The Application Of Level Set Method In Generalized Interface Treatment Problems

Level set method,an effective tool for dealing with the geometric topology changes of the closed moving interface over time,has become one of the most important methods for conducting the problem of generalized interface.It has been widely used in the scientific research and engineering calculation fields related to various curve evolution,having important theoretical research significance and application background.With the constant deepening of scientific research and the higher demands of engineering calculation problem,it has become more important to effectively capture and track the moving interface.The most common problem in generalized interface refers to multi-medium interface and image contour interface,so this paper combines theoretical analysis and numerical simulation to explore the improvement of level set method in reinitialization and the application of that in the problem of Euler multi-medium interface calculation;and the improvement of level set method in variational theory and the application of it in the problem of image contour interface capturing.The main work is described as follows:(1)The basic idea and basic theory of level set method is explained in detail,and it also introduces the current research status at home and abroad and the development trend of level set method in the field of multi-medium interface and image contour interface processing.In addition,it also concludes the general steps of solving the problem through level set method,and analyzes the advantages and disadvantages of level set method.(2)A fixed-interface level set method is proposed on the basis of the problem of the deviation of the interface position caused by reinitialization,in which the main improvement is about correcting the fixed smooth parameters in the traditional level set method to the changed smooth parameters.It has effectively improved the mass conservation of level set method through the fixed interface,which has a higher resolution.The basic idea of the fixed-interface level set method is to construct a equation condition that keeps the interface immobile based on the the basic principle of the fixed interface in the process of the reinitialization of the adjacent two iterations,in which the calculation formula satisfied by the smooth parameters has been consequently deduced.And the numerical examples of reinitialization,constant flow field,rotating flow field and shear flow field are also discussed and analyzed.It could be shown from the result that the fixed-interface level set method improves the conservation of fluid volume and could capture the sharp,narrow,slender interface compared with the traditional level set method,in which the geometrical changes of the interface do not affect the speed of the surrounding flow field.(3)It discusses the application of the fixed-interface level set method in the calculation of the Euler multi-medium fluid calculation,effectively suppressing the numerical oscillation and dissipation generated near the fluid interface,improving the resolution at the discontinuity and improving the mass conservation of the bubble and having stronger ability to capture the fluid interface.It not only briefly describes the relevant basic theories,governing equations and numerical methods,but also summarizes the detailed steps of the Euler multi-medium fluid solved by the fixed-interface level set method.The numerical simulations of the bubble problems such as gas-gas shock tube,gas-liquid shock tube and shock-acting are also discussed and analyzed.It could be shown from the result that the fixed-interface level set method effectively eliminates the numerical dissipation of the shock wave compared with the traditional level set method,in which the numerical solution of density,isobaric pressure and velocity is more consistent with the exact solution.In addition,it could more accurately capture the position of shock wave,expansion wave and contact discontinuity,and could more finely describe the deformation process of bubble under shock wave and reduce the loss of bubble quality.(4)It has effectively avoided the deviation of detonation wave front caused by error accumulation through the discussion about the application of the fixed-interface level set method in the calculation of detonation wave front spreading.The method could conduct a comparatively accurate description about the spreading of the detonation wave front due to its higher calculation accuracy and resolution.It not only briefly describes the relevant basic theories,governing equations and numerical methods,but also summarizes the detailed steps of the detonation wave front spreading solved by fixed-interface level set method.In addition,the numerical simulation of the center one-point detonation,one-point detonation,two-point detonation and the detonation with arc explosive plane is discussed and analyzed.It could be shown from the result that compared with the traditional level set method,the fixed-interface level set method would more accurately capture the reasonable detonation wave front with higher numerical calculation results.(5)An adaptive variational level set method is proposed on the basis of the problem of boundary sticking appearing in the image contour interface that is handled by the traditional variational level set method,which has mainly modified the constant in the external energy functional to the function that depends on the image information.The adaptive variational level set method is characterized by fast evolution rate,stable numerical calculation,and strong validity and applicability.The new parameter function could automatically determine the direction of the zero contour evolution by means of the second derivative of the image,and automatically regulate the evolution speed of the zero contour to ensure the length and area of the evolution curve with a global minimum simultaneously.Furthermore,numerical examples of the contour interfaces of artificial images,medical images,and multi-target images are discussed and analyzed.The results show that,compared with the traditional variational level set method,the adaptive variational level set method is not sensitive to the initial position of the evolution curve and could complete adaptive moving.It could also capture the inner and outer contour interface of the image,the boundary of the concave region with narrow depth and the boundary of the multi-target object at the same time,which is especially suitable for the contour interface capture of the boundary contour of the multi-target object with small-distance interval as well as the image contour of its weak boundary.