerical examples have shown that the pseudo arc-length numerical algorithm have advantage in eliminating or weaking the discontinuous singularity of physical solution compare with general numerial method.(2) In order to further improve the computational efficiency, a more targeted local pseudo arc-length algorithm is presented. First of all, we define a new form of arc length parameters which is easy to expand to the high dimensional space firstly, and establish the mathematical model of the local pseudo arc-length method combining the equipartition principle. Then we dicrete and compute the model by using the general numerical methoddirectly, and the non-oscillation solution of shock wave can be obtained by adjusting the control factor and smooth factor. Numerical examples have proved this new approach can be apply to one-dimensional shock wave, rarefraction wave and contact discontinuities propagation.(3) The method of establishing the mathmatical model and choosing the suitable numerical discrete agrithm is studied for the discontinuous singularity problem in multidimensional space. At first, we are presented the method introducing the multidimensional arc-length parameter from the tensor analysis standpoint, and the derivation process of moving mesh velocity is studied from the discrete and continuous perspective, respectively. Then the unified mathmatical model of detonation and shock wave propagation problems in the multidimensional arc-length space is established. Next, the numerical discrete agrithm of arc-length space modle is proposed according to the finite volume method and conservative interpolation method. Finally, the feasibility of the parameter selection problem is discussed from the view of theoretical analysis, and the approximation of function viewpoint is also given, then the boundedness and convergence of the pseudo arc-length numerical method for physical problems are analyzed.(4) The main research of this section carries on the application of pseudo arc-length numerical method for the classic examples of explosion and impact, including the shock wave propagation, interaction between shock wave and obstacles, detonation wave reflection and diffraction, and so on. The different arc-length parameters effect are emphatically analyzed for solving the physical problem, and the method to choose the proper arc-length form is also studied for satifing different physical problem and calculation demand. The numerical result comparisons between pseudo arc-length method and genernal numerical method have proved that our method has the adavantages in dealing with multidimensional shock wave propagation. As a new approach, the pseudo arc-length numerical method can be widely applied to practical shock wave problems in science and engineering. Finally, the validity, the grid quality and the three-dimensional extension of the pseudo arc length numerical method are discussed.(5) The multiphase pseudo arc-length numerical method is established by combining the pseudo arc-length method with the mathematical model of multiphase compressible flow, which is applied to the simulation of shock wave interaction with a deformable particle. Through the flow flied changes and data analysis of key points, it can be found that the complex wave structures are presented after the interactions between the planar incident shock wave and the metal particle, and all these waves interaction will lead to the deformation of metal particle, the interaction between shock wave and the deformable particle can be studied on the basis of physical properties of explosive mediums.